US Domestic Flight Passenger Data

Presented by: Elio Aybar, Lev Tyomkin, Matt Fligiel & Matt Norgren

Table of Contents

• Introduction
• Data Overview
• Key Charts (ACF/PACF) & Interpretation
• First difference
• Second difference
• Ordinary Least Squares (OLS)
• Exponential Smoothing
• Holt-Winters
• ARIMA
• VAR Modeling
• Future Work
• Conclusion - Performance
• Conclusion

Introduction

Over the course of 17 years:

• Domestic Air Travel has increased 47%
• International Air Travel has doubled Related to the United States and aircraft leaving or returning to it.

Data Overview

What: Air Travel Passenger counts with All Carriers & Airports Source: U.S. Dept of Transportation Date Range: October 2002 - December 2019 (2020 removed) Key Features:

• Domestic Passenger Count
• International Passenger Count
• Total Passenger Count

Key Features:

• Seasonality
• Trend

Key Charts (ACF/PACF) & Interpretation

First difference

KPSS test

H0: series is stationary HA: series is not stationary

Augmented Dickey-Fuller test

H0: series is not stationary HA: series is stationary

Second difference

KPSS test

H0: series is stationary HA: series is not stationary

Augmented Dickey-Fuller test

H0: series is not stationary HA: series is stationary

Ordinary Least Squares (OLS)

• Unemployment Level

• Personal Savings (US)

• Domestic Passenger Data

• Log Differenced Unemployment Level

• Log Differenced Personal Savings (US)

Exponential Smoothing

Using the fpp2() library, we applied a couple methods for Exponential Smoothing

• Simple Exponential Smoothing and Holt’s Method
  • Used an algorithm to identify the optimal alpha and beta values respectively
  • Looked at lowest RMSE in relation to x-plot of alpha/beta values from 0 - 100
  • Then forecasted 12 months on differenced data
    • Used differenced approach to try to address clear trend
• Concluded that both models overfitted the data and despite forecasting on differenced data, saw our performance metrics remain higher for test/train
  • Lesson here reaffirms that it is difficult to apply SES and Holt on data with trend and seasonality like our plane data

Holt-Winters

Using hw() we forecasted the next 12 months of our T.S.

• We experimented with the following four methods
  • Linear trend with additive seasonality
  • Linear trend with multiplicative seasonality
  • Exponential smoothing
    • Linear trend with additive seasonality and damping
    • Linear trend with multiplicative seasonality and damping
• Comparing the four approaches, we identified our best Holt Winters model to be multiplicative with damped trend
  • The multiplicative approach makes sense because we, from plotting our time series object, we observe data with a positive trend but with seasonality that appears to increase over time
  • By dampening the trend to be turn flat over time, we achieve better accuracy metrics (lowest RMSE) as early as 12 months forecasted out

ARIMA

An initial Auto-ARIMA identified our best model as an ARIMA(2,1,2)(1,1,2)[12].

• This makes sense, as there is a strong seasonal pattern, as well as a trend, implying the need for differencing
• Overall, this model performed well, with AICc 5590
• Could it be trimmed?

Tried multiple models

• Decreased Parameters
• Final ARIMA
  ARIMA(2,1,2)(0,1,2)[12]
  • Performed better on AICc; Error Metrics
• Residuals non concerning:

VAR Modeling

• With a combination of international and domestic flight data, we were able to create a strong VAR model
  • We tried multiple, but inevitably a high order model was required to account for seasonality

Future Work

Given the unique circumstances surrounding 2020:

• Additional data could be added
• An intervention would need to be calculated
  • Pulse Function
  • Intervention effects that die out gradually:
  
• A shorter window training window

Conclusion - Performance

• Ultimately, the ARIMA model did better than any others
  • While the VAR would be expected to do well, variations between patterns of international and domestic travel prevented it from performing quite as strongly as the ARIMA
  • OLS was not able to properly use the time aspect of the dataset
  • This model outperformed holt-winters as well on RMSE and other statistics

Conclusion

Individual Contributions:

• Matt N: Intro, OLS, Future Work
• Elio: Key Charts, Data Overview, OLS
• Lev: Holt-Winters, Exponential Smoothing
• Matt F: Arima, VAR