CHAPTER 1 INTRODUCTION 1

CHAPTER 1
INTRODUCTION
1.1Background of Study
Time series is a series of measurement over time, usually obtained at the same manner spaced intervals. Meanwhile, time series analysis is a statistical technique that deals with time series data, or trend analysis ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “ISBN” : “0387953515”, “author” : { “dropping-particle” : “”, “family” : “Brockwell”, “given” : “Peter J”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Davis”, “given” : “Richard A”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “0” }, “title” : “Introduction to Time Series and Forecasting , Second Edition Springer Texts in Statistics”, “type” : “book” }, “uris” : “http://www.mendeley.com/documents/?uuid=8e8c016c-bc76-482a-ad69-5e44f9f5324c” } , “mendeley” : { “formattedCitation” : “(Brockwell & Davis, n.d.)”, “manualFormatting” : “(Brockwell & Davis, 2001)”, “plainTextFormattedCitation” : “(Brockwell & Davis, n.d.)”, “previouslyFormattedCitation” : “(Brockwell & Davis, n.d.)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Brockwell and Davis, 2001). Furthermore, time series forecasting is a techniques for the prediction of events through a sequence of time. By analysing the time series, it is used to describe the fundamental structure and the phenomenon as represent by the sequence of observations in the series. Forecasting can be used in variety of studies such as airline industry. Nowadays, airlines has become one of the necessity in people lives, it also helps to improve the national economic and tourism ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Min”, “given” : “Jennifer C H”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Kung”, “given” : “Hsien-hung”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Liu”, “given” : “Hsiang Hsi”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issue” : “10”, “issued” : { “date-parts” : “2010” }, “page” : “2121-2131”, “title” : “Interventions affecting air transport passenger demand in Taiwan”, “type” : “article-journal”, “volume” : “4” }, “uris” : “http://www.mendeley.com/documents/?uuid=aaf21f22-ba94-455e-9b38-3a62b0bfba0c” } , “mendeley” : { “formattedCitation” : “(Min, Kung, & Liu, 2010)”, “plainTextFormattedCitation” : “(Min, Kung, & Liu, 2010)”, “previouslyFormattedCitation” : “(Min, Kung, & Liu, 2010)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Min, Kung and Liu, 2010). Moreover, forecasting can be considered as one of the tool for a better airline management and planning ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Ming”, “given” : “Wei”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Bao”, “given” : “Yukun”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Hu”, “given” : “Zhongyi”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Xiong”, “given” : “Tao”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “2014” }, “title” : “Multistep-Ahead Air Passengers Traffic Prediction with Hybrid ARIMA-SVMs Models”, “type” : “article-journal”, “volume” : “2014” }, “uris” : “http://www.mendeley.com/documents/?uuid=b61ab13a-c3a0-4a1c-b7ab-d819e4ec24cc” } , “mendeley” : { “formattedCitation” : “(Ming, Bao, Hu, & Xiong, 2014)”, “plainTextFormattedCitation” : “(Ming, Bao, Hu, & Xiong, 2014)”, “previouslyFormattedCitation” : “(Ming, Bao, Hu, & Xiong, 2014)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Ming et al, 2014). According to Aderamo (2010), any airline organisations need to have estimation of expected future demands in order to improve their airline service.
Forecasting has many benefit towards the development of airline and it is depends on number of passenger on that time period ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Andreoni”, “given” : “Alberto”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Postorino”, “given” : “Maria Nadia”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “2006” }, “title” : “A MULTIVARIATE ARIMA MODEL TO FORECAST”, “type” : “article-journal” }, “uris” : “http://www.mendeley.com/documents/?uuid=2f63ef10-8b22-4a0e-b754-89ff03bc6827” } , “mendeley” : { “formattedCitation” : “(Andreoni & Postorino, 2006)”, “plainTextFormattedCitation” : “(Andreoni & Postorino, 2006)”, “previouslyFormattedCitation” : “(Andreoni & Postorino, 2006)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Andreoni & Postorino, 2006). Despite experienced a challenging moments such as political issues, economic issues and many more, the airline industry demand continuously rising. Even though it is keep rising, it has slightly give an impacted towards airline markets. In response to this issue, airlines are constantly improve their service structures in order to eliminate lose and to have continuous profit. Airlines’ passengers may have interest in the demand modelling and simulation, normally when there is a competition among airlines’ market and they need to choose which service they should take ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Andreoni”, “given” : “Alberto”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Postorino”, “given” : “Maria Nadia”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “2006” }, “title” : “A MULTIVARIATE ARIMA MODEL TO FORECAST”, “type” : “article-journal” }, “uris” : “http://www.mendeley.com/documents/?uuid=2f63ef10-8b22-4a0e-b754-89ff03bc6827” } , “mendeley” : { “formattedCitation” : “(Andreoni & Postorino, 2006)”, “plainTextFormattedCitation” : “(Andreoni & Postorino, 2006)”, “previouslyFormattedCitation” : “(Andreoni & Postorino, 2006)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Andreoni & Postorino, 2006).
In Malaysia, the list of airlines’ company are AirAsia, AirAsia X, Firefly, Malindo, Malaysian Airlines and others. The passenger traffic growth in 2017 is expected to overtake growth rates in 2016. In airline companies as well as for all types of companies, demand forecasting is a very significance issue. The success of the managers and companies are much related with suitable strategies which are composed with accurate future forecast. Demand forecasting for available seats in airlines is important to maximize the expected revenue by setting the appropriate fare levels for those seats. The accuracy of the forecast is the most significant tool of the revenue management systems, (MAVCOM).
