0 Differences Graph - seasonality?

[economicsstudent]

When looking at a '0 Differences' graph of correlations and partial correlations of stock market returns, when the corr and partial lines go over the thick black horizontal line, suggesting correlation, what reasons might there be for this? Seasonality might be one? Are there others?

[TomDoan]

When looking at a '0 Differences' graph of correlations and partial correlations of stock market returns, when the corr and partial lines go over the thick black horizontal line, suggesting correlation, what reasons might there be for this? Seasonality might be one? Are there others?

If they are at the short lags (particularly 1 and 2), they are typically the result of an inadequate mean model. Otherwise, they are most commonly the result of sampling error.

[economicsstudent]

could you please explain both of those reasons, inadequate mean model and sampling error?

[TomDoan]

could you please explain both of those reasons, inadequate mean model and sampling error?

If you have a series which is supposed to be white noise, but has significant correlations at short lags (like 1 and 2), that generally is due to the model having the wrong dynamics. If you don't even have a "model" for the mean, so you're just taking a fixed sample mean out, that would imply that you need at least a low order AR or MA to take care of the correlation. If you already have a low order AR or MA, but it's leaving significant correlation at the short lags, you probably need to adjust that model. For instance, if an AR(1) is "correct" an MA(1) will leave correlation like that and vice versa.

If you do 40 autocorrelations on white noise, you would expect that, due to sample error, roughly 2 (5%) of them would be significant at the 5% level, and any number between 0 and 5 wouldn't be at all unreasonable, particularly if they are at scattered lags. With a very large data set, it will generally be even more than that in practice, simply because no real world data set is going to behave exactly the way the asymptotics require.