# autocorrelation

definition: Serial correlation (autocorrelation) means the error terms are correlated. I get that. Question: How many autocorrelations should I get from a software package display? Is it T-1? I’m looking at Schweser, book 1, page 226. There are 12 lags (autocorrelations) and 102 observations. Why is there only 12? Please tell me what I am missing. Are they just pooling a sample of 12 residuals from a population of 102?

I don’t have your book, but here’s a random guess: are these monthly returns, and are they looking to see if there’s evident seasonality?

That’s what’s frustrating, it does not say… From the book, “The correlations of the error terms from the estimation of an AR(1) model using a sample with 102 observations are presented in the following figure. Determine whether the model is correctly specified”. Then it just gives 12 autocorrelations. There is no mention of monthly returns, etc.

I’m no stats wiz (and there are plenty of posters around who are) but I stayed at a Holiday Inn last night. So I’ll give you a guess as to what’s going on, which you’ll have to confirm (or wait for a smarter poster to jump in). I think they’re questioning whether the model (AR(1)) is underpowered. If there are autocorrelations present you need to increase the model’s power/sophistication until the autocorrelations are gone. E.g. if you see high autocorrelation with the 3-mo lag, there’s quarterly seasonality, so add that variable to the model and re-test.

DH, thank you sir for your time. I think I have figured it out: per CFA text: “For seasonally unadjusted data, analysts often compute the same number of autocorrelations as there are observations in a year (ie. four for quarterly data). The number of autocorrelations computed also often depends on sample size…” I think for sake of saving space, CFAI omitted all of the autocorrelations. Most of the examples, they just show 4, even though the number of observations far exceeds that number. I’m not going waste any more time on this. I have bigger issues to figure out, like comparing and contrasting convertible securities with common stock.

When you fit autoregressive time series models you look at that plot (called a correlogram) to figure out graphically how many terms are worth putting into the model. I find those hard to use straight-up because, e.g., an AR(1) model certainly has a correlation at lag 2. There’s something better called a partial autocorrelation plot which I can read better. People who do time series analysis all the time get down the “finger prints” though and can use either.