PSTAT-174-Final-Project (2).pdf - Modelling Cellular Phone...

Modelling Cellular Phone Subscriptions in India
PSTAT 174
June 6, 2018
Group Theta:
Jeremy Berkov
Maximilian Broekhuis
Lauren Wong
Winson Li
Crystal Chau

Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Initial Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Box Cox Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Removing Trend and Seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
ARMA Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Diagnostics Checking on Test Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
ARIMA(1,1,1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
ARIMA(2,1,0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
ARIMA(0,1,1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
ARIMA(1,1,2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Analyzing Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Initial Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Box Cox Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Removing Trend and Seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
ARMA Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Diagnostic Checking on Test Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Abstract
The purpose of our project was to accurately forecast the number of mobile cellular phone subscriptions
in India, based on previous rates. This is of interest in relation to the recent and massive incorporation of a
digital identity system named Aadhaar. Aadhaar is a 12-digit unique identity number that can be obtained
by residents of India, based on their biometric and demographic data. In our analysis of the time-series,
we used various techniques, including Box-Cox transformations and differencing to make the time series
stationary and thus allowing us to identify potential models by looking at ACF and PACF plots.
During our analysis, we were able to come up with many candidate models, however, only one of our
candidates was most suitable for forecasting: ARIMA(1,1,2) model. The ARIMA(1,1,2) model passed the
Box-Ljung and Shapiro-Wilk tests, is viable for forecasting, and best satisfies the principle of parsimony,
compared to our other candidates. Through forecasting we were able to plot a potential trajectory with 95%
confidence for four years in the future. Despite certain validation points being outside the confidence interval,
our forecasted values still remain valid.
Introduction
The Aadhaar Act, passed in 2016, is a money bill from the Parliament of India that is aimed at providing
legal backing for the unique digital identification system implemented by Aadhaar. The Aadhaar Act is also
known as the Targeted Delivery of Financial and other Subsidies, Benefits and Services Act, which perfectly
describes the motives behind its implementation. Though China is often brought up during discussions of
overpopulation and population density, India faces many of the same issues and has been actively solving the
problems, evidenced by Aadhaar and its great success. The Aadhaar act has seen authentication success
rates for government services of up to 96.4% in 2013, though the rates have fallen to around 88% currently.
In general, Aadhaar is aimed at increasing financial inclusion and benefit participation for all Indian citizens,
and we believe that looking at mobile cellular phone subscriptions is a strong indicator of these factors.