You Have Collected Quarterly Data on Canadian Unemployment (UrateC)and Inflation

Essay

You have collected quarterly data on Canadian unemployment (UrateC)and inflation (InfC)from 1962 to 1999 with the aim to forecast Canadian inflation.
(a)To get a better feel for the data, you first inspect the plots for the series. Inspecting the Canadian inflation rate plot and having calculated the first autocorrelation to be 0.79 for the sample period, do you suspect that the Canadian inflation rate has a stochastic trend? What more formal methods do you have available to test for a unit root?
(b)You run the following regression, where the numbers in parenthesis are homoskedasticity-only standard errors: $\widehat{\triangle \operatorname{Inf} C_{t}}=0.49-0.10 \operatorname{Inft}-1-0.39 \Delta \operatorname{Inf} C_{t-1}-0.33 \Delta \operatorname{Inf} C_{t-2}-0.21 \Delta \operatorname{Inf} C_{t-3}+0.05 \Delta \operatorname{Inf} C_{t-4}$
$\begin{array}{lllll}(0.28)(0.05) & (0.09) & (0.09) & (0.09)& (0.08)\end{array}$
Test for the presence of a stochastic trend. Should you have used heteroskedasticity-robust standard errors? Does the fact that you use quarterly data suggest including four lags in the above regression, or how should you determine the number of lags?
(c)To forecast the Canadian inflation rate for 2000:I, you estimate an AR(1), AR(4), and an ADL(4,1)model for the sample period 1962:I to 1999:IV. The results are as follows:
In addition, you have the following information on inflation in Canada during the four quarters of 1999 and the first quarter of 2000:
Inflation and Unemployment in Canada, First Quarter 1999 to First Quarter 2000 $\begin{array}{|c|c|c|c|c|}\hline \text { Quarter } & \begin{array}{c}\text { Unemployment } \\\text { Rate }\end{array} & \begin{array}{c}\text { Rate of } \\\text { Inflation at an }\end{array} & \begin{array}{c}\text { First Lag } \\(\text { Inf } \mathrm{t}-1)\end{array} & \begin{array}{c}\text { Change in } \\\text { Inflation }\end{array}\\&\left(\text { Urate }_{\mathrm{t}}\right) & \begin{array}{c}\text { Annual Rate } \\\left(\operatorname{Inf} f_{t}\right)\end{array} && \left(\Delta \operatorname{Inf} f_{t}\right)\\\hline 1999: I & 7.7 & 0.8 & 0.8 & 0.0 \\\hline 1999: \text { II } & 7.9 & 4.3 & 0.8 & 3.5 \\\hline 1999: \text { III } & 7.7 & 2.9 & 4.3 & -1.4 \\\hline 1999: \text { IV } & 7.0 & 1.3 & 2.9 & -1.5 \\\hline 2000: I & 6.8 & 2.1 & 1.3 & 0.8 \\\hline\end{array}$ For each of the three models, calculate the predicted inflation rate for the period 2000:I and the forecast error.
(d)Perform a test on whether or not Canadian unemployment rates Granger-cause the Canadian inflation rate.