In this study, we focus on Air Asia airlines as our case study. We would like to forecast the number of Air Asia passengers in Malaysia. In airline industry, it consists of two types of operations namely Full cost carriers (FCC) and low cost carriers (LCC) and Air Asia is one of the low cost carriers type. There are also several LCC such as Air Asia X, Firefly, Berjaya Air, and Sabah Air Aviation (David, 2011). Air Asia is the first low cost carriers company in Malaysia. Moreover, Air Asia also known as the largest and the best low fare in Asia. Air Asia continuously expand with their efficient services, passion toward business and has made a revolution in airline industry. Thus, more people are choosing Air Asia as their choice of airlines.
1.2 Problem Statement
As we know, the airline transport has become a demand nowadays. Based on the previous study (Asrah et al 2018) is a case study about airlines in Malaysia which is AirAsia and Malaysian Airlines. In this study, they compare the distributional behaviour data from the number of Air Asia and Malaysian Airline passenger. As MAS passenger airlines data set are not govern by geometric Brownian motion (GBM), they forecast the number of MAS airline passenger by using Box Jenkins method. Asrah et al, 2013 they forecast the number of Air Asia passenger by using geometric Brownian motion (GBM). As for this research, we use Box Jenkins method to forecast the number of airline passenger of Air Asia. By using forecasting method, it can help in terms of upgrading and improving an airline sector.
1.3 Objective
To study the behaviour of the Air Asia passenger data
To find the best model for Air Asia passenger in Malaysia by using Box Jenkins method
To forecast the number of Air Asia passenger by using the best model
1.4 Scope of Study
In this study, the data have been obtained from Malaysia Airport Holdings Berhad (MAHB). The data obtained were about the total number of passengers that arrived to Kuala Lumpur International Airport (KLIA). These set of time series data are for the number of Air Asia passengers from January 2009 until August 2012.
1.5 Significant of Study
This study has contribute to forecast the number of passenger in Air Asia airline. Besides that, this study also contribute to compare method used to forecast the number of airline passenger which is Air Asia as from previous study they used geometric Brownian motion (GBM) to forecast. This study also helps to enhance better understanding and knowledge about airline industry in Malaysia. This study also will helps the airline industry with the result obtain for them to set appropriate policy for a better management. Moreover, this study also give an overview about the relevant literature in order to explain and develop a better understanding about the airline industry and also the method used. Even though the objective of this study is to forecast the number of Air Asia passenger by using the best model, it is also give a knowledge about other method that has been used by the previous researcher.
CHAPTER 2
LITERATURE REVIEW
2.1 Research in Airlines Industries
Airline Industry has become one of the customer choice as their transport. After a few tragedy happen such as the September 11 terrorist attacks, economic slowdown, several accidents involving airplanes and many mores, this has impacted passenger trust towards airline industry ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Radoslaw R. Okulski”, “given” : “Almas Heshmati”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issue” : “January 2010”, “issued” : { “date-parts” : “2014” }, “title” : “Passengers Transportation Industry Technology Management , Economics and Policy Papers Time Series Analysis of Global Airline”, “type” : “article-journal” }, “uris” : “http://www.mendeley.com/documents/?uuid=c2c180af-de78-4159-8400-8094ff64fdf8” } , “mendeley” : { “formattedCitation” : “(Radoslaw R. Okulski 2014)”, “manualFormatting” : “(Radoslaw, 2014)”, “plainTextFormattedCitation” : “(Radoslaw R. Okulski 2014)”, “previouslyFormattedCitation” : “(Radoslaw R. Okulski 2014)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Radoslaw, 2014). Due to this, there are numerous of study regarding this issue. For example, survey are conducted in order to have an overview a passengers’ needs towards airline industry ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “ISBN” : “9781467315821”, “author” : { “dropping-particle” : “”, “family” : “Asrah”, “given” : “Norhaidah Mohd”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “2012” }, “page” : “479-482”, “title” : “Malaysia Commercial Flight Passengers u201f Safety ( NEWS )”, “type” : “article-journal” }, “uris” : “http://www.mendeley.com/documents/?uuid=7e23f74e-bbee-4c73-91d3-c31ab813f876” } , “mendeley” : { “formattedCitation” : “(Asrah 2012)”, “plainTextFormattedCitation” : “(Asrah 2012)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Asrah 2012). In this research, the survey called People NEWS (Needs, Expectation, Wants and Satisfaction) was conducted to obtain public opinion regarding air travel safety and process in Malaysia. In this paper, they concentrate more on check in and check out steps. Eventually, this survey can be a useful recommendations not only for airlines’ company but also to government for future development of airlines. In a research conducting in Nigeria, they suggest the need for the government to improve the airline system ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Aderamo”, “given” : “Adekunle J”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issue” : “1”, “issued” : { “date-parts” : “2010” }, “page” : “23-31”, “title” : “Demand for Air Transport in Nigeria”, “type” : “article-journal”, “volume” : “1” }, “uris” : “http://www.mendeley.com/documents/?uuid=479ad472-fdf1-44bf-854b-0f2d06bc7802” } , “mendeley” : { “formattedCitation” : “(Aderamo 2010)”, “manualFormatting” : “(Aderamo, 2010)”, “plainTextFormattedCitation” : “(Aderamo 2010)”, “previouslyFormattedCitation” : “(Aderamo 2010)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Aderamo, 2010). For determine future planning, they collect the data on passenger, aircraft and cargo movement to determine the pattern of airlines industry in order to have a future planning.

