Johansen’s Cointegration Tests
Johansen’s Cointegration Tests
Johansen co-integration test is to test the co-integration of the series. It is used to recognize the long run relationship among different variables. It is also means that although many developments can lead to permanent changes in the individual variable, there is some long-run equilibrium relation tying the individual variables together, represented by some linear combination of them.
Johansen’s have two test statistics: The trace statistics and the maximum eigenvalue statistic. The trace test examines the number of linear combinations (i.e. K) to be equal to a given value (K0¬), and the alternative hypothesis for K to be greater than K0.
Ho: K = Ko
Ho: K > Ko
To test for the existence of Cointegration using the trace test, we set Ko= 0 (no cointegration), and examine whether the null hypothesisi can be rejected.
For the maximum eigenvalue test, we ask the same central question as the Johansen test. The difference, however, is a proxy hypothesis:
Ho: K = Ko
Ho: K = Ko + 1
Given K0= 0 and rejecting the null hypothesis indicates that there is only one possible combination of the non-stationary variables to yield a stationary process.
3.2.3 Vector Error Regression Model (VECM)
The VECM is a multivariate time series model takes after the step in testing the co-integration (Johansen Test). The model appends the error correction framework trying to filling the defect in Vector Auto Regression (VAR) also known as multi-factor model1. It is introduce by Engel (1987) and Granger (1981), generally used for causality test and examine whether the variables have long run statistical co-integration relationship even though the variables’ level series are non-stationary2. Aim of adopt VECM in the research to examine the co-integration relationship of dependent variable with independent variables. If the long-run co-integration relationship spotted between the variable series in Johansen test (co-integration test), the next step adopting VECM to identify the short run features of the co-integrated variable series as the equation shown:
〖∆Y〗_t = a1+p1e1+∑_(i=0)^n▒〖β_i ∆Y_(t-i) 〗+∑_(i=0)^n▒〖δ_i ∆X_(t-i) 〗+∑_(i=0)^n▒〖γ_i Z_(t-i) 〗
〖∆X〗_t = a2+p2e_(i-1)+∑_(i=0)^n▒〖β_i Y_(t-i) 〗+∑_(i=0)^n▒〖δ_i ∆X_(t-i) 〗+∑_(i=0)^n▒〖γ_i Z_(t-i) 〗
The e_(i-1) point out any short term variation between the variables (dependent and independent) will cause exist of a stable long run correlation between the variables3.
3.2.3 Vector Error Regression Model (VECM)
The VECM is a multivariate time series model takes after the step in testing the co-integration (Johansen Test). The model appends the error correction framework trying to filling the defect in Vector Auto Regression (VAR) also known as multi-factor model1. It is introduce by Engel (1987) and Granger (1981), generally used for causality test and examine whether the variables have long run statistical co-integration relationship even though the variables’ level series are non-stationary2. Aim of adopt VECM in the research