Question

4. (20 pts) Suppose Y and Xi are two independent random walk processes. Using data on Y and Xt, we estimate the following regression: Source MS Number of obs500 P1 498).47 Prob E R-squared Adj R-aquared0.0147 Root MSE Mo 189.257801 189.257801 Residual 11194.2389 498 22.4783914 0.00 39 -0.0166 Total 11383.4967 499 22.8126187 4-7411 Y-vis Coef. Std. Err e> ti t95% cont. Interval t X vls 0445639 0153581 2.90 0.004 .0143891 0747386 cons9.334493 3067104 -30.43 0.000 93799 8.731887 (a) Using the estimation output above, test whether series Y, and X, are related. Critical values of t-statistic for 10%, 5% and 1% significance levels are 1.64, 1.96, and 2.33 respectively for a two-tailed test. Hint: if they are not related, we would expect the coefficient to be zero. (b) Given the information that Y and Xt are independent random walk processes, do we expect the coefficient on Xt be statistically significant? Why do we get the result in part (o)? Hint what tim sri ie d ram walk series have?

Answer 1

A)

Here hypothesis will be:

H₀: B_i = 0 (Null)

H_a: B_i is not equal to 0 (Alternate)

As the P value in the above case is less than 0.05, 0.1 and 0.01, so yes the two variables are related. In this case, the alternate hypothesis is accepted and hence the coefficient can't take the value of 0.

B)

For X_t, the corresponding P value is 0.004 (refer the output)... As this value is less than 0.05, so it can be stated that this coefficient is not statistically significant. This coefficient can't take the value of 0 as in this case the alternate hypothesis is accepted...

End of the Solution