《计量经济学导论》Chapter 11.pptVIP

Chapter 11 ;The assumptions used so far seem to be too restricitive Strict exogeneity, homoscedasticity, and no serial correlation are very demanding requirements, especially in the time series context Statistical inference rests on the validity of the normality assumption Much weaker assumptions are needed if the sample size is large A key requirement for large sample analysis of time series is that the time series in question are stationary and weakly dependent Stationary time series Loosely speaking, a time series is stationary if its stochastic properties and its temporal dependence structure do not change over time;Stationary stochastic processes Covariance stationary processes;Weakly dependent time series Discussion of the weak dependence property An implication of weak dependence is that the correlation between , and must converge to zero if grows to infinity For the LLN and the CLT to hold, the individual observations must not be too strongly related to each other; in particular their relation must become weaker (and this fast enough) the farther they are apart Note that a series may be nonstationary but weakly dependent;Examples for weakly dependent time series Moving average process of order one (MA(1)) Autoregressive process of order one (AR(1));Asymptotic properties of OLS Assumption TS.1‘ (Linear in parameters) Same as assumption TS.1 but now the dependent and independent variables are assumed to be stationary and weakly dependent Assumption TS.2‘ (No perfect collinearity) Same as assumption TS.2 Assumption TS.3‘ (Zero conditional mean) Now the explanatory variables are assumed to be only contempo-raneously exogenous rather than strictly exogenous, i.e.;Theorem 11.1 (Consistency of OLS) Why is it important to relax the strict exogeneity assumption? Strict exogeneity is a serious restriction beause it rules out all kinds of dynamic relationships between explanatory variables and the error term In particular, it rules out feedba