bsfc phoenix final report team 5 · bsfc - us airways final project megan hanson, delfin de las...

Business Forecasting with Prof. Shmuéli, Term 7 2012

Planning Ahead: Forecasting US Airways’ international passenger traffic in PHOENIX: How do historical information and other hubs’ performance influence prediction? Team 5: Megan Hanson, Delfin Rico, Filippo Sclafani, Yating Yu

BSFC - US Airways Final Project Megan Hanson, Delfin de las Heras Rico, Philip Sclafani, Yating Yu

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EXECUTIVE SUMMARY

Our analysis aims to reveal insights from monthly international passenger traffic data in

the three major U.S. Airways hubs, Charlotte (CLT), Philadelphia (PHL), and Phoenix (PHX), to

predict future implications at the newest international hub, Phoenix. Operations in PHX

international hub began more recently (2007) than the other two hubs (2000), leading us to focus

on creating a forecasting model to predict the monthly flow of international passengers to

and from the PHX hub with fuller accuracy using the combination of insights.

Conclusions of the analysis revealed that, even after de-seasonalizing data from the

other two hubs using different methods, any model or combination of models using the data from

the other two hubs performed worse in predicting the flow of international passengers in Phoenix

than models based on PHX data only. Test results proved that the influence of the flow

passenger series in PHL and CLT is not statistically significant when predicting the flow

passenger series in PHX. Such conclusion is also intuitive considering that each hub runs flights

to different destinations, has different trend patterns, and reaches unique seasonal peaks.

Based on our research, we recommend a model using a combination of three

forecasting techniques that together are parsimonious in their simplicity, yet robust and flexible

enough to react to unique events like the travel advisory to Mexico during peak season 2011 and

create a reliable prediction. The first technique of the model is an additive multiple linear

regression, then the autocorrelation within seasons is removed by adjusting the errors using

ARIMA techniques. The 12-month out forecasting model is then further followed by naïve

error forecasting. Within this last component, the model should easily be used on a month to

month rolling forward basis, as data becomes available, given the high degree of fluctuation in

the airline industry. Consistent updating is necessary, and creates even more utility in

coordinating the level of multipurpose ground staff and airport services with the expected

number of passengers.


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PROBLEM DESCRIPTION

Compared to established hubs in Philadelphia and Charlotte, Phoenix Sky Harbor

International Airport is US Airways most recent and fastest growing hub for international flights.

US Airways’ international flights to and from Phoenix began in October 2007. As a result, US

Airways has limited historic data on its international passenger traffic in Phoenix.

The goal of our project is to understand the patterns that describe international

passenger traffic in Phoenix using the most current forecasting techniques and publically

available airline data from the Bureau of Transportation Statistics. Our research focus includes

data from all three of US Airways international hubs, Phoenix, Charlotte, and Philadelphia, to

examine if the evolution of international passenger traffic at other established international hubs

can be used to better predict Phoenix traffic. Through our analysis we seek to provide US

Airways, our principal stakeholder, with a model using time series data that helps forecast its

international passenger traffic in the Phoenix airport for the next 12 months. Secondary

stakeholders are airport facility advisors, support services provided by Phoenix airport, and

secondary service providers that rely on the flow of international passengers, such as foreign

language bookshops and souvenir shops. Each stakeholder should take our model and derive

the ability to adapt their services to the evolving needs of US Airways international

passengers more predictably.

As the fastest-growing and most cost-effective of the five largest U.S. airlines, US

Airways is particularly sensitive to increasing operational efficiency. If US Airways can use

historical information and other hubs’ performance to better predict Phoenix air traffic, then US

Airways will be able to better manage its sales and operations as our predictions can impact the

future use of airplanes, flexible ground crews, and optimal scheduling of prized

international flights, a major component of the airline’s growth.

As consultants to US Airways, we want to ensure that our model is sophisticated enough

to predict their international air traffic better than an internal analyst, proving both the value

of competent forecasting and our own credibility. Concurrently, we want to create a dynamic

model that the airline can use to help forecast international air traffic each month, independently

of our efforts. Because stakeholders include air traffic and operations management, it is possible

to adjust the model to slightly over- or under- forecast, correct it for external predictors, and


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create flexibility to account for historical “black swan” unpredictability that allow the airline to

optimize its use of planes and services.

DATA DESCRIPTION

As mentioned above, we utilized US Airways’ monthly international passenger data

from all three of its major hubs over the time periods available from bts.gov sources.

