【正文】
bles were expressed in their natural logarithm. Logarithmic transformations of variables are very popular in econometrics for a number of reasons。 firstly many economic time series data exhibit a strong trend, secondly, taking the natural logarithm of a series effectively linearizes the exponential trend (if any) in the time series data since the log function is the inverse of an exponential function (Asteriou and Price,2020). Thirdly, advantage is that it allows the regression coefficients to be interpreted as elasticity. In a study dealing with time series data, opting for log of the variables may prevent cumbersomeness in the modelling and inference (Rahaman and Salahuddin, 2020). Provided all series are I(1), then Dynamic Ordinary Least Square (DOLS) is robust to estimate the single cointegrating vector that characterizes the longrun relationship among the variables (CamachoGutierrez, 2020). The StockWatson DOLS model to be effective in estimating longrun parameters, the analysis must be in conformity with the existence a cointegration relation among sets of I(1) variables. Thus, it is pertinent to establish the presence of the unit root and then test the cointegrating relationship. Fortunately, there are variant ways of checking stationarity of series however Augmented Dickey Fuller (ADF) (1981) is the most widely applied econometric method for testing unit root in order to avoid problems of the spurious regression results. A series which is stationary after being differenced once is said to be integrated of order 1 and was denoted by I (1) (Dickey and Fuller, 1979). In general a series, that is stationary after being differenced n times is integrated of ordern , denoted by I (n ) while a series that appears stationary without differencing, is said to be I (0) (Shabbir, 2020). ADF (1981) unit root test for stationarity test is based on the following regression model: ? ?1.......1110t tjtkj jt YdaYTY ??? ??????? ??? ? Where tY , T and ? respectively confers a time series, a linear time trend and first difference operator, 0? is a constant, k is respecting the optimum number of lags on the dependent variable, and t? is random error term. The null hypothesis for testing nonstationarity is 0H : α = 0 meaning economic series are nonstationary. If the hypothesis of nonstationary is established for the underlying variables, it permits the assessments for cointegration relations. In econometrics two or more variables are said to be cointegrated if they share mon trends . they have longrun equilibrium relationships between them (Aqeel and Butt, 2020。 Shahbaz, 2020). There are various methods of detecting these longrun relations between variables. Engle and Granger’s (1987) approach for cointegration is simple and popular for its certain agreeable attributes. However, it did not permit the testing of hypotheses on the cointegrating relationships themselves. Contrarily, the Johansen setup does permit the testing of hypotheses about the equilibrium relationships between the variables all provided the variables have same order of integration (Brooks, 2020). Johansen and Juselius (henceforth JJ) (1990) cointegration technique is based on the Vector Autore