Modelling Air Passenger Traffic Flow in Murtala Muhammad International Airport Lagos, Nigeria: a Time Series Approach
Chapter One
Aim and Objectives of the Study
This study is aimed at comparing the forecast performances of time series models in approximately predicting the air passenger traffic flow in MMIA Lagos, Nigeria. This is achieved through the following objectives; by
- fitting three time series models (ANN,SARIMA andHWES);
- evaluating the accuracy of the proposed models using some performance criteria comprising Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) using monthly forecast of air passenger flow atMMIA;
- evaluate the out-of-sample forecast performance of these models using some classical loss functions such as MAPE and RMSE and be able to say which among them is better than the
CHAPTER TWO
LITERATURE REVIEW
INTRODUCTION
The aviation sector has been a vital component of the Nigerian economy, contributing immensely to its growth and development. Over the years, the sector has recorded increase in air passenger traffic. Airlines registered in Nigeria carry 6 million passengers and 119,000 tonnes of freight a year, to, from and within Nigeria. These airlines directly employ 7,000 people locally and support, through their supply chain, a further 33,000 jobs and 21,000 jobs supported through household spending of those employed by the airlines and their supply chain, contributing about NGN 29 billion to the Nigerian economy ( IATA 2010).
According to the NBS report (2014), the airline sector grew at an average growth rate of 14.3% between 2010 and 2013 and about 50 percent of average total passenger air travel between 2012 and 2013 were via Lagos airports (domestic and international), while about 25% were through Abuja airport.
With the emergence of more airlines, improved safety of the Nigerian airspace and increase of the Nigerian economy, passenger traffic has continued to increase. The steady growth of air passenger traffic was interrupted by the tragic air flight crash in June 2012. Since then, the sector has continued to record increase in air passenger traffic.
Nigeria recorded 68.84 percent domestic travels by air in the first quarter of 2014 out of a total of 3.4 million passengers that used Nigerian Airports, approximately 2.4 million travelled domestically (68.84 percent). According to recent data released by the National Bureau of Statistics (2014).
Nigerian air passenger traffic has been on a steady growth over the years. This could be attributed to the robust economic activities and the rebasing of Nigerian economy making it the largest in Africa in 2014.
Despite interruptions of air passenger traffic as a result of air crashes, hike in air fare, airlines recapitalization etc. The aviation sector has had a remarkable progress evidenced by yearly increase of air passenger traffic, emergence of new airlines and building of additional airports in the country. This has led to the creation of thousands of jobs and immense contribution to the strength of Nigerian economy. The aviation sector supports long run prosperity of the economy supplying benefits which aid the increase in the economy’s level of productivity and long term sustainable rate of growth.
Air transport also contributed NGN32.6 billion to Nigeria rebased GDP in 2010, 36.6bn in 2011, NGN42.7bn in 2012 and 48.8bn in 2013 and an average of 0.05 percent of total nominal GDP during the period whilst passenger traffic increased by 1.3 percent between 2012 and 2013 (National Bureau of Statistics, 2014).
Various time series models, univariate or multivariate, have been used in different capacities in modelling and forecasting in the aviation sector. This chapter provides a comprehensive review of previous studies.
Literature on Time Series Models
A large body of published literature regarding air passenger traffic flow forecast tend to concentrate on three specific regions: the United States, Europe and the Pacific region Andreoni and Postorino (2006). The work of Emiray and Rodriguez (2003) on their long study on Canada, provided monthly forecast of enplane/deplane air passengers flow for three market segments (domestic, international and trans-border flights), based on data covering the period ranging from January 1984 to September 2002. The study considered six time series models (Autoregressive AR(p), AR(p) with seasonal unit roots, Seasonal Autoregressive Integrated Moving Average (SARIMA), Periodic Autoregressive Model (PARM), Structural Time Series Model (STSM) and the seasonal unit roots model). They concluded that forecasting performance depends on two key elements: the market segment considered and the forecasting horizon. They showed that short memory models are better for short term forecasting whereas long memory models are better for long term forecasting.