International passenger data for Charlotte and Philadelphia was available from January 2000

through July 2011. In Phoenix, because of the airport’s more recent introduction of international

service, data was available from October 2007 through July 2011. Our analysis utilized all three

data sets, but our core analysis focuses on our primary data set, Phoenix, given our goals.

Our first visualization (below) of the Phoenix data helped us understand the

multiplicative seasonality and upward trend reflected in the data. Seasonality patterns in

Phoenix follow a twelve month cycle. At PHX, a peak is the spring is followed by a consistent

drop in international passenger traffic every September. An additional not of interest is the

anomalous variation towards the end of the time series (highlighted in yellow below). Upon

further research, we determined that this was due to a unique, historic event – in the spring of

2011, Departments of Public Safety across the United States warned U.S. citizens against

traveling in Mexico because of violence related to drug trafficking. As a result, we believe

travel through Phoenix was negatively impacted.1 Despite this anomaly, we decided to leave in

all of the data points to account for the relative frequency of similar events.

1 http://www.dallasnews.com/news/state/headlines/20110301-texas-dps-tells-spring-breakers-to-avoid-mexico-because-of-drug-cartel-violence-and-other-crime.ece


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TECHNICAL SUMMARY

Method: In order to take into account seasonality and trend, we tried modeling the data using

a few different approaches: Naïve Forecasting (to establish a benchmark for our subsequent

models), Additive and Multiplicative Multi-Linear Regression, Polynomial, and Holt-Winter’s

Smoothing.

Naïve Forecast (full details in Appendix A)

Description: After running all of the models, looking at the performance statistics (MAE, Ave.

Error, MAPE, RMSE) and, most importantly, evaluating the residual charts (full charts available

for every model in Appendix B-E), we determined that the Additive MLR model was the best

predictor for Phoenix international passenger traffic (independent of the other two hubs).

However, the chosen model, MLR – Additive Seasonality, did not adequately account

for seasonality (per the comparison of residual charts below). We tried different variations

using ARIMA and found that the most accurate solution was to adjust for the error using AR

methods.

Original MLR – Additive Seasonality Adjusted MLR – Additive Seasonality

Naive MLR – Additive Seasonality

MLR –Multiplicative Seasonality

2nd Degree Polynomial Holt-‐Winter’s

MAE 7,732.50 5,711.19 6,718.70 7,036.27 18,229.08

Avg. Error (4,870.33) (113.12) 187.99 -‐3,363.21 17,836.09

MAPE 13.07% 9.19% 10.51% 10.92% 27.87%

RMSE 8,744.07 6,674.69 7,966.12 9,145.30 23,591.47


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After choosing the best model for predicting US Airways international passenger traffic

at Phoenix, we then layered on Philadelphia and Charlotte international passenger traffic in

numerous ways to see if and how other international hubs can help forecast Phoenix’s

international passenger traffic. First, we added inputs for each hub representing Lag-1. Second,

we added inputs for each hub representing the naïve forecast (essentially Lag-12) which uses

data from twelve months past. Upon running the regression, we found that all of the variables

relating to these two hubs were insignificant and thus concluded that there is no real or visible

relationship between Phoenix international traffic and traffic at other major hubs for US

Airways. Full details are available in Appendix F, as well as the full spectrum of Philadelphia

and Charlotte data, models, and charts (Appendix G – Philadelphia, Appendix H – Charlotte).

Equation: (the additive MLR model + adjustment for error with AR(1))

yt = b0+ b1 t +b2 D2 +b3 D3 +b4 D4 +b5D5 +b6 D6 +b7 D7 +b8 D8 +b9 D9 +b10 D10

+b11 D11 + (� + AR1 *�t-1 + SAR1t)

Forecast: Using our previously chosen model, we forecasted the next twelve months following

our Phoenix data set (e.g. Month 140-151, August 2011 through July 2012). This forecast has

immediate relevance to shift or increase resources day by day, and week by week for US

Airways and Phoenix airport management. The more data becomes available, the more uses

can be derived. Evolution of international passenger traffic makes it likely that the model

should be verified and even revised regularly. We suggest updating it at least every six months

in the interest of using the most recent data, while keeping the forecasting fairly parsimonious

and easy to use for US Airways’ analytic team. Our full forecast and prediction interval is

Lags ACF0 11 0.727892942 0.438580483 0.17266544 -0.033437215 -0.061519736 -0.136615687 -0.238891278 -0.263408849 -0.3712710 -0.4182786611 -0.4933197212 -0.54856366

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags

ACF Plot for Residual

ACF UCI LCI

Lags ACF0 11 0.285933642 0.197171613 -0.029017374 -0.224547955 -0.042975236 -0.052337387 -0.248199948 -0.098597649 -0.3385156410 -0.22361711 -0.1828054612 -0.2484265

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags

ACF Plot for New Residual

ACF UCI LCI


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found in Appendix J. The chart below depicts our modeled forecast beyond actual data

available through July 2011.

