Question

Question 1 From the U.K. private sector housing starts (X) for the period 1948 to 1984, Terence Mills obtained the following regression results': AX,31.03 0.188x, se(12.50) (0.080) 2.35) Note: The 5 percent critical t value is-2.95 and the 10 percent critical value is 2.60 a. On the basis of these results, is the housing starts time series station- ary or npnstationary? Alternatively, is there a unit root in this time se- ries? How do you know? l b. If you were to use the usual / test, is the observed value statistically significant? On this basis, would you have concluded that this time series is stationary? c. Now consider the following regression results: Δ2Xt= 4.76 1.39AX,-1+0.313Ax,- se (5.06) (0.236) (0.163) (-5.89) where Δ' is the second difference operator, that is, the first difference of the first difference. The estimated value is now statistically sig- nificant. What can you say now about the stationarity of the time se- ries in question?

Answer 1

From the U.K private sector housing starts (x) for the period 1948 to 1984, Terence Mills obtain the following results: delta x_t = 31.03 - 0.188 x_t - 1 Se = (12.50)(0.080) (t =)_tau -(2.35) Critical value at 5 % level - 2.95 Critical value at 10 % level - 2.6 Null Hypothesis_0 - stationary Alternative Hypothesis H_1 - non stationary From the given estimated result, tau = -2.35 < 2.95 tau = -2.35 < 2.6 so, cannot reject the null hypothesis Therefore, The housing starts time series become nonstationary. And from the given estimated result the time series data has the unit root. For t-test: - As t = 2.35 or t = 2.95 (5 % critical value) but the time series is a unit root function. \r\n So absolute t value is 2.95 not the estimated value of 2.35. This shows that the use of the usual t-test indiscriminate. Consider the regression results: - delta x_1 = 4.76 - 1.39 delta x_t-1 + 0.313 delta^2 x_t-1 Se