Question

Consider a regression model of monthly time series data where we model the price of petrol which is dependent on the Crude Oil price and Exchange rate (against US$). Data for the three variables were collected over a 50 month period. Suppose the estimation results showed that the Durbin-Watson (DW) test value d is 1.38. Perform the DW test for first order positive autocorrelation of the error terms at the 5% level of significance.

      

       Model: e_t = r e_t-1 + v_t

      

       H_o:

       H_A:

       Test statistic:

       DW Critical values:             n =                               k =                    a =

                                                From the DW table,       d_L =                  d_U =

       Decision rule:

       Value of the test statistic: d = 1.38

       Conclusion:

Answer 1

Ho: No first order autocorrelation

HA: First order correlation exists

Test statistic:

DW Critical values:             n = 50                k = 3                   a = 0.05

                                  From the DW table,       dL = 1.245         dU = 1.491

Decision rule: Reject Ho if d < 1.245 or d > 1.491

Value of the test statistic: d = 1.38

Conclusion: Since, d is neither less than 1.245 nor greater than 1.491, do not reject the null hypothesis and conclude that there does not exist first-order autocorrelation.

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