Season Regression Model

Hello, I dont understand how schweser came up with the answer for the question below. Based on my reading to adjust for seasonality you add a lag ofthe dependent variable to the model. Couldnt A also be an answer? Give me your take on this Thanks ________________________________________________________________________ Which of the following is a seasonally adjusted model? A) Salest = b0 + b1 Sales t-1 + b2 Sales t-2 + åt. B) Salest = b1 Sales t-1+ åt. C) (Salest - Sales t-1)= b0 + b1 (Sales t-1 - Sales t-2) + b2 (Sales t-4 - Sales t-5) + åt. Your answer: A was incorrect. The correct answer was C) (Salest - Sales t-1)= b0 + b1 (Sales t-1 - Sales t-2) + b2 (Sales t-4 - Sales t-5) + åt. This model is a seasonal AR with first differencing.

A is just an AR(2) model. C incorporates a lagged difference, and a difference for 4 periods ago…hence the seasonality term. It appears the data is implicity quarterly sales. How would a two-period lagged sales term pick up on any seasonality?

note that it’s an AR(1) model with a seasonal lag for the different between period 4 and 5 so let’s drop first differencing for a moment X = b0 + b1*Y(X-1) + b2*(X-2) + b3*(X-4) This is an AR(2) model with a 4th seasonal lag Now, define X as X - (X-1), so you subtract the previous X on each term and voila, you have solution C Solution A above is AR(2) model, you *can’t* distingusih whether or not the second term is a lag because it’s the next term to come in an AR(2) model anyway,905960,905966#msg-905966