The modeling strategy adopted in this study involves three steps. Prior to modeling time series data, firstly we determine the order of integration of the variables and ensure that it is equal for all series. The unit root tests, namely Augmented Dickey and Fuller (Dickey and Fuller, 1979) (ADF test) and Philips Perron (Phillips and Perron, 1988) (PP test), are used to check the nonstationarity of the series. For the series that are integrated of the same order, the next step is to perform conventional cointegration tests for long-run relationship. The existence of any bivariate and multivariate cointegration is tested by employing Engle and Granger and Johansen and Juselius methods, respectively.
Johansen’s method based on vector autoregressive (VAR) analysis utilizes the maximum likelihood estimates and allows testing and estimation of more than one cointegrating vector in the multivariate system. read more

The elements of a are known as the adjustment parameters in the vector error correction model. Johansen’s method is to estimate the II matrix from an unrestricted VAR and to test whether we can reject the restrictions implied by the reduced rank of II. In determining the rank of matrix II (number of cointegrating vectors), the characteristic roots or eigenvalues, I, of II are calculated. The hypothesis of the existence of r cointegrating vectors can be tested by using the maximum likelihood-based trace (lfr£1£B) and maximum eigenvalue (Am£LJP). Xtrace is based on the null hypothesis that the number of cointegrating vectors is less than or equal to r against a general alternative, while Am£LJP is based on the null hypothesis that the number of cointegrating vectors is r against the alternative r + 1 cointegrating vectors. If the computed values of Aff-Cl-,.and ArTi are less than critical values provided by Osterwald-Lenum, then the null hypothesis cannot be rejected. The optimal system lag length is determined by employing the Schwarz Bayesian Criterion.
Apart from the examination of the long-term relationships between the sector indices of the ISE, the direction of the short and long-term relationship between the same set of variables is investigated using the Granger’s causality tests. Granger’s causality approach (Granger, 1969) stated a testable definition of causality in terms of predictability in a set of noncointegrated variables. Then, Granger extended the definition of causality to a set of cointegrated variables. In the presence of cointegration among the variables, the causal relationships should be examined within the framework of the vector error correction model (VECM). VECM approach permits the distinction between causality based on short-run dynamics of VAR and on the disequilibrium adjustment of ECT.
The variance decomposition analysis is employed to investigate the short-run dynamics by determining the amount of information each variable contributes to the other variables in VAR models. Especially, the forecast error variances give information about the percentage of the movements caused by own shocks vis-a-vis shocks in other variables. To investigate long-run and short-run dynamics across sub-sector indices, the order of integration in each series is tested, using Augmented Dickey-Fuller (ADF) and Phillips and Perron (PP) unit root tests. The unit root test statistics reported in Table 3 reveal that each series is nonstationary in log levels but stationary in log first differences. Therefore, it is noted that all sub-sector index price series are integrated of order one, I.

Table-3: The Results of Unit Root Tests

ADF Philips-Perron
Level/First Difference No Trend Trend No Trend Trend
XHOLD Level -1.135 -2.379 -1.078 -2.361
First Difference -20.967 20.969 -48.811 -48.806
XMANA Level -0.554 -2.401 -0.562 -2.415
First Difference -50.016 -50.009 -50.018 -50.011
XILTM Level -0.806 -3.897 -0870 -3.857
First Difference -21.703 -21.726 -49.487 -49.493
XBANK Level -0.583 -2.321 -0.619 -2.378
First Difference -21.568 -21.571 -49.028 -49.022
XTCRT Level 0.369 -3.360 0.396 -3.339
First Difference -22.020 -22.090 -49.835 -49.870
XKMYA Level -0.608 -2.779 -0.518 -2.674
First Difference -21.959 -21.973 -51.714 -51.718