# The Variance Decomposition Analysis: Granger

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Variance Decomposition Analysis
The variance decomposition analysis has applied to quantify the extent up to which the selected indices one influenced by each other. We can also examine the short run dynamic relationship by variance decomposition. While impulse response functions trace the effects of a shock to one endogenous variable in the VAR, variance decomposition separates the variation in an endogenous variable in to the component shocks to the VAR. Thus, the variance decomposition provides information about the relative importance of each random innovation in effecting the variables in the VAR.
Impulse Response
Impulse responses have been applied to trace out the responsiveness of the dependent variables in the VAR to shocks to each
Granger Causality Test
Now we proceed to perform the granger causality analysis for the selected benchmark indices. The granger causality test conducted to see whether Bharat stock market cause other markets and vice versa in short run. Table 3 present the findings of granger’s causality test for the stock exchanges under study. Table 3: Pair Wise Granger Causality Test
Lags:
R H.K. granger causes R Bharat
2. R Bharat granger causes R H.K.
3. R China granger causes R Bharat
4. R Bharat granger causes R China
5. R U.S. granger causes R Bharat
The bidirectional causal relationship is found between Bharat stock market and the stock market of Hong Kong and China. Also, there exists unidirectional relationship between Bharat and US.
Johansen’s Co-Integration Analysis
Cointegration of two or more time series suggests that there is a long run equilibrium relationship between them. In Johansen’s approach, we applied Johansen’s cointegration test to see whether Bharat stock market is co integrated with other stock markets under the study. It must be noted that the closing prices (which are non stationary in nature) of the selected indices are used to test the cointegration among the markets not the return series. The results of Johansen’s cointegration test are as follows:
Table 4: Unrestricted Cointegration Rank Test (Trace)

Hypothesized
No. of CE(s) Eigenvalue Trace Statistic 0.05 Critical Value Prob.**
None 0.003793 32.98893 47.85613 0.5574
At most 1 0.003626 18.1342 29.79707 0.5562
At most 2 0.000895 3.933184 15.49471 0.9088
At most 3 0.00011 0.431646 3.841466 0.5112
Source:

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