Question

Why is not possible to employ OLS to estimate the parameters of a non stationary stochastic process?

Answer 1

Answer. Time series that diverge away from their mean over time are said to be non-stationary. Therefore, the classical estimation of variables with this relationship most times gives misleading inferences or spurious regression.
A non-stationary time series is a stochastic process with unit roots or structural breaks. However, unit roots are major sources of non-stationarity. The presence of a unit root implies that a time series under consideration is non-stationary while the absence of it entails that a time series is stationary. This depicts that unit root is one of the sources of non-stationarity. A non-stationary stochastic process could be Trend Stationary (deterministic) Process (TSP) or Difference Stationary Process (DSP).
It should be made clear that if a time series is TSP, but treated as DSP, this is called over-differencing. On the other hand, if a time series is DSP, but treated as TSP; this is referred to as under-differencing. The implications of these types of specification error can be serious, depending on how the serial correlation properties of the resulting error terms are handled. However, it has been observed that most time series are DSP rather than TSP. Therefore, when such non-stationary time series (DSP) are used in estimation of an econometric model, the Ordinary Least Square (OLS) traditional diagnostic statistics for evaluation of the validity of the model estimates such as, coefficient of determination (R2), Fisher’s Ratio(F Statistic), Durbin-Watson(DW-Stat), t-statistic etc. become highly misleading and unreliable in terms of forecast and policy. In such series, the mean, variance, covariance and autocorrelation functions change overtime and affect the long run development of the series. The presence of unit root in these series leads to the violation of assumptions of constant means and variances of OLS.