CHAPTER THREE
METHODOLOGY
Introduction
This chapter discusses more about the models: Box-Jenkings Seasonal Auto-Regressive Integrated Moving Average Model, the Holt-winters Exponential Smoothing model and the Artificial Neural Network approach in modelling the air passenger traffic flow in Murtala Muhammad International Airport for domestic and international flights.The steps employed in the model selection for the SARIMA are elaborated and the procedures for calculating accuracy measures are discussed.
Data for the Study
The data used in this dissertation are the monthly air passenger traffic flow for international and domestic flights over the period of January 2003 to December 2015. This was obtained from the Nigerian Airspace Management Agency(NAMA).
The domestic air passenger traffic comprises of local passenger arrival and departure to and from Murtala Muhammed International Airport whereas the international air passenger traffic comprises of air passengers from international flights from and to other countries other than Lagos, Nigeria. The data set consists of 156 monthly observations of air passenger traffic flow for domestic flights and 156 monthly observations for international flights.
This study uses the R version 3.2.4(2016), Eviews 9 and Zaitun software for its analysis.
CHAPTER FOUR
ANALYSIS, RESULTS AND DISCUSSION
Introduction
The univariate models for modelling the air passenger traffic flow in Murtala Muhammad International Airport are evaluated and the empirical results of the analysis are presented. The time series plot for the air passenger traffic for the types of flights are obtained so as togive a visual representation of the characteristics. Most airline data are seasonal in nature with likely presence of trend and outliers. These characteristics could easily be inferred at times by having a quick glance at the time plot.
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS
Introduction
This chapter presents a summary of the procedure undergone to achieve the set objectives of the dissertation. The conclusion and recommendations based on the inference from the results obtained from the 3 models, ANN,SARIMA and Holt-Winters exponential smoothing are discussed.
Summary
In this dissertation, two sets of time series data from 2003 to 2015, monthly air passenger traffic for domestic and international flight were obtained.
Three time series model were employed in order to achieve the set objectives aimed at employing time series forecasting models to approximately predict air passenger traffic flow in Murtala Muhammad International Airport Lagos, Nigeria.
The data were divided into two sets, training and test sets. The time series models considered were evaluated on these data set so as to measure the accuracy of the models for in-sample and out-sample performance. The time series data were log transformed in order tostabilize the variance,so as to obtain more desirable results in the models considered.
The time plots of the air passenger traffic reveal non-stationarity, presence of trend, seasonality and noise. After first differencing, the Augmented Dickey Fuller test shows that the time series data attained stationarity.
The Jarque-Bera test for normality however reveals that the time series data are not normally distributed.
The Box-Jenkins methodology was employed in building the best SARIMA models for obtaining a fairly good forecast for air passenger traffic flow in Murtala Muhammad international airport.
After the necessary diagnostics using AIC, BIC, error measurements based on in-sample and out- sample forecast performance, SARIMA (1,1,1)(0,1,1)12 andSARIMA (3,1,1)(2,1,2)12 were selected, as the best SARIMA models for modelling the air passenger traffic for domestic and international respectively.The summary of these models show that, they gave better fit for the air passenger traffic. This was also compared with the other proposed models.
In selecting the best Holt-Winters model, the additive and multiplicative models were considered so as to select the best models. The appropriate smoothing parameters, , and which best minimize the sum of squared errors for the level, trend and seasonality were used in determining the best Holt-Winters model.In modelling the air passenger traffic, additive model appeared to be the bettermodel based on the AIC and BIC.
The Holt-Winters gave a generally good performance for in and out of sample forecast, it outperforms the SARIMA and ANN in the out-sample forecast in the international sector based on the MAPE and RMSE.
The feed forward neural network, using the back propagation algorithm was used to model the time series data. Eviews 9, Zaitunand R version 3.2.4 software were used to obtain the desired results.
A three layered feed forward neural network was used, with the number of neurons in the hidden layer varied to obtain the neural network architecture that best models the time series data.
