Note: MacKinnon critical values for the rejection of unit root test at 1% are -3.4340,-3.4377 and -3.4382 for the respective sample sizes ADF-Augmented Dickey Fuller Test statistics, PP-Philip Perron Test statistic Null Hypothesis: the series in non-stationary Co integration Test Results To check the long-term relationship, the Johansen co-integration test between the indices for the total time periods as well as the two sub-periods was conducted. Two variables will be cointegrated if they have a long-term, or equilibrium relationship between them. The Johansen method is applied in the present study. The method can be illustrated by suing the following general autoregressive representation for the vector Y. Where, Yt is a (n x 1) vector on non-stationary I(1) variables, is the number of lags, p ɛt is an independently and identically distributed n-dimentional vector with zero mean and variance matrix The above equation can be reparametrized and turned into a vector correction model as: Where, And, The can be interpreted as a long-run coefficient matrix, since in equilibrium, all the π will be zero, and setting the error terms, to their expected value of zero will leave ΔYt-p ɛt, π = 0. The key feature in (2) is the rank of the matrix the rank of is equal to the number ΔYt-p π, π of independent cointegrating vectors. The Johansen test centres on the examination of the π matrix via eigen values. If the rank = 0, the matrix is null and (2) becomes the usual VAR π model in first difference. If the rank = 1, there is a single cointegrating vector and the π is the error correction term. For other cases in which there are expression πYt-1 1<rank(π)<n, multiple cointegrating vectors.
Note: MacKinnon critical values for the rejection of unit root test at 1% are -3.4340,-3.4377 and -3.4382 for the respective sample sizes ADF-Augmented Dickey Fuller Test statistics, PP-Philip Perron Test statistic Null Hypothesis: the series in non-stationary Co integration Test Results To check the long-term relationship, the Johansen co-integration test between the indices for the total time periods as well as the two sub-periods was conducted. Two variables will be cointegrated if they have a long-term, or equilibrium relationship between them. The Johansen method is applied in the present study. The method can be illustrated by suing the following general autoregressive representation for the vector Y. Where, Yt is a (n x 1) vector on non-stationary I(1) variables, p is the number of lags, ɛt is an independently and identically distributed n-dimentional vector with zero mean and variance matrix The above equation can be reparametrized and turned into a vector correction model as: Where, And, The π can be interpreted as a long-run coefficient matrix, since in equilibrium, all the ΔYt-p will be zero, and setting the error terms, ɛt, to their expected value of zero will leave π ΔYt-p = 0. The key feature in (2) is the rank of the matrix π, the rank of π is equal to the number of independent cointegrating vectors. The Johansen test centres on the examination of the π matrix via eigen values. If the rank π = 0, the matrix is null and (2) becomes the usual VAR model in first difference. If the rank π = 1, there is a single cointegrating vector and the expression πYt-1 is the error correction term. For other cases in which 1<rank(π)<n, there are multiple cointegrating vectors.
4-An_Empirical_Investigation_of_Linkages_between_India_and__Major_Asian_Stock_Markets.docx