Forecasted Section


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Appendix A. Naïve Forecasting.


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Appendix B. Additive MLR.

Lags ACF0 11 0.727892942 0.438580483 0.17266544 -0.033437215 -0.061519736 -0.136615687 -0.238891278 -0.263408849 -0.3712710 -0.4182786611 -0.4933197212 -0.54856366

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags


ACF UCI LCI


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Appendix C. Multiplicative MLR

Lags ACF0 11 0.721856472 0.459106393 0.220348754 0.021202455 -0.008150376 -0.12315537 -0.249621518 -0.260192399 -0.369432310 -0.4108701611 -0.5017022512 -0.60175997

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags


ACF UCI LCI


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Appendix D. 2nd Degree Polynomial

Lags ACF0 11 0.664378232 0.362590643 0.057191534 -0.208811955 -0.489209126 -0.605575567 -0.49026628 -0.243296599 -0.0623819810 0.1663718111 0.3807587612 0.44822583

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags

ACF Plot for Actual Value

ACF UCI LCI


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Appendix E. Holt-Winter’s Smoothing.

Lags ACF0 11 0.820901042 0.62391463 0.438870164 0.293168515 0.20084046 0.146558547 0.083116118 0.05565669 0.0105912410 -0.0101716411 0.016852412 0.04724447

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags

ACF Plot for Residuals

ACF UCI LCI


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Appendix F. Model of Philadelphia and Charlotte data to predict Phoenix international passenger traffic

The Regression Model

Coefficient Std. Error p-value SS34059.65625 36204.42969 0.36000499 94254340000 17418.0504456 122.8245697 0.003381 518875100 0.9046262749855.724609 6510.30127 0.14842966 354820000 5144.0385749713.866211 6724.275879 0.16675071 451665000 4498393008229.101563 7449.505371 0.28470105 10715290009889.301758 11357.90625 0.39604846 580195800-8905.42676 13937.03418 0.53135455 17472270-9111.32129 23054.61719 0.69760585 18091630-4168.74414 24546.38086 0.86714745 2297245-10351.6738 26320.81055 0.69899482 14793040-24691.2012 32295.86523 0.45503291 769933900-10468.335 23223.64648 0.65785742 228943200

-7385.17529 8559.124023 0.40023336 175488500-0.31917939 0.26289284 0.24130528 43256210-0.06092461 0.27132195 0.82500821 326264.34380.31263313 0.41695362 0.46362436 14620290-0.2271006 0.55385715 0.68690151 4448868Char Int NF

Season_9Season_10Season_11Philly Int L1Char Int L1Philly Int NF

Season_3Season_4Season_5Season_6Season_7Season_8

Input variablesResidual dfMultiple R-squaredStd. Dev. estimateResidual SS

Constant termMonthSeason_1Season_2


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Appendix G. Philadelphia Hub Data, Visualization, and Models

Visualization


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Naïve Forecast

Residual

Linear Regression

40,000

60,000

80,000

100,000

120,000

140,000

160,000

-‐10 10 30 50 70 90 110 130 150

International Passengers

Month (Jan 2000-‐Jul 2011)

US Airways International Passengers -‐ Philadelphia

INTERNATIONAL -‐ Actual Predicted

-‐30000

-‐20000

-‐10000

0

10000

20000

30000

-‐10 10 30 50 70 90 110 130 150


Residual

Residual

Of the Validation Set


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Linear Regression

40000

60000

80000

100000

120000

140000

160000

-‐10 10 30 50 70 90 110 130 150


Month (Jan 2000 -‐ Jul 2011)

