Time Series Analysis and Prediction of AirPassenger Data using ARIMA Model
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This presentation discusses the application of time series analysis on the AirPassenger dataset using ARIMA model. It covers descriptive statistics, plots, ARIMA model, prediction, conclusion and recommendations. The presentation is relevant for students studying statistics, data analysis, and forecasting.
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3 Introduction •Several statistical models are used for the prediction (forecasting) of future values of data. The models include regression models, neural networks and time series models. In cases where the data has a time component, the time series models are best fit for the prediction of future values. •Time series have three components: trend component, cyclic (seasonal) component and the random component (Anderson, 2011). •This research applied time series analysis on the AirPassenger dataset available in the R Software. An ARIMA (p, d, q) model was developed and applied with predictions made based on the resultant ARIMA model. Autocorrelation and Partial autocorrelation graphs are used to determine the values of p and q in the model (Zhu and Wang, 2010; Getis, 2010).
4 Descriptive Statistics •The describe () function in the psych R package was used for the descriptive statistics. The results of the descriptive statistics are given in table below: StatisticValue Mean280 Minimum104 Maximum622 Range518 Standard Deviation120 Kurtosis0.57
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5 Plots •The figure on the side is the plot for the time series data, AirPassenger data. •From the time series plot we observe an increase in the passenger numbers over time. •This is evidence of a generally increasing trend in the data.
6 •The first plot on the side represents the boxplot for the AirPassenger data. •From the boxplot we observe that there were high passengers numbers between July and August showing the existence of the seasonality component of the time series. •The second plot on the side represents the decomposition of the time series. •The graph shows that there was passenger number fluctuations from year to year. The remainder graph however shows that the fluctuations had no defined trend in comparison to to the trend in the original data.
7 ARIMA Model •The ARIMA model is dependent on the assumption of stationarity. The table on the side represents the results form the ADF stationarity test on the AirPassenger data. The results in the table show that the p-value = 0.01 < 0.05. Hence we conclude that the AirPassenger data is stationary.
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8 •The first plot on the side represents the Autocorrelation plot. From the plot the upward line (above the blue line) immediately before the first downward line falls on 1, thus q = 1. •The second plot on the side represents the Partial Autocorrelation plot. From the plot the upward line (above the blue line) immediately before the first downward line falls on 0, thus p = 0.
9 Prediction •The eventual time series model is ARIMA (0,1,1) •The plot on the side represents the 10 year prediction of the number of passengers using the ARIMA (0,1,1) model. •The model predicts a continuous increasing trend over the next ten years to the year 1970.
10 Conclusion and Recommendations •The plot of the AirPassenger data shows a general increase in the passenger numbers between 1949 and 1960 with peak numbers achieved in the months of July and August. •The ARIMA (0, 1, 1) successfully predicts the passenger numbers over the next decade from 1960. The prediction shows a continuous increasing trend over the 10 year period in the passenger numbers. •Using the inferences and conclusion drawn from this research, the aviation company can adequately prepare for increasing passenger numbers every year over the next decade by setting up appropriate strategies. The aviation company can also increase the flight changes in the peak months of July and August in order to capitalize on the high passenger numbers.
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11 References Anderson, TW 2011,The statistical analysis of time series1st edn. John Wiley & Sons, New York. Getis, A 2010, ‘Spatial autocorrelation’, InHandbook of applied spatial analysis(pp. 255-278), Springer, Berlin. Marazzo, M, Scherre, R & Fernandes, E 2010, “Air transport demand and economic growth in Brazil: A time series analysis”,Transportation Research Part E: Logistics and Transportation Review, vol.46, no.2, pp.261-269. Pioneer 2019, Aviation, viewed 15 September 2019 < https://www.pioneer.com.ph/products/aviation> Zhu, F & Wang, D 2010, “Diagnostic checking integer-valued ARCH (p) models using conditional residual autocorrelations”,Computational Statistics & Data Analysis, vol.54,no.2, pp.496-508.