Besides that, it is also important to improve our understanding towards airlines’ passenger decision making ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1016/j.jairtraman.2004.06.001”, “ISBN” : “0969-6997”, “ISSN” : “09696997”, “abstract” : “This paper seeks to improving our understanding of air passengers’ decision-making processes by testing a conceptual model that considers service expectation, service perception, service value, passenger satisfaction, airline image, and behavioural intentions simultaneously. For this testing, path analysis via maximum likelihood estimator is applied to data collected from Korean international air passengers. Service value, passenger satisfaction, and airline image are each found to have a direct effect on air passengers’ decision-making processes. u00a9 2004 Elsevier Ltd. All rights reserved.”, “author” : { “dropping-particle” : “”, “family” : “Park”, “given” : “Jin Woo”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Robertson”, “given” : “Rodger”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Wu”, “given” : “Cheng Lung”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Journal of Air Transport Management”, “id” : “ITEM-1”, “issue” : “6”, “issued” : { “date-parts” : “2004” }, “page” : “435-439”, “title” : “The effect of airline service quality on passengers’ behavioural intentions: A Korean case study”, “type” : “article-journal”, “volume” : “10” }, “uris” : “http://www.mendeley.com/documents/?uuid=9ee7cb84-0250-4e2f-ad41-739c7c179873” } , “mendeley” : { “formattedCitation” : “(J. W. Park, Robertson, and Wu 2004)”, “manualFormatting” : “(J. W. Park, Robertson, and Wu ,2004)”, “plainTextFormattedCitation” : “(J. W. Park, Robertson, and Wu 2004)”, “previouslyFormattedCitation” : “(J. W. Park, Robertson, and Wu 2004)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(J. W. Park, Robertson, and Wu ,2004). Service with high quality has become a requirement for gaining customer support and increase the profit. Giving a high quality service has become one of the marketing needs (Ostrowski et al., 1993). It is vital to understand what the passenger need and expect from the service organizations (Jin and Julie, 2000). The effect of airline passengers’ expectations on service perception and passenger satisfaction has to be fully investigated. In Malaysia, ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1016/j.jairtraman.2005.01.007”, “ISBN” : “0969-6997”, “ISSN” : “09696997”, “abstract” : “Direct competition between full service airlines and no-frills carriers is intensifying across the world. US and European full service airlines have lost a significant proportion of their passengers to low cost carriers, the experience now being repeated in the domestic markets of Asia. This paper attempts to provide answers to a number of critical questions: What are the key drivers of each type of airline’s business model? Is there a difference in passengers’ perceptions between low cost carriers and full service incumbents in a mature European market and in a rapidly developing Asian economy? What are the principle reasons why a passenger chooses a particular airline model? How could a legacy carrier encourage passengers to return and so regain their domestic market share? These questions are addressed using information obtained in passenger surveys that were recently conducted in Europe and Asia. u00a9 2005 Elsevier Ltd. All rights reserved.”, “author” : { “dropping-particle” : “”, “family” : “O’Connell”, “given” : “John F.”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Williams”, “given” : “George”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Journal of Air Transport Management”, “id” : “ITEM-1”, “issue” : “4”, “issued” : { “date-parts” : “2005” }, “page” : “259-272”, “title” : “Passengers’ perceptions of low cost airlines and full service carriers: A case study involving Ryanair, Aer Lingus, Air Asia and Malaysia Airlines”, “type” : “article-journal”, “volume” : “11” }, “uris” : “http://www.mendeley.com/documents/?uuid=efe14a73-6f34-44e8-99ba-a626d0bde237” } , “mendeley” : { “formattedCitation” : “(Ou2019Connell and Williams 2005)”, “manualFormatting” : “(Ou2019Connell and Williams ,2005)”, “plainTextFormattedCitation” : “(Ou2019Connell and Williams 2005)”, “previouslyFormattedCitation” : “(Ou2019Connell and Williams 2005)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(O’Connell and Williams ,2005) seeks passengers’ perceptions of low cost airlines and full service carriers. Survey have been conducted to determine why passenger are choosing one particular airline over another. The growth of low cost airline industry has become one of the passengers’ choice recently ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1016/j.jairtraman.2005.01.007”, “ISBN” : “0969-6997”, “ISSN” : “09696997”, “abstract” : “Direct competition between full service airlines and no-frills carriers is intensifying across the world. US and European full service airlines have lost a significant proportion of their passengers to low cost carriers, the experience now being repeated in the domestic markets of Asia. This paper attempts to provide answers to a number of critical questions: What are the key drivers of each type of airline’s business model? Is there a difference in passengers’ perceptions between low cost carriers and full service incumbents in a mature European market and in a rapidly developing Asian economy? What are the principle reasons why a passenger chooses a particular airline model? How could a legacy carrier encourage passengers to return and so regain their domestic market share? These questions are addressed using information obtained in passenger surveys that were recently conducted in Europe and Asia. u00a9 2005 Elsevier Ltd. All rights reserved.”, “author” : { “dropping-particle” : “”, “family” : “O’Connell”, “given” : “John F.”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Williams”, “given” : “George”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Journal of Air Transport Management”, “id” : “ITEM-1”, “issue” : “4”, “issued” : { “date-parts” : “2005” }, “page” : “259-272”, “title” : “Passengers’ perceptions of low cost airlines and full service carriers: A case study involving Ryanair, Aer Lingus, Air Asia and Malaysia Airlines”, “type” : “article-journal”, “volume” : “11” }, “uris” : “http://www.mendeley.com/documents/?uuid=efe14a73-6f34-44e8-99ba-a626d0bde237” } , “mendeley” : { “formattedCitation” : “(Ou2019Connell and Williams 2005)”, “manualFormatting” : “(Ou2019Connell and Williams, 2005)”, “plainTextFormattedCitation” : “(Ou2019Connell and Williams 2005)”, “previouslyFormattedCitation” : “(Ou2019Connell and Williams 2005)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(O’Connell and Williams, 2005). Graham (2006) identifies the majority of the low-cost airline demand is from leisure travellers while Mason (2005) identifies the number of business traveller that used low cost carrier are increasing and they also view the low cost carrier as good indicator towards business demand. Thus, to maintain consumer interest, airlines need to continue to innovate, providing tourism destinations which meet these requirement.

