Question

Explain what assumptions are needed in order for the OLS estimator to be unbiased in a time series environment.

Answer 1

The assumptions required for the OLS estimator to be unbiased in a time series environment are discussed as follows:

-- Assumption of Linearity: When the model is linear to a data that is non-linearly related, the model will be unreliable because it is likely to be incorrect.

-- Assumption of Homoscedasticity : When errors are heteroscedastic then it will be hard to trust the OLS estimation standard errors. Thus the confidence intervals will be either too wide or too narrow. Moreover, violation of this assumption is likely to provide too much weight on certain portion (subsection) of the data. Thus it is vital to fix this if error variances are not constant.

-- Assumption of Independence/No Autocorrelation: This assumption has a tendency to be violated in time series regression models and, thus intuition states that there is no requirement to investigate it. But it can still be checked for autocorrelation by looking the residual time series plot.

-- Assumption of Normality of Errors: When error terms are not normal, then the OLS estimates standard errors will not be reliable, which state that the confidence intervals would be too wide or narrow.