# stationarity in one period regression model

Wilson fits a regression model for the Albitania data to use in the simulation. From the results, she determines that the stock market index return for Albitania should be expressed as

R = –0.11 + 0.23 GDP + 3.85 UNEMP + 5.10 BOND – 19.60 INF

where

R = return on the Albitania stock market index

GDP = one-year change in the GDP

UNEMP = unemployment rate

BOND = return on the 10-year government bond

INF = inflation rate

Yang tells Wilson that their analysis is not quite complete because they have failed to address several additional areas:

1. They may need to add a decision tree analysis of non-sequential risk.
2. The statistical distributions chosen for the inputs may not be stationary.
3. The error term in the regression may not have a mean of zero.

With respect to Yang’s final concerns, the most important issue to consider is: statement 2 is the correct answer. justification is "Even when the data fit a statistical distribution in one time period, non-stationarity may cause the parameter of the distribution to change in subsequent periods… 3 is incorrect because regression forces the mean of the error term to zero by definition.

this confused me for 2 reasons

1. i thought stationarity is a problem associated with time series. what does it mean by “non-stationarity may cause the parameter of the distribution to change in subsequent periods”- this isnt something i have come across

2. “3 is incorrect because regression forces the mean of the error term to zero by definition.”- this is true if you are modeling a linear regression but what if the parameters are non-linear then this wouldn’t hold right? i re-read the question on this again-am I supposed to interpret that this is not an issue b/c the graphs look linear?

Assume you do a regression of the nasdaq price against time during the dot com crash. You may find that the nasdaq price is strongly negatively correlated with the passage of time (negative, large coefficient in your regression that may even be highly significant using e.g. t-tests). That finding itself may not be stationary and if you redo your analysis later you may find that there is a totally different relation between passage of time and nasdaq price (and hence a different coefficient).

I don’t think their reasoning or wording is particularly good. The mean error equal to zero assumption can often be violated due to misspecification.

Unless I am missing something they’re trying to say.