2.2 Forecasting method
In order to use forecasting techniques, different situation used different kind of techniques. Firstly, we have to know different forecasting techniques if we want to do a forecasting according to its situation. Some of the techniques are moving average, exponential smoothing (simple, Holt’s method, and winters method), linear regression and Box–Jenkins models. Forecasting have many fields including business and industry, government, economics, environmental sciences, medicine, social science, politics, and finance ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.5465/AMR.1979.4289149”, “ISBN” : “0471823600”, “ISSN” : “0363-7425”, “PMID” : “18491586”, “abstract” : “Comprehensively covering all aspects of long-range forecasting methods relevant to the social, behavioral and management sciences, this book is a synthesis of research in economics, sociology, psychology, transportation, education, and management – with occasional references to work in medicine, meterology, and technology. It describes a variety of forecasting methods, their strengths and weaknesses, and how to use them effectively, shows how to structure a forecasting problem, and gives detailed procedures for evaluating forecasting models in order to select the appropriate method for a particular problem. The book draws upon material from approximately 1300 books and articles, and includes original research by the author.”, “author” : { “dropping-particle” : “”, “family” : “Anderson”, “given” : “C. R.”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Academy of Management Review”, “id” : “ITEM-1”, “issue” : “3”, “issued” : { “date-parts” : “1979” }, “page” : “474-475”, “title” : “Long-Range Forecasting: From Crystal Ball to Computer.”, “type” : “article”, “volume” : “4” }, “uris” : “http://www.mendeley.com/documents/?uuid=5887c1eb-1517-4c51-98e9-292c9d2cfc8d” } , “mendeley” : { “formattedCitation” : “(Anderson 1979)”, “plainTextFormattedCitation” : “(Anderson 1979)”, “previouslyFormattedCitation” : “(Anderson 1979)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Anderson 1979). Forecasting are often classified as short-term, medium-term, and long-term ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1016/j.jairtraman.2005.01.007”, “ISBN” : “0969-6997”, “ISSN” : “09696997”, “abstract” : “Direct competition between full service airlines and no-frills carriers is intensifying across the world. US and European full service airlines have lost a significant proportion of their passengers to low cost carriers, the experience now being repeated in the domestic markets of Asia. This paper attempts to provide answers to a number of critical questions: What are the key drivers of each type of airline’s business model? Is there a difference in passengers’ perceptions between low cost carriers and full service incumbents in a mature European market and in a rapidly developing Asian economy? What are the principle reasons why a passenger chooses a particular airline model? How could a legacy carrier encourage passengers to return and so regain their domestic market share? These questions are addressed using information obtained in passenger surveys that were recently conducted in Europe and Asia. u00a9 2005 Elsevier Ltd. All rights reserved.”, “author” : { “dropping-particle” : “”, “family” : “O’Connell”, “given” : “John F.”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Williams”, “given” : “George”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Journal of Air Transport Management”, “id” : “ITEM-1”, “issue” : “4”, “issued” : { “date-parts” : “2005” }, “page” : “259-272”, “title” : “Passengers’ perceptions of low cost airlines and full service carriers: A case study involving Ryanair, Aer Lingus, Air Asia and Malaysia Airlines”, “type” : “article-journal”, “volume” : “11” }, “uris” : “http://www.mendeley.com/documents/?uuid=efe14a73-6f34-44e8-99ba-a626d0bde237” } , “mendeley” : { “formattedCitation” : “(Ou2019Connell and Williams 2005)”, “manualFormatting” : “(Ou2019Connell and Williams ,2005)”, “plainTextFormattedCitation” : “(Ou2019Connell and Williams 2005)”, “previouslyFormattedCitation” : “(Ou2019Connell and Williams 2005)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(O’Connell and Williams ,2005). For example, in the research by ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Park”, “given” : “D C”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Marks”, “given” : “R J”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Atlas”, “given” : “L E”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Damborg”, “given” : “M J”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issue” : “2”, “issued” : { “date-parts” : “1991” }, “page” : “442-449”, “title” : “Electric load forecasting using an artificial neural network – Power Systems, IEEE Transactions on”, “type” : “article-journal”, “volume” : “6” }, “uris” : “http://www.mendeley.com/documents/?uuid=fe8978ce-71dd-49a0-9e72-09de31db9a0e” } , “mendeley” : { “formattedCitation” : “(D. C. Park et al. 1991)”, “plainTextFormattedCitation” : “(D. C. Park et al. 1991)”, “previouslyFormattedCitation” : “(D. C. Park et al. 1991)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(D. C. Park et al. 1991), this paper presents an artificial neural network(ANN) approach to electric load forecasting. Neural networks (NNs) have been vigorously promoted in the computer science literature for tackling a wide variety of problems. Recently, statisticians have started to investigate whether NNs are useful for tackling various statistical problems (Cheng and Titterington, 1994) and there has been particular attention to pattern recognition (Bishop, 1995; Ripley, 1996). NNs also appear to have potential application in time series modelling and forecasting but nearly all such work has been published outside the mainstream statistical literature. Besides that, they are also different forecasting techniques that can be used that suited with the field needed. One of the forecasting method was geometric Brownian motion (GBM). This method has a criteria of stationary, normally distributed and independent ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1080/00137910590949904”, “ISBN” : “0013791X”, “ISSN” : “0013791X”, “PMID” : “17552395”, “abstract” : “Abstract The geometric Brownian motion (GBM) process is frequently invoked as a model for such diverse quantities as stock prices, natural resource prices and the growth in demand for products or services. We discuss a process for checking whether a given time series follows the GBM process. Methods to remove seasonal variation from such a time series are also analyzed. Of four industries studied, the historical time series for usage of established services meet the criteria for a GBM; however, the data for growth of emergent services do not.”, “author” : { “dropping-particle” : “”, “family” : “Marathe”, “given” : “Rahul R.”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Ryan”, “given” : “Sarah M.”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Engineering Economist”, “id” : “ITEM-1”, “issue” : “2”, “issued” : { “date-parts” : “2005” }, “page” : “159-192”, “title” : “On the validity of the geometric Brownian motion assumption”, “type” : “article-journal”, “volume” : “50” }, “uris” : “http://www.mendeley.com/documents/?uuid=2774ff10-c013-4ab1-9aa3-f54ed4007d75” } , “mendeley” : { “formattedCitation” : “(Marathe and Ryan 2005)”, “plainTextFormattedCitation” : “(Marathe and Ryan 2005)”, “previouslyFormattedCitation” : “(Marathe and Ryan 2005)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Marathe and Ryan 2005). In paper by ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1063/1.4823977”, “author” : { “dropping-particle” : “”, “family” : “Mohd”, “given” : “Norhaidah”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Universiti”, “given” : “Asrah”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Hussein”, “given” : “Tun”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Djauhari”, “given” : “Maman”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Bina”, “given” : “Tjahaja”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Indonesia”, “given” : “Statistika”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “View”, “given” : “Plus Highway”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Asrah”, “given” : “Norhaidah Mohd”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issue” : “February”, “issued” : { “date-parts” : “2013” }, “title” : “Time Series Behaviour of the Number of Air Asia Passengers : A Distributional Approach”, “type” : “article-journal” }, “uris” : “http://www.mendeley.com/documents/?uuid=4349d9e3-63b4-46a9-9b42-db03d138022d” } , “mendeley” : { “formattedCitation” : “(Mohd et al. 2013)”, “manualFormatting” : “(Asrah, 2013)”, “plainTextFormattedCitation” : “(Mohd et al. 2013)”, “previouslyFormattedCitation” : “(Mohd et al. 2013)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Asrah, 2013), they has been used GBM method to forecast the number of Air Asia passenger.
2.3 Forecasting Airline Passenger by using Box Jenkins Method
