Breush-Godfrey test for AR(q)___Understand and Correct

[Buffy Summer]

Hi Everyone,
I am running a Breush-Godfrey test for AR(q) in order to identify the lags to use in Newey (if needed). I am running the following command:

bgodfrey, lags(1,2,3,4)

the first two lags have a very high ChiSq while the last two have a very low one (below 0.1). Does that suggest an AR(3)/ AR(4)? Or since the first two lags are very high the lag 3 and lag 4 n are not relevant? How do I know when to stop in adding lags (I have daily data)? And how do I correct for AR(q)?


Thank you so much

Buffy

[Jeff Wooldridge]

The B-G test won't really tell you how many lags to include in the Newey-West standard errors. The AR(q) model implies that there is some correlation between all errors, no matter how far apart in time. The Newey-West approach ignores all correlations more than m periods apart, where m is the chosen lag. Newey-West does better against moving average type errors.

If you have lots of daily data, I would try something like 1,5, 10, 30 lags to see if the standard errors settle down. A 30 lag allows for up to a month. This may be enough, but it's an empirical question. A lag of one could be enough.

Newey-West suggested the integer part of 4*((n/100)^(2/9)), where n is the number of observations, so you might try that, too.

[Buffy Summer]

Thank you so much Dr. Wooldridge. I used several of your books during my undergraduate and my graduate school. Unfortunately we did not properly discussed time series in my class, and I am now self training myself. Would you recommend any book or online lecture/code sample?

There is a lot of confusion on how to proceed once you have time series data. Clearly we need to check for stationarity (dfuller), Serial Correlation (Breush-Godrey test-- or dwatson if AR(1)) and Heteroskedastisity (Breush-Pagan). Clearly we need to correct for serial correlation and heteroskedasticity if observed. Computing Newey-West will correct for both.

However in this scenario there is a little bit of confusion on how to use ac (to check for the degree of AR) and pac (to check for the degree of MA). These "tests" are often applied to one variable, while the Breush-Godrey tests for the AR (q) in the regression (y on x). How are these two information combined together? Someone might find that y is AR(3) and x is AR(1), but after regressing x on y the B_G test could suggest AR(20).

Thank you so much__Buffy

[Jeff Wooldridge]

It's true you want to guard against spurious regression, so if you think y(t) or some x(t) have unit roots then you should check. Looking at the AR(1) coefficient of the residuals then allows you to determine whether there is cointegration [if y(t) and some x(t) have unit roots]. But the AR(q) tests don't say much about the Newey-West standard error. And the degree of autocorrelation in the errors has nothing to do with how much is in x(t), as you seem to imply. Use the Newey-West rule of thumb and report that's what you are doing. JW

[Chiara Giuliani]

Thank you for your help!

[Jeff Wooldridge]

Oh, are you no longer the vampire slayer?! :-)