From the book, it says nonstationarity means the mean and variance are not constant through time. I understand that a changing variance would cause heteroskedasticity, but how is changing mean bad? All linear regression models with a non-zero slope mean that the mean is changing, how come this is not acceptable?
Thank you!
Changing mean is not bad. Means that do not lead to mean reversion are a problem. Non stationarity is exact same that.
When the mean is changing, some statistical tests cannot be applied.
Bill, that does not solve his predicament. OP compares the Lin. Regression slope (beta) with stationarity.
Hi! Does this mean that the concept of stationarity or covariance stationarity only applies to autoregressive time series models and when regressing 2-time series together, but does not apply to normal linear regression models or linear trend models?
The mean has to be stationary. Be it any time series. Stationary mean does not necessarily mean a constant value. If you apply moving average to a series of data points the means do keep on changing but in a systematic defineable manner… around which a normal distribution can be thought of and thus the forecasting becomes easy. Of course longer the time period smoother the results.
We also need the variance to hold the same property. Both of them put together lend to covariance stationarity and mean reverting time series. Without this it will be impossible to construct the Line of regression.
Violation leads to a series generating Random walk which of course also defies the property of unit root. In fact the the biggest question then becomes to estimate what part of data can be termed stationary , where is the boundary ( if any) and can we distinctly identify the non stationary time series. If yes, then this whole dataset is still useful to the practitioner.
I invite Magician’s views as well as I believe he may correct if there are conceptual error in my narrative.