Forecasting airline has been known around the world. For example the research by ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Hong”, “given” : “Wai”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Tsui”, “given” : “Kan”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Ozer”, “given” : “Hatice”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Gilbey”, “given” : “Andrew”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Gow”, “given” : “Hamish”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issue” : “2014”, “issued” : { “date-parts” : “2015” }, “title” : “Forecasting of Hong Kong airport u2019 s passenger throughput”, “type” : “article-journal”, “volume” : “42” }, “uris” : “http://www.mendeley.com/documents/?uuid=da29eb30-65dd-4a5a-a759-e9d5a9b7e492” } , “mendeley” : { “formattedCitation” : “(Hong et al. 2015)”, “plainTextFormattedCitation” : “(Hong et al. 2015)”, “previouslyFormattedCitation” : “(Hong et al. 2015)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Hong et al. 2015), they forecast airport passenger traffic for Hong Kong International Airport and also predict its future growth trend to 2015. They believe that forecasting result obtained can give an overview regarding the developing of HKIA’s future passenger traffic. Thus, in this research they used Box Jenkins ARIMA model for forecasting HKIA’s future passenger throughput. According to prior study, it stated that ARIMA model can accurately forecast airport traffic demands (Abdelghany and Guzhva, 2010). SARIMA model was used to model HKIA’s passenger traffic. SARIMA models predict a steady growth in future airport passenger traf?c, Hong Kong. In addition, scenario analysis suggests that Hong Kong airport’s future passenger traf?c will continue to grow in different magnitudes. In Ming et al (2014), they also applied ARIMA models to forecast air traffic passengers travel. Thus, ARIMA model are suitable to be used as a model to forecast by using airline data.
In a past decade, technological development and the global economic crisis are considered as one of the factors of development that can affect the airline industry. The research by (Rdoslaw and Almas 2010) was conducted to investigate time series analysis of airline industry. They decided to use ARIMA model as it suitable with airline market because it allows us to process regular seasonal fluctuation time series ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1029/WR013i003p00577”, “ISSN” : “19447973”, “author” : { “dropping-particle” : “”, “family” : “McLeod”, “given” : “Angus Ian”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Hipel”, “given” : “Keith William”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Lennox”, “given” : “William C.”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Water Resources Research”, “id” : “ITEM-1”, “issue” : “3”, “issued” : { “date-parts” : “1977” }, “page” : “577-586”, “title” : “Advances in Boxu2010Jenkins modeling: 2. Applications”, “type” : “article-journal”, “volume” : “13” }, “uris” : “http://www.mendeley.com/documents/?uuid=4d7f1ec6-83a9-4781-b944-e81bcb0f75be” } , “mendeley” : { “formattedCitation” : “(McLeod, Hipel, and Lennox 1977)”, “plainTextFormattedCitation” : “(McLeod, Hipel, and Lennox 1977)”, “previouslyFormattedCitation” : “(McLeod, Hipel, and Lennox 1977)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(McLeod, Hipel, and Lennox 1977). They use ARIMA (0,1,1)×(0,1,1)12 as the final model for measuring the prediction performance of the model. The purpose of this research basically to analyse the exact future growth of passenger transportation. Thus, in the future it can be expected that an anticipated average of 10,000 more passengers will utilize the world airlines services every month. Furthermore, the research by Asrah et al (2018) they forecast the number of passenger Malaysian Airline (MAS) by using Box Jenkins method. The suitable time series model for data in 2009 is SARIMA (0,0,1)(1,0,0) while the suitable time series model for data in 2012 is SARIMA (2,0,0)(0,1,1). In this study, we use Box Jenkins method to forecast the number of passenger airline of Air Asia.
CHAPTER 3
METHODOLOGY
3.1 Description data
In the airline industry, passenger flows from a source to a destination represent a statistical time series adopted daily, monthly, quarterly, or yearly numbers of air passengers. In this study, the set of data obtain from Malaysia Airport Holdings Berhad (MAHB). The data obtained were about the total number of passengers that arrived to Kuala Lumpur International Airport (KLIA). These set of time series data are for the number of Air Asia passengers from January 2009 until August 2012.
3.2 Normality Test
Normality tests can be conducted in many way such as the Shapiro-Wilk test, the Lilliefors test, the Cramer-von Mises test, the Anderson-Darling test, D’Agostino–Pearson test, the Jarque–Bera test and chi-squared test ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1080/00949655.2010.520163”, “author” : { “dropping-particle” : “”, “family” : “Yap”, “given” : “B W”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Sim”, “given” : “C H”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issue” : “May”, “issued” : { “date-parts” : “2011” }, “title” : “Comparisons of various types of normality tests”, “type” : “article-journal”, “volume” : “9655” }, “uris” : “http://www.mendeley.com/documents/?uuid=0c2fbdde-39df-4e26-bdd1-477e19db5f67” } , “mendeley” : { “formattedCitation” : “(Yap and Sim 2011)”, “plainTextFormattedCitation” : “(Yap and Sim 2011)”, “previouslyFormattedCitation” : “(Yap and Sim 2011)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Yap and Sim 2011). A normality test is used to determine whether the sample data has been drawn from a normally distributed population (within some tolerance). Normal distribution is significance as it is fundamentally assumption of many statistical procedures. Other than that, it is also the most frequents distribution used in statistical theory and application.
3.2.1 Shapiro-Wilk Test
There are nearly 40 test of normality available in the statistical literature .The Shapiro-Wilks is one of the normality designed to detect all departures from the normality. Shapiro and Wilk (1965) test was at first allowed for only sample size of less than 50. It has become the preferred among other test because it has a good power propertiesCITATION Nor11 l 17417 (Mohd Razali , 2011). The hypotheses for Shapiro-Wilk test for normal distribution which are
H0 : The data follow normal distribution
H1: The data do not follow normal distribution
From the hypothesis, the null hypothesis state that the data are normally distributed meanwhile the alternative hypothesis state that the data are not normally distributed. By using Shapiro- Wilk test, the p-value are determined whether the test are significant or not. If the p-value has higher value, the null hypothesis is not rejected, meaning that the data follow normal distribution. The formula for Shapiro-Wilk test is
W=(i=1naiyi)²i=1n(yi-?)² (3.1)
Where ai =constant
3.3 Independent
The independent variable is one of the characteristic of the data where the correlation between the values of the same variable is based on related objects ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “ISBN” : “0387953515”, “author” : { “dropping-particle” : “”, “family” : “Brockwell”, “given” : “Peter J”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Davis”, “given” : “Richard A”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “0” }, “title” : “Introduction to Time Series and Forecasting , Second Edition Springer Texts in Statistics”, “type” : “book” }, “uris” : “http://www.mendeley.com/documents/?uuid=8e8c016c-bc76-482a-ad69-5e44f9f5324c” } , “mendeley” : { “formattedCitation” : “(Brockwell and Davis n.d.)”, “manualFormatting” : “(Brockwell and Davis, 2002)”, “plainTextFormattedCitation” : “(Brockwell and Davis n.d.)”, “previouslyFormattedCitation” : “(Brockwell and Davis n.d.)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Brockwell and Davis, 2002)
3.3.1 Durbin Watson Test
The Durbin Watson Test is a measure of autocorrelation in residual from regression analysis ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1016/0304-4076(85)90012-0”, “ISBN” : “0709-9231 ;”, “ISSN” : “03044076”, “PMID” : “977649”, “abstract” : “We study two Durbin-Watson type tests for serial correlation of errors inregression models when observations are missing. We derive them by applying standard methods used in time series and linear models to deal with missing observations. The first test may be viewed as a regular Durbin-Watson test in the context of an extended model. We discuss appropriate adjustments that allow one to use all available bounds tables. We show that the test is locally most powerful invariant against the same alternative error distribution as the Durbin-Watson test. The second test is based on a modified Durbin-Watson statistic suggested by King (1981a) and is locally most powerful invariant against a first-order autoregressive process. u00a9 1985.”, “author” : { “dropping-particle” : “”, “family” : “Dufour”, “given” : “Jean Marie”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Dagenais”, “given” : “Marcel G.”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Journal of Econometrics”, “id” : “ITEM-1”, “issue” : “3”, “issued” : { “date-parts” : “1985” }, “page” : “371-381”, “title” : “Durbin-Watson tests for serial correlation in regressions with missing observations”, “type” : “article-journal”, “volume” : “27” }, “uris” : “http://www.mendeley.com/documents/?uuid=a5cd9d1e-928d-48be-bb8d-5fda1191725a” } , “mendeley” : { “formattedCitation” : “(Dufour and Dagenais 1985)”, “manualFormatting” : “(Dufour and Dagenais, 1985)”, “plainTextFormattedCitation” : “(Dufour and Dagenais 1985)”, “previouslyFormattedCitation” : “(Dufour and Dagenais 1985)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Dufour and Dagenais, 1985). This test is easy to compute and has optimal power properties against first-order serial dependence (Durbin and Watson, 1950).Autocorrelation is the similarity of a time series over successive time intervals.
DW=t=2T(et-et-1)²t=1Tet² (3.2)
The formula above is for Durbin-Watson where et = yt- ?t and D lies between 0 to 4. The Durbin- Watson statistic interpreted as follow:
If D is close to zero (0), then positive autocorrelation is probably present.

