# Autoregressive model steps

Can someone pls explain what is difference between A and B ? " Q:The procedure for determining the structure of an autoregressive model is: A) estimate an autoregressive model (for example, an AR(1) model), calculate the autocorrelations for the model’s residuals, test whether the autocorrelations are different from zero, and add an AR lag for each significant autocorrelation. B) estimate an autoregressive model (e.g., an AR(1) model), calculate the autocorrelations for the model’s residuals, test whether the autocorrelations are different from zero, and revise the model if there are significant autocorrelations. C) test autocorrelations of the residuals for a simple trend model, and specify the number of significant lags. Your answer: A was incorrect. The correct answer was B) estimate an autoregressive model (e.g., an AR(1) model), calculate the autocorrelations for the model’s residuals, test whether the autocorrelations are different from zero, and revise the model if there are significant autocorrelations. The procedure is iterative: continually test for autocorrelations in the residuals and stop adding lags when the autocorrelations of the residuals are eliminated. Even if several of the residuals exhibit autocorrelation, the lags should be added one at a time." It seems to me that the explanation provided by shweser is indeed for answer A . What am i missing? Thanks

Anyone?

If you run an AR model, and let’s suppose that residual autocorrelation is significant for Lags 1, 2 and 3. Choice A would imply that we simply add more variables to the model (curiously in this example, Lag 1 was already included and yet it’s autocorrelation is significant) and be done with it