Running time-series regressions on a dataset with large gaps: is it legitimate?
| I would like to run a simple time-series regression, to estimate the sensitivity of my dependent variable to a set of explanatory variables. |
However, instead of running the regression on the entire time-series, I would like to running it only over specific time periods, all stacked together as one continuous dataset. For example, a time-series of stock returns could be subdivided into a bull market subset and a bear market subset. I would like to run the regression over bull-market periods only, or bear market periods only.
The issue is that these market conditions (regimes) are discontinuous. In other words, you have a time period of bull market, followed by one of bear market, then bull, then bear,... The discontinuity between two bull market periods or two bear periods could be several years.
Is it legitimate to stack all the subsets of the same regime, e.g. bull, and run the regression? The purpose is to get a regime-specific sensitivity to the explanatory variables.
Re: Running time-series regressions on a dataset with large gaps: is it legitimate?
The question you should first answer is if the response variable(s) are continuous. If this is the case the predictors can be of any kind (continuous, ordinal, categorical etc).
If you want to run a conditional regression, then you can absolutely do this (and do many advanced models particularly in SAS).
If there are discontinuities at the boundaries of each season (which I think is what you are concerned about) where prices "jump" then you can add regression terms to your model that factor in this discontinuity. All you have to do is add an extra term in your regression.
The term is typically something like (x-a)+ where it equals 0 if x < a and 1 if x >= a. If you add these kinds of terms you can adjust for the discontinuities or "jumps" between seasons. Alternatively you can use the season directly as an ordinal variable.