Time Series Analysis and Forecasting- ARMA

ARMA & ARIMA

1. Time Series Analysis and Forecasting of Passenger Enplanements Mohini Moharir Chirag Siddarmaiah

2. Aviation Industry

3. Federal Aviation Administration's (FAA) investments in the airport and airway system Passenger enplanement : a person boarding in the United States in scheduled or unscheduled service on aircraft in intrastate, interstate, or foreign air transportation.”

4. Why forecast Passenger Enplanements? Most important metric in aviation industry. Revenue generated by airports is directly related to this metric. Helps aviation authorities to plan decisions in the air transport infrastructure. Key element in airport planning process - future airport requirements, analyzing development plans, etc. Helps airlines to manage revenue - reduces risk by evaluating air transportation business. Plan the allocation of resources - aircrafts, pilots, fuel, etc.

5. Data Collection Monthly Passenger Enplanements data for domestic and international flights obtained from the Bureau of Transportation Statistics (BTS) Our dataset has total monthly passenger enplanements for scheduled and non- scheduled flights from Jan 2000 to Aug 2020. Link - https://www.transtats.bts.gov/TRAFFIC/

6. Evaluation of Raw Data Training dataset – Jan 2000 to Dec 2017 Testing dataset- Jan 2018 to Aug 2020 Deterministic Trend and Seasonality is evident Slight downward trend from 2007 to 2009 due to recession Drastic reduction after 2019 due to COVID-19 global pandemic

7. Evaluation of Raw Data Peak demand can be seen in month of June ,July and August .Considerable increase in passenger enplanements every year.

8. Decomposition- Seasonal, Trend &Remainder 1)Raw data=100%                                  2) Seasonal Portion = 73.1% 3) Trend Portion = 17.6 % 4) Residuals = 9.3 %

9. Polynomial Fit Fstatistic= 0.00018 < F(1,218)=3.84 Polynomial of order 1 is adequate Polynomial Trend  First Order  Second order  RSS  8060.814 8060.807

10. Deterministic Seasonality Parameters Periodicity RSS Fstat Ftable sin_cos1 12 7143     sin_cos2 12& 6 6879 4.06 3 sin_cos3 12,6&4 6680 3.12 3 sin_cos4 12,6,4&3 6667 0.2 3 Upon inspection of the parameters and their respective p-values, we eliminated the highest p-value variable and refit the model to ascertain whether the smaller model was adequate. Periodic trend was best represented by cosine function of periodicity 12,6 and 4

11. Autocorrelation Plots of Residuals from the deterministic model

12. ARMA modelling ARMA F statistic F table Comparison Conclusion (2,1) vs (4,3) 35.78 2.37 Fstat> Ftable Choose ARMA(4,3) (4,3) vs (6,5) 69.66 2.37 Fstat> Ftable Choose ARMA(6,5) (6,5) vs (8,7) 28.61 2.37 Fstat> Ftable Choose ARMA(8,7) (8,7) vs (10,9) 12.27 2.37 Fstat> Ftable Choose ARMA(10,9) (10,9) vs (12,11) 15.02 2.37 Fstat > Ftable Choose ARMA(12,11) (12,11) vs (14,13) 2.17 2.37 Fstat< Ftable Choose ARMA(12,11) (12,11) vs (11,10) 1.44 3 Fstat< Ftable Choose ARMA(11,10) (11,10) vs (11,9) 53.98 3.84 Fstat> Ftable Choose ARMA(11,10) Initial Estimates of ARMA(11,10)  

13. As the Green’s function is gradually approaching 0 ,we can say that ARMA(11,10 ) is stable . Green’s Function of ARMA(11,10)

14. Joint Optimization of parameters Joint estimates are nearly as same as initial estimates

15. Integrated model fit  

16. Autocorrelations plots of residuals from the Integrated Model

17. Forecasting Confidence Interval  MSE preCOVID-19 MSE with 2020 data  95% 16.32 648.9675

18. LSTM -Long short-term memory neural network LSTM is an artificial recurrent neural network (RNN) with  feedback connections unlike standard feedforward neural networks. A LSTM unit is composed of a cell , an input gate , an output gate and a forget gate LSTM networks are well-suited to classifying, processing and making predictions based on time series data, since there can be lags of unknown duration between important events in a time series

19. Time Series Prediction of Passenger Enplanements using LSTM Using the same data as used above ,we get MSE of 55.5017 Not as accurate as ARMA modelling procedure above Can be improved further by using Hyperparameter tuning.

20. Thank You Questions ?