# Standard error for rolling regression

I am reading this paper: "The price of sin: the effect of social norms on market"

In this paper, on the top of page 29:

A reports the average coefficients obtained from the time-series regressions of a portfolio (SIN–COMP) that is long SIN (the monthly return for an equal-weighted portfolio of sin stocks—alcohol, gaming, and tobacco) and short COMP (the monthly return for an equal-weighted portfolio of comparable stocks) on a host of well-known factors. Each regression is estimated using a 36-month window of data for the period of 1965–2006 as well as for the period of 1926–2006.

Then it reports the following:

                  ALPHA    MKTPREM
SIN-COMP         0.0025     0.0060
(0.0014)   (0.0399)


The regression is basically

Sin-Comp = alpha + beta x MKTPREM


with rolling 3-year window.

I interpret the rolling 3 year window as rolling periods: Jan 1965 - Dec 1967, Feb 1965 - Jan 1968, Mar 1965 - Feb 1969 (rather than distinct 3 year window, else why wouldn't you say we divide the data into distinct 3 year windows and perform a regression for each of this period?)

Each regression was calculated with Newey-West standard error. The coefficients are averaged to obtain the mean, but how is the standard error calculated? Surely, it must be wrong just to calculate the standard error of these (highly correlated) coefficients and calculate t-statistics using these? However, I do not see how else it can be calculated?

This just seems like very bad statistics.

Is there a way of calculating significance for rolling window regressions? Is there any literature on this?

(The only software package which calculate rolling regression seems to be pandas in Python, which is now deprecated and not replaced in a statistical module)

• I don't have a copy next to me, but moving ols is covered in Greene, Econometrics. – user27182 Aug 27 '17 at 0:17
• @user27182, I did a quick search for "moving" and "rolling" in Greene but did not find rolling windows regression (only MA, ARMA, ARIMA and the like whenever the acronym is spelled fully; there was nothing for "rolling", really). Perhaps I went too fast, I don't know. – Richard Hardy Aug 27 '17 at 8:16
• thanks guys, really appreciate this. I will check myself. the thing is, I did some googling and found nothing. (I would have assumed if it is something in a standard textbook, I would have been able to find traces of this on Google.) – Lost1 Aug 27 '17 at 11:12