ECO327Y5 Study Guide - Midterm Guide: F-Test, Confidence Interval, Seat Belt
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12. 1 we can reason this from equation (12. 4) because the usual ols standard error is an estimate of. When the dependent and independent variables are in level (or log) form, the ar(1) parameter, , tends to be positive in time series regression models. Further, the independent variables tend to be positive correlated, so (xt . ) which is what generally appears in (12. 4) when the {xt} do not have zero sample average tends to be positive for most t and j. With multiple explanatory variables the formulas are more complicated but have similar features. If < 0, or if the {xt} is negatively autocorrelated, the second term in the last line of (12. 4) )(xt+j could be negative, in which case the true standard deviation of is actually less than. 12. 2 this statement implies that we are still using ols to estimate the j. Ols; we are using feasible gls (without or with the equation for the first time period).
