Team Members: Apurv Garg, Bhabesh Senapati, Daksh Gupta, Dibyajyoti Panda, Rajiv Hemanth, Tran Minh Duc
Reason for Study
The Auto industry uses a tremendous number of materials to build cars, among which most of the weight comes from steel. Most of the modern cars weigh around 3,000 pounds out of which 2,400 pounds is steel. In cars, steel is used to build the chassis, door beams, roof, body panels, exhaust etc.
TATA Steel is the largest producer of steel in India and on the other hand Maruti Suzuki is one of the most extensively purchased brand in automobile industry. So, there should be a relation existing between the stocks of both the big giants.
- TATA STEEL stock prices (15 years data with monthly frequency): https://www.investing.com/equities/tata-steel-historical-data
- MARUTI SUZUKI stock prices (15 years data with monthly frequency): https://www.investing.com/equities/maruti-suzuki-india-historical-data
Figure 1: Time Series Plot
Log transformation was applied to the stock prices of both the companies as they helped in better identification of time series patterns by reducing the variance.
For the 1st iteration the Y (dependent) variable is selected as the TATA steel stock prices and the X(independent) variable is MARUTI stock price.
Before starting with the model building of a time series sequence it is very important for the series to be stationary, and if not stationary then it should be converted to a stationary sequence by taking a difference with its lag. Augmented Dicky Fuller test is used to test the stationarity of a series.
Augmented Dicky Fuller test has the following hypothesis:
Ho –> Level series contains a unit root
H1 –> Level series does not contain a unit root
Depending on the Significance of the p value we reject or fail to reject the null hypothesis. If we fail to reject the null hypothesis the series is non-stationary and if we reject the null hypothesis the series is a stationary series.
Both the series were tested for stationarity and both failed to reject the null hypothesis due to insignificant value of p. Hence both were non-stationary and were differenced with a lag of 1 to make the series stationary.
The input series i.e. Maruti stock price series is made to fit the best combination of ARIMA series. The value of I = 1 was determined in the above step.
Illustration 1: The Seasonal ARIMA (2,1,2)(0,0,2) model was finally selected as the best fit with all variables significant and a MAPE of 1.07
Illustration 2: Parameter Estimates
Both the series were then pre whitened on the following parameter values:
p = 2 | I = 1 | q = 2 | P = 0 | Is = 0 | Q = 2
Illustration 3: Cross-Correlation plot between tata steel and Maruti Suzuki stock prices.
After the pre whitening of the series the cross-correlation plot was analysed to determine the transfer function parameters. But the cross-correlation plot showed hikes on both the negative as well as the positive lags. Hence indicating a case of cointegration where both the series are correlated to each other. This can be seen in the illustration shown below.
The p value for Engle – Granger Test is much closer to being significant for the case
Y = Log_TISC and X= Log_MRTI (p = 0.09) as compared to
Y = Log_MRTI and X = Log_TISC.
Hence, the dependent variable was finally selected as Tata Steel price and the independent variable as Maruti Suzuki price.
An error correction model as it is now a problem of Cointegration Regression, with a difference [D=1] (to make the series stationary). The illustration below shows the result for the Ordinary least Square Model made:
Model: OLS, using observations 2003:10-2018:09 (T = 180)
Dependent variable: d_Log_TISC
coefficient std. error t-ratio p-value
d_Log_MRTI_1 −0.134663 0.115003 −1.171 0.2432
e_1 −0.0925064 0.0280208 −3.301 0.0012 ***
d_Log_TISC_1 0.194640 0.0854004 2.279 0.0239 **
Mean dependent var 0.007540 S.D. dependent var 0.140167
Sum squared resid 3.274077 S.E. of regression 0.136006
Uncentered R-squared 0.071713 Centered R-squared 0.069012
F(3, 177) 4.557955 P-value(F) 0.004207
Log-likelihood 105.2140 Akaike criterion −204.4279
Schwarz criterion −194.8490 Hannan-Quinn −200.5441
rho −0.017859 Durbin-Watson 2.022787
P-value was highest for variable 10 (d_Log_MRTI_1)
Delta Y(t) = 0.194* Delta Y(t-1) – 0.134* Delta X(t-1) – 0.092*E
Y(t) –> Log value of Tata Steel stock price at time t.
Y(t-1) –> Log value of Tata Steel stock price at time t-1
X(t-1) –> Log value of Maruti Suzuki stock price at time t-1
E –> Random error