At first, i thought i had a clear understanding on serial correlation & seasonality. But now, these two confuses me. What is difference between these two? the way to detect them is the same? use t-value? And if serial correlation is found in AR(1) model, does it mean that this AR(1) model has seasonality problem as well?. So need to add one more lag to improve it? then AR(1) will become AR(2); AR(3)…? Right? Thank you to everyone. Cheer up.

Serial correlation is when error terms are not independent, meaning the previous residual/error term will give some sort of prediction for the next error term. Positive serial correlation means the error term in the next period will likely be positive if the current error term is positive. Negative serial correlation means the error term in the next period will likely be negative (positive) if the current error term is positive (negative). It really means that a predicted value will have a correlation with the previous predicted value, so we should try using an autoregressive model for our predictions. You use autocorrelation tests to see if autocorrelation is present, specifically the Durbin-Watson test. If serial correlation exists in the AR(1) model, it is mispecified or you should add more lags, test for autocorrelation again, and repeat until there are no more statistically significant correlations remaining

How about seasonality? My confuse is the difference or connection between autocorrelation and seasonality. Really appreciate ur great comment.

Seasonality simply refers to a situation where the correlation seems to occur at a specific lag (usually 4th lag for quarterly data, or 12th lag for monthly data). Seasonality is a subset of autocorrelation. Autocorrelation is a generalized term referring to the presence of correlation in errors terms irrespective of which term is correlated with which.

But you don’t use the Durbin-Watson method for autoregressive models I don’t think. You use: t-statistic=[correlation(error at time t, error at time t-1)]/(1/squareroot of t), with t-2 degrees of freedom.

Right rellison, sorry I didn’t mean to mislead you, I meant that Durbin-Watson is used to test autocorrelation in a normal time series model (I placed it in the wrong place in the paragraph)

Serial Correlation & Seasonality are two totally different concepts. Serial correlations occurs when the residual errors are correlated with each other. I.E. errors in one time period affect the errors in other time periods. This is going to affect your standard errors, thus t-values and p-values. Seasonality - Think of Christmas, during the holidays people buy a ton of stuff, more then any other month. so you have to adjust the pooling of your data to adjust for this holiday effect, otherwise the sample data is incorrect leading to incorrect estimated coefficients. How would you correct for seasonality?

Put a lag on that b@tch!