ANN(12-4-1),ANN(12-6-1),ANN(12-8-1) and ANN(12-12-1) were considered usingthe sigmoid and bipolar sigmoid functions. ANN(12-12-1) in both domestic and international sector produced the best in-sample performance. However the out-sample performance was least, relative to the other ANN models. ANN(12-4-1) appeared to be the best model for modelling the domesticair passenger traffic, considering the in-sample and out-sample errors. For the international air passenger traffic, ANN(12-4-1) had the least out-sample result.
Conclusion
Generally, in achieving the aim of this dissertation, three time series models were considered, the seasonal auto-regressive integrated moving average (SARIMA), Holt-Winters Exponential Smoothing model and the Artificial Neural Network. These time series models were tested on the international air passenger and domestic traffic, to evaluate their performances and test the predictive capability of the artificial neural network relative to the other models.
The models were estimated on the training data set which covers the period from January 2003 to December 2013. The test set which covers the period from January 2014 to 2015 December was used to obtain the forecast accuracy measure of these models based on RMSE(Root Mean Squared Error) and MAPE(Mean Absolute Percentage Error).Empirical results show that all the models provide good forecasts of the air passenger traffic for international and domestic.
Comparing results across the models, it was observed that no model completely outperforms the other in all the sectors. However, the ANN model was found to be very efficient and had the best in-sample performance across the two sectors.
In modelling the domestic air passenger, the ANN model was seen to be significantly dominant, while for the international air passenger traffic the ANN also gave the best in-sample accuracy performance but the least out-sample performance. The Holt-Winters exponential smoothing and SARIMA both yielded good results. The Holt-Winters exponential smoothing out-performed the SARIMA and ANN for the out-of-sample forecast of international air passenger traffic while the SARIMA was more dominant than Holt-Winters in the domestic sector.
Conclusively,this study has been able to establish the effectiveness of the ANN in modeling and forecasting time series data and also select time series models that gave fairly accurate forecast of air passenger traffic in Murtala Muhammed International Airport Lagos, Nigeria.
Recommendations
This section gives a presentation of recommendations inferred from the results obtained from the time series models. The dissertation recommends;
The time series models considered from the Box-Jenkins methods, Holt-Winters and artificial neural network are appropriate in modelling and forecasting air passenger traffic flow in Murtala Muhammed International Airport Lagos, Nigeria.
That the artificial neural network representing a class of non-linear time series model, gives a very good in-sample and out-sample forecast accuracy and can be relied on as an alternative to the conventional methods in making forecasts for future plans, policies and decision making.
The artificial neural network model tends to give a better accuracy of forecast performance in an erratic time series data, due to its non-linear characteristic than the conventional time series model. Time plots show that the domestic sector is more unstable than the international sector. The ANN did well in the domestic than in the international sector which is less volatile. However, it would be recommended that due to the stable nature of international air passenger time series data, less complex conventional time series model could be relied on for better forecast accuracy.
The common characteristic of the time series data for the domestic and international air passenger is the presence of an obvious upward trend. This indicates increase demands in domestic and international flights. Better measures, policies, accommodation establishment, facilities, enhanced air traffic management have to be put in place to sustain and accommodate the increasing demands.
Future research on this dissertation could be extended to other types of machine learning, artificial intelligence based forecasting methods, which includes;Adaptive Neuro-Fuzzy Inference System Genetic Algorithm (ANFISGA) &Support Vector Machines (SVMs). Factors affecting the nature of the time series data in both sectors could also be captured using appropriate time series models, including such factors as exogenous input variables.
Contribution To Knowledge
- This research work has been able to employ appropriate time series models in modelling the air passenger traffic flow in Murtala Muhammad International Airport Lagos,
- The ANN, compared to the other models considered, was able to mimic the pattern of the time series data more accurately. This establishes the pattern recognition ability of ANN as could be observed from the in sample
- In modelling the International air passenger traffic, which appears to have a simpler time series, ANN had the least out-sample forecast accuracy. This implies that complex models may not necessarily yield the best forecast accuracy in modelling simple time series data.
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