I encountered an issue not addressed in Elan’s guide. See practice question 17 of the Time Series Analysis. The model is log first-differenced The t-stat for the Lag1 is -0.7683 which is not outside the range of the t-critical 2.02 Hence I’d expect the model to not be correctly specified. But the solution skips that issue. In the readings, on page 195 an similar example is covered but the t-stats for the independent variables are all outside the t-critical range and hence significantly different from 0. So my question is, what to do in the case when a log first-differenced model has a t-stat on one of its independent variable that is not significantly different from 0? Should I simply conclude that the independent variable is 0 and move on? Thanks for shedding light on this issue.
I belive if you have any of the lags significantly different from zero that means that that AR model of particular order ehibits serial correlation and should re specify it on a new order. So if your first model is AR(1) and one of the lag variable is signifcantly different from zero that means that the particular lag has serial correlation and you should re run the model on AR(2) and re examine the lags until none of them exhibit significance from zero
Sorry I wasn’t clear, The autocorrelations of the residulas from the AR(1) are not significantly different from zero, so there is no serial correlation. It’s the Lag1 as an independent variable that is not significantly different from zero and that’s bothering me.
I gotcha, I believe then, that while you can be confident in the standar error of the slope estimate since there is no serial correlation you cannot say that the slope has any meaninful explanatory value.
I see, thanks.