# What is lag length?

I've been looking up all across the internet to see what "lag length" is.

I want to perform an Engle Granger - Augmented Dickey Fuller test, but for ADF, it always asks to specifiy a lag. It seems to me that whenever I look up lag length, most people just have trouble determining what it should be.

What is the lag length? What does it mean?

• By ADF, do you mean Augmented Dickey–Fuller? What do you mean by EG? – Avraham Jun 18 '14 at 16:10
• The EG-ADF test. EG just stands for Engle Granger. By ADF I do mean Augmented Dickey Fuller – whuan0319 Jun 18 '14 at 18:16
• This is a very valid question to ask. According to eurequa.univ-paris1.fr/membres/Ahamada/cours/nsss.pdf An important practical issue for the implementation of the ADF test is the speciﬁcation of the lag length p. • If p is too small then the remaining serial correlation in the errors will bias the test. • If p is too large then the power of the test will suﬀer. • Monte Carlo experiments suggest it is better to error on the side of including too many lags. – forecaster Jun 18 '14 at 19:21

## 2 Answers

The lag length is how many terms back down the AR process you want to test for serial correlation. Is checking the prior one alone enough, or do you need to check in groups of 3, 4, or more. This page synopsizes the trade-offs for more or fewer lags.

• Hey thanks. So say I am using data on say, bonds whose time scale is by minutes. If i have say, 300 or so data points (so 300 minutes), do you think checking the prior one is enough? Also would you happen to know of my previous post about SE? stats.stackexchange.com/posts/103868/revisions – whuan0319 Jun 18 '14 at 19:03
• I don't have enough expertise in either fixed income asset prices or time series to give you a good answer on that, other than to say that 1) the link I brought in the answer implies to err on the side of more lag than less and 2) unless you're a high-frequency trader who makes or loses money in intervals measured in seconds, why would you need to be so granular? – Avraham Jun 18 '14 at 19:08
• I am actually working for a high-frequency trader who is asking this of me and has given me data in minutes. Would you happen to know how lag length affects the t-stat? If so, do you know how it does mathematically? – whuan0319 Jun 18 '14 at 19:51
• Well, then your request for data scaled in minutes makes sense. I don't know how the size of the lag-length affects the t-stat; I'm sorry. I'd suggest starting with the paper that I and forecaster quoted, and searching from there. Perhaps this is worth a new question ("how does lag affect t-stat in ADF") – Avraham Jun 18 '14 at 19:55

Besides my comment above, according to this the maximum lag length can be chosen by rule of a thumb formula:

$$P_{max}=[12.(\frac{T}{100})^{1/4}]$$

See page 121 in the above referenced link:

An important practical issue for the implementation of the ADF test is the speciﬁcation of the lag length p. If p is too small then the remaining serial correlation in the errors will bias the test. If p is too large then the power of the test will suﬀer. Ng and Perron (1995) suggest the following data dependent lag length selection procedure that results in stable size of the test and minimal power loss. First, set an upper bound pmax for p. Next, estimate the ADF test regression with p = pmax. If the absolute value of the t-statistic for testing the signiﬁcance of the last lagged diﬀerence is greater than 1.6 then set p = pmax and perform the unit root test. Otherwise, reduce the lag length by one and repeat the process. A useful rule of thumb for determining pmax, suggested by Schwert(1989), is

$$P_{max}=[12.(\frac{T}{100})^{1/4}]$$