**Team Ensemblers: **Ankita Avadhani, Bethapudi Keerthnana, Rajan Dhingra, Sabrish Gopalakrishnan

## 1. Background

Singtel and Airtel, on 14th June 2016, announced a strategic alliance.

The development of this combined network increased FDI from US$16 billion to US$22 billion in the first half of 2015 compared to the second half of 2014. Through this partnership, Singtel also strengthened its lead as the largest IP VPN provider in Asia Pacific with strong domestic data network in Australia, India and Singapore.

Singtel currently has a significant stake in Bharti Airtel in India and considers it as one of its chief associates in the Asia Pacific Region. Lately (since 2018), due to Reliance Telecomm, Bharti Airtel has seen considerable reduction in number of subscriptions, chiefly due to migration of users from Airtel to Reliance Jio and this has reduced the share price on average for Bharti Airtel stocks in BSE.

Coincidently, Singtel stocks have also dropped in this time-period. Several expert articles have cited one of the reasons as declining performance of Airtel.

Thus, it becomes an interesting exercise to determine the cause and effect between these entities and their stock prices. We try to see if any correlation is to be found with decrease in daily closing price between Airtel and Singtel using Transfer Functions.

## 2. Data Understanding

The data has been pulled from Yahoo finance.

The Airtel stock prices and Singtel stock prices have been pulled from 10 January 2018 – 10 September 2018. We consider the daily closing price as the variable of interest.

## 3. Bi-Variate Plot

From the plot, we can see that the Airtel and Singtel stock prices move roughly together.

## 4. Independent Variable (Airtel_Close):

** **We begin by choosing Airtel_Close as independent variable.

ADF tau statistics for the causal co-variate without trend and with trend including an intercept model in either case is -2.87 and -3.17:

Checking for significance, under first difference, both trend and otherwise show insignificance, which may be deemed sufficient for our purpose. Thus, we select d = 1 for pre-whitening under alternative, i.e. the process is stationary under d = 1.

### 4.2 Fitting a stochastic model

We see a non-linear decay for autocovariance. We see insignificant partial auto-covariance post 1 lag. Thus, we start by fitting an ARI(1,1) model, but the model parameters is not significant. However the residual is a white noise

Thus, we run the ARIMA Model Group to determine the stochastic model that would give the least AIC and significant parameters. We found out the least AIC is with the following ARIMA(2,2,3)

The residuals post fit show no significant autocorrelation and partial autocorrelation, so the residual is having white noise.

### 4.3 Pre-Whitening:

After performing pre-whitening of the time series by fitting ARIMA(2,2,3), we see significant cross-correlation between the covariates, however from lag -9 to lag -21 with peak at -15.

This indicates that our initial choice of cause and effect needs to be reversed. Thus, we proceed further with reversing the dependent and independent variable roles.

## 5. Independent Variable (Singtel_Close):

### 5.1 Fitting a stochastic model

Based on the above Cross-correlation plot, we find the out that

b = 9

s = 15 – 9 = 6

r = 2/1 (begin with 2). Fitting the Transfer Function with these parameters yields:

However, we find that not all variables are significant. We now try with r=1, Which gives a better model.

**Thus, we choose our parameters as b = 9, s = 6 and r = 1. **

We checked the residual plot and found the white noise in the residuals

## 6 Results & Conclusion

Thus, in our search for a relationship between Singtel and Airtel Stock prices, we found that Airtel stock prices may be modelled as a response to changes in Singtel stock prices. More noticeably, we see a delay in response of approximately 9 timestamp units since a change in the Singtel stock price. Thus, we can say that roughly, Airtel stock price proportionately reacts to change in Singtel stock price after 9 days.