If D is close to two (2), then the model is likely free of autocorrelation.

If D is close to four (4), then negative autocorrelation is probably present.
A rule of thumb is that test statistic values in the range of 1.5 to 2.5 are relatively normal. Values outside of this range could be cause for concern. The test statistic is compared to lower and upper critical values which are DL and DU for specific level of significance ? to test for the autocorrelation. Furthermore, DL are Durbin Watson lower control limit whereas DU are Durbin Watson upper control limit.
The hypothesis testing for positive autocorrelation of the Durbin Watson test are
H0 : ? = 0
H1: ? > 0
This is the criteria for positive correlation
If D < DL rejects H0 If D > DU do not reject H0 If DL <D< DU the test is inconclusive
The hypothesis testing for negative autocorrelation of the Durbin Watson test are
H0 : ? = 0
H1: ? > 0
This is the criteria for negative correlation
If 4-D < DL reject H0 If 4-D > DU do not reject H0 If DL < 4-D < DU the test is inclusive
3.4 Stationary
A time series has a stationarity if a shift in time does not cause a change in the shape of the distribution. Basic properties of the distribution like the mean, variance and covariance are constant over the time. Most forecasting methods assume that a distribution has stationarity. For example, auto-covariance and autocorrelation rely on the assumption of stationarity. It is hard to tell whether the model is stationary or not. Thus, if we are not sure about the stationarity of the model, several testing can be done such as Unit root test ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.5093/cl2010v21n1a6”, “ISSN” : “1130-5274”, “abstract” : “The theme of unit roots in macroeconomic time series have received a great amount of attention in terms of theoretical and applied research over the last three decades. Since the seminal work by Nelson and Plosser (1982), testing for the presence of a unit root in the time series data has become a topic of great concern. This issue gained further momentum with Perron’s 1989 paper which emphasized the importance of structural breaks when testing for unit root processes. This paper reviews the available literature on unit root tests taking into account possible structural breaks. An important distinction between testing for breaks when the break date is known or exogenous and when the break date is endogenously determined is explained. We also describe tests for both single and multiple breaks. Additionally, the paper provides a survey of the empirical studies and an application in order for readers to be able to grasp the underlying problems that time series with structural breaks are currently facing.”, “author” : { “dropping-particle” : “”, “family” : “Glynn”, “given” : “John”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Perera”, “given” : “Nelson”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Verma”, “given” : “Reetu”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “container-title” : “Journal of Quantitative Methods for Economics and Business Administration”, “id” : “ITEM-1”, “issue” : “1”, “issued” : { “date-parts” : “2007” }, “page” : “63-79”, “title” : “Unit Root Tests and Structural Breaks: A Survey with Applications”, “type” : “article-journal”, “volume” : “3” }, “uris” : “http://www.mendeley.com/documents/?uuid=5ede21ae-6a9d-4a2b-8cf4-d297fd8071f3” } , “mendeley” : { “formattedCitation” : “(Glynn, Perera, and Verma 2007)”, “plainTextFormattedCitation” : “(Glynn, Perera, and Verma 2007)”, “previouslyFormattedCitation” : “(Glynn, Perera, and Verma 2007)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Glynn, Perera, and Verma 2007), KPSS test, a run sequence plot, The Priestley-Subba Rao (PSR) Test or Wavelet-Based Test.

