# AR Model

How would adding more lags improve an AR Model…I’m trying to understand it conceptualy?

An easy way to see this is with a seasonal model: suppose that you’re creating an AR model for monthly sales for a toy store. There will be a big spike in sales in November and December (for Christmas), so you won’t get a good fit from an AR(1) model (only a 1-month lag), or from an AR(2) model (only 1-month and 2-month lags), or from AR(3), AR(4), . . . AR(11) models. But you’ll likely get a good fit with an AR(12) model: last year’s January sales are a good predictor of this year’s January sales, last year’s February sales are a good predictor of this year’s February sales, . . . last year’s November and December sales are good predictors of this year’s November and December sales (respectively).

An awesome explanation!

So you’re doing this to smooth out the data and make sure the residuals are not persistant, correct?

Also, in the example with monthly sales, would it be more apporopriate to use AR Model or log-linear model…Whats a good way to compare the 2 models and know which is best to use??

You’re not doing it to smooth out the data. The method is employed to accurately capture the relationship in order to have a valid model.

An AR model is appropriate when past values in a series are predictors of the current value. So, as S2000 said, last January’s sales are best for predicting this January’s sales (a past (lagged) value of the DV is useful in predicting the DV).

You might use a log-linear model if you were looking at monthly sales changing with respect to the previous (or current) month’s advertising expenditure, for example. Given \$100,000 in advertising last month, how much do we expect the sales to be this month? The idea supporting this would be that a given change in the independent variable will cause a constant percentage change in the DV (semi-elasticity).

Overall, the nature of the data and the relationships with between variables will dictate the model used (along with checking assumptions to determine if a remedy is needed).

Hope this helps!

Yup, Thanks tickersu & S2000 magician.

No problem!

I forgot to mention that you might also use a log-linear model in the event that there is heteroscedasticity in your data set. (A variance stabilizing transformation such as Ln(y) can often remedy the heteroscedasticity, depending on the data type.) However, this point is more for complete understanding than it is for preparation for the exam.

You’re quite welcome.