International Passengers by Day -‐ Philadelphia -‐ Linear Regression

Predicted Actual

-‐30000

-‐20000

-‐10000

0

10000

20000

30000

-‐10 10 30 50 70 90 110 130 150


ErrorOf the Validation Set


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ACF Chart

Lags ACF0 11 0.779110792 0.565246763 0.375680124 0.181334385 0.051954456 0.012051897 0.070165118 0.161001899 0.2268183210 0.2480409611 0.3394291412 0.33980766

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags

ACF Plot for Error

ACF UCI LCI


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Second-Degree Polynomial

40000

60000

80000

100000

120000

140000

160000

-‐10 10 30 50 70 90 110 130 150


Month (Jan 2000-‐Jul 2011)

International Passengers -‐ Philadelphia -‐ Polynomial Regression

Predicted Actual

-‐25000

-‐20000

-‐15000

-‐10000

-‐5000

0

5000

10000

15000

20000

25000

-‐10 10 30 50 70 90 110 130 150


Error



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Lags ACF0 11 0.725428462 0.448388763 0.203191374 -0.02896575 -0.178794356 -0.18736387 -0.090189788 0.063116369 0.1749769710 0.2143886411 0.2961700612 0.25871855

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags

ACF Plot for Error

ACF UCI LCI


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Holt-Winter Smoothing Model

30000

50000

70000

90000

110000

130000

150000

170000

-‐10 10 30 50 70 90 110 130 150


Month (Jan 2000 -‐ Jul 2011)

International Passenger Data -‐ Philadephia -‐ Holt-‐Winter's Smoothing Model

Actual Forecast

-‐40000

-‐30000

-‐20000

-‐10000

0

10000

20000

30000

40000

50000

-‐10 10 30 50 70 90 110 130 150


Error



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Lags ACF0 11 0.745900032 0.523990693 0.291489184 0.069408145 -0.089279176 -0.130413777 -0.100537268 -0.027118429 0.005978610 0.0036608911 0.0607258512 0.07369822

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags


ACF UCI LCI


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Appendix H. Charlotte Hub Data, Visualization, and Models

Visualization


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Naïve Forecast



23

Linear Regression



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Lags ACF0 11 0.832736372 0.672086953 0.512105414 0.395605035 0.325604116 0.292568687 0.263537568 0.285036569 0.3352407810 0.3655091811 0.3605510912 0.30536404

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags


ACF UCI LCI


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2nd Degree Polynomial Regression



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Lags ACF0 11 0.745107832 0.503648943 0.285808894 0.120560435 -0.002439466 -0.06826827 -0.126615768 -0.097209119 -0.030565610 0.0085102911 0.0098193712 -0.05770537

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags


ACF UCI LCI


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Holt-Winter’s Smoothing Model



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Lags ACF0 11 0.688838012 0.406006013 0.143953234 -0.106071675 -0.275335616 -0.318840037 -0.295816248 -0.178329079 0.0242169410 0.1462660111 0.2082496412 0.26288953

ACF Values

-‐1

-‐0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12

ACF

Lags


ACF UCI LCI


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Appendix I. Model Forecast and Useful Prediction Intervals

The Regression Model

Coefficient ARIMA Coefficient

13579.98242 Const. term -0.00035575

411.3641968 AR1 0.66156042

2993.385742 SAR1 -0.12542911

1503.771484

6685.907227

757.5430908

-9556.07129 MonthMLR

PredictionPrevious Mo. Error

Naïve Prev. Mo.

Error

Predicted Error

Model prediction

-8846.43555 140 54,805 2,410 1,594 56,399 -10158.2998 141 39,956 (4,522) (2,992) 36,965 -16366.2285 142 57,479 (2,686) (1,777) 55,702 -31625.9258 143 62,965 (3,710) (2,454) 60,510 -14514.5215 144 72,816 (3,373) (2,232) 70,585 -9440.38574 145 76,221 589 390 76,611

146 75,143 (1,169) (774) 74,369 147 80,736 1,396 924 81,660 148 75,219 1,061 702 75,921 149 65,317 2,315 1,531 66,848 150 66,438 2,928 1,937 68,375 151 65,538 4,241 2,806 68,343

Season_10

Season_11

ARIMA Model

PredictionSeason_4

Season_5

Season_6

Season_7

Season_8

Season_9

Input variables

Constant term

Month

Season_1

Season_2

Season_3

Forecasted Section


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Final comparison of three graph lines: Naïve, Our Model and Actual Data

bsfc phoenix final report team 5 · bsfc - us airways final project megan hanson, delfin de las...

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