Figure 4.1: The plot on the left is a stationary with no obvious trend while the plot on the right shows seasonality and is non stationary ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “ISBN” : “0387953515”, “author” : { “dropping-particle” : “”, “family” : “Brockwell”, “given” : “Peter J”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” }, { “dropping-particle” : “”, “family” : “Davis”, “given” : “Richard A”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “0” }, “title” : “Introduction to Time Series and Forecasting , Second Edition Springer Texts in Statistics”, “type” : “book” }, “uris” : “http://www.mendeley.com/documents/?uuid=8e8c016c-bc76-482a-ad69-5e44f9f5324c” } , “mendeley” : { “formattedCitation” : “(Brockwell and Davis n.d.)”, “manualFormatting” : “(Brockwell and Davis, 2001)”, “plainTextFormattedCitation” : “(Brockwell and Davis n.d.)”, “previouslyFormattedCitation” : “(Brockwell and Davis n.d.)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Brockwell and Davis, 2001).

3.4.1 The Augmented Dickey-Fuller (ADF) test
The Augmented Dickey Fuller Test (ADF) is a unit root test for stationarity ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Ac”, “given” : “The”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “0” }, “title” : “Checking for stationarity”, “type” : “article-journal” }, “uris” : “http://www.mendeley.com/documents/?uuid=89f9b333-bf90-401a-872b-0c06bd824e67” } , “mendeley” : { “formattedCitation” : “(Ac n.d.)”, “manualFormatting” : “(Ac , 2010)”, “plainTextFormattedCitation” : “(Ac n.d.)”, “previouslyFormattedCitation” : “(Ac n.d.)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Ac , 2010). Unit roots can cause unpredictable results in a time series analysis. This test can be used with serial correlation. The hypothesis testing is followed by
H0:?=0 (There is a unit root and the series is nonstationary)
H1:?<0 (There is no unit root and the series is stationary)
The decision is to reject the null hypothesis if the t-statistics is greater than the critical value from the Dickey-Fuller table. Therefore, it conclude that the data is not stationary data.

3.5 Box Jenkins Method
The Box-Jenkins method is a time series analysis, forecasting and can be used in many areas and situation which involve in choosing a suitable model. The Box-Jenkins method is one of the most popular time series forecasting methods in business and economics. The method uses a systematic procedure to select an appropriate model, namely, Integrated Autoregressive Moving Average (ARIMA) models. Following Johnson (1997), the general notation for the order of a seasonal ARIMA model with both seasonal and non-seasonal factors is ARIMA(p,d,q)×(P,D,Q), and the term (p,d,q) gives the order of the non-seasonal part of the ARIMA model, the term (P,D,Q) gives the order of the seasonal part. A general ARIMA model has the following form (Bowerman and O’Connell, 1993 ).

?p(B)?p(BL)(1-BL)D(1-B)dyt=a+?q(B)?Q(BL)?t (3.3)
where
? (B) = autoregressive operators
?(B) = moving average operators
B = back shift operator
?t = random error with normal distribution N (0, ?2 );
a = constant,
yt = time series data, transformed if necessary.
Figure 4.2 shows the flowchart of Box Jenkins method.

Figure 4.2 The flowchart of Box Jenkins method ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “author” : { “dropping-particle” : “”, “family” : “Madsen”, “given” : “Henrik”, “non-dropping-particle” : “”, “parse-names” : false, “suffix” : “” } , “id” : “ITEM-1”, “issued” : { “date-parts” : “0” }, “title” : “Time Series Analysis”, “type” : “article-journal” }, “uris” : “http://www.mendeley.com/documents/?uuid=ed26418a-a8b9-4b88-aa20-9a22666368e4” } , “mendeley” : { “formattedCitation” : “(Madsen n.d.)”, “manualFormatting” : “(Madsen, 2015)”, “plainTextFormattedCitation” : “(Madsen n.d.)” }, “properties” : { “noteIndex” : 0 }, “schema” : “https://github.com/citation-style-language/schema/raw/master/csl-citation.json” }(Madsen, 2015) .

By using the following process, the Box-Jenkins method can be carried out. The first step in Box Jenkins is Model identification. By using Historical data, it can be used to identify appropriate Box Jenkins model. Firstly, time series plotting can be used to check whether there is a liner trend, stationarity, outliers, seasonal pattern and others in the time series, as well as the mean of the time series is constant or not. Then, the natural logarithmic transformation is applied to stabilise the variance if the mean of the time series is not relatively constant over time.

In order to decide whether the variable need to transform or not, can be determine by using time series plot. The Box-Cox transformation is one of the method to transform the data into normality ADDIN CSL_CITATION { “citationItems” : { “id” : “ITEM-1”, “itemData” : { “DOI” : “10.1093/hcr/28.4.612”, “ISBN” : “1468-2958”, “ISSN” : “03603989”, “PMID” : “21270539”, “abstract” : “BACKGROUND: Many different sexual isolation and sexual selection statistics have been proposed in the past. However, there is no available software that implements all these statistical estimators and their corresponding tests for the study of mating behaviour.\n\nRESULTS: JMATING is an easy-to-use program developed in Java for the analysis of mating frequency data to study sexual selection and sexual isolation effects from laboratory experiments as well as descriptive studies accomplished in the wild. The software allows the re-organization of the data previous to the analysis, the estimation of the most important estimators, and a battery of complementary statistical tests.\n\nCONCLUSION: JMATING is the first complete and versatile software for the analyses of mating frequency data. 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Power family of transformation are used to deal with nonconstant variance given by
y(?)= y?-1 ? , if ??0; logy , if ?=0. y(?)= (y+?2)?1-1? , if ?1?0; log(y+?2 ), if ?1=0. (3.4)
According to Montgomery et al (2015), if ?= 1, there is no transformation. The value of ? used with time series data is ?= -2(reciprocal square transformation), ? = -1(reciprocal transformation), ?=-0.5(reciprocal root transformation), ?=0(logarithm transformation), ?=0.5(square root transformation) and ?;1(square transformation). The table below shows the summary of transformation based on the value of ?.

Table 3.1 summary of transformation based on the value of ?
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Power Transformation
1 “raw”
-2 Reciprocal square
-1 Reciprocal
-0.5 Reciprocal root
0 Logarithm
0.5 Square root
;1 Square
After that, if the mean is still not stationary, differencing can be applied to transform it into stationary if it is not stationary. Differencing is one of the way that can make time series stationary. It also help to stabilize the mean of a time series by removing changes in the level of a time series, and so eliminating or reducing trend and seasonality.The first differencing operater, defined by
yt’=yt -yt-1=1-Byt (3.5)
where
B= backward shift operator
Sometimes, the differenced data are not appear stationary so it is need to difference the data second time in order to obtain stationary series. The second differencing is
= yt’ – yt-1′ =(yt-yt-1)-(yt-1-yt-2)
=yt-2yt-1+yt-2 =(1-B)²yt =(1-2B+B²) (3.6)
When the time series has seasonal component, a seasonal differencing can be used. A seasonal difference is the difference between an observation and the corresponding observation from the previous year. So,
yt’= yt-yt-m (3.7)
where m=number of seasons.

These are also called “lag-m differences” as we subtract the observation after a lag of m periods.
When the time series is in a stationary condition, the model order of autoregressive (AR) compnent and moving average (MA) component can be determined by using graphical plot of autocorrelation function (ACF) and partial autocorrelation function (PACF) . Autoregression model used a linear combination of past values of the variable. The autoregressive model of order p can be written as
yt=c+?1+yt-1+?2yt-2+…+?pyt-p+et (3.8)
where et = white noise
?= coefficient
It is AR(p) model. Rather than use past values of the forecast variable in a regression, a moving average model uses past forecast errors in a regression-like model. Then, the moving average model of order q can be written as
yt= c+et+?1et-1+?2et-2+…+?qet-q (3.9)
where et is a white noise. This is a MA (q) model.

The value of p can be determined from the partial autocorrelations function (PACF). If the ACF exponential decay and PACF cuts off, the model suggested the AR term. The value of q can be determined by autocorrelation function (ACF). If the ACF cut offs and PACF exponential decay, the model suggested the MA term. If the ACF and PACF shows the exponential delay, then the model is ARMA process. The behaviour of ACF and PACF for stationary are summarized in Table 3.2
Table 3.2 The summary behaviour of ACF and PACF for stationary
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Model ACF PACF
MA(q): moving average of order q Cut off after lag q Dies down
AR(p): autoregressive of order p Dies down Cuts off after lag p
ARMA(p,q):mixed autoregressive moving average of order (p , q) Dies down Dies down
AR(p) or MA(q) Cuts off after lag q Cuts off after lag p
No order AR or MA (White Noise or Random process) No spike No spike
The full model can be written as
yt’= c+ ?1 +…+ yt-1′ ?p + …+ yt-p’+?1et-1+…+?qet-q+et (3.10)
where
yt’ = differenced series
We can call this an ARIMA (p,d,q) model, where
p = order of the autoregressive part
d = degree of first differencing involved
q = order of moving average part
Next, the general seasonal ARIMA model of orders (p,d,q)x(P,D,Q) with period d is
(1-?pB)(1-?pBm) (1-B)(1-Bd)yt = (1-?qB)(1+?Q Bm)et (3.11)
where
m = number of observations per year
?pB = seasonal autoregressive operator for non-seasonal part of model
?pB= seasonal autoregressive operator for seasonal part of model
?qB = seasonal moving average operator for non-seasonal part of model
?QB= seasonal moving average operator for seasonal part of model
During a second stage which is estimation stage, estimate the model coefficients by selecting the best-fit model based on the smallest values of AIC and SIC tests. Furthermore, in order to check the adequacy of the estimated model diagnostic checking is carried out and if need to, alternative models may be considered. By using ACF and PACF residuals, it can verify the “white noise” characteristics of the residual series from the selected model when the ACF and PACF residuals is within the 0.05 significance level.
Next, Ljung–Box Chi-Square statistic can be used as a diagnostic tool to test the lack of fit of a time series model (Ljung ; Box, 1978). Ljung–Box Chi-Square statistic is one of the way to assess if the residual from the Box Jenkins model follow the assumptions. Hypothesis testing for the Ljung–Box Chi-Square statistic is:
H0 : The model is adequate
H1 : The model is inadequate
If the p-value of the Ljung-Box Chi Square statistic is small (say, p-value;0.05), the null hypothesis are rejected thus the selected model is considered inadequate, and then a modified model will be established until a satisfactory model can be determined.

Next, forecast can be calculated. The main purpose of fitting ARMA schemes is to project the series forward beyond the sample period or out of sample. It should be noted that, in all that follows we will assume that observations are only available for periods 1 to n, and that all forecasts are made conditional on information available at time n. We look at the residuals to determine how accurate the model predicts. The desired accuracy of the forecasts depends on the analyst’s goal.

3.6 Mean Absolute Percent Error (MAPE)
The MAPE (Mean Absolute Percent Error) measures the size of the error in percentage terms. It is calculated as the average of the unsigned percentage error. Percentage errors have the advantage of being scale-independent, and so are frequently used to compare forecast performance between different data sets.
MAPE= (1n|Actual-Forecast||Actual|)*100 (3.12)
where
n= number of predicted values
The smaller the value of MAPE, the more accurate the forecast. The judgement of forecast accuracy based on MAPE value was summarized in the Table 3.3 below
Table 3.3 The judgement of forecast accuracy based on MAPE value
MAPE Judgement of forecast accuracy
Less than 10% Highly accurate
11% to 20% Good forecast
21% to 50% Reasonable forecast
More than 51% Inaccurate forecast
3.7 Mean Square Error (MSE)
The Mean Square Error (MSE) is a widely used criterion for the choice of a forecasting performance rule. The minimum the value of MSE, the more accurate the forecast. Mean Square Error (MSE) is a measure of dispersion of forecast errors by taken the average of the squared individual errors.
Formula:
MSE = (actual-forecast)²n (3.13)
n= number of predicted values
CHAPTER 4
EXPECTED RESULT
4.1 Expected result
In this study, our objective is to study the behaviour of the Air Asia passenger data by identify whether there is a trend or pattern by using time series plot. By using the result obtained from the time series plot, we can determine whether the data have trend, seasonality or cyclic behavior that can be seen clearly from the output.
Moreover, we need to apply ARIMA model in Air Asia passenger data from January 2008 until Ogos 2012 in order to find the best forecasting model. We are expecting the best model will be determined which is seasonal ARIMA model.
Furthermore, we need to forecast the future of Air Asia passenger for January 2008 until Ogos 2012 by using Box Jenkins Method so that the researchers can obtain a wide knowledge regarding Air Asia passenger data besides other literature review on Air Asia passenger that we can make it as a reference. Based on the result, the trend of the Air Asia passenger can be identified in the future.
Last but not least, we have to evaluate the forecasting performance of ARIMA model. The best forecasting model will be determined and chosen from the forecasting accuracy measure which is MAPE and MSE. The forecasting model with the most minimum forecasting error will be selected as the best forecasting model.
David, J. R. (2011). Budget airlines. Retrieved November 11, 2011, from http://blog.malaysia-asia.my/2011/08/budget-airlines.html
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APPENDIX
GANTT CHART
TITLE: TIME SERIES ANALYSIS OF AIRLINE PASSENGERS IN MALAYSIA BY USING BOX JENKINS
WEEKS W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14
1. Resource collection (Articles, Journal and books) 2. Introduction 3. Literature Review 4. Methodology 5. Expected Results 6. Submission of BDP proposal to supervisor 7. Submission of BDP proposal approved by supervisor to examiners 8. preparation for oral presentation 9. Oral Presentation 10. Final proposal correction (after oral presentation) 11. Submission of corrected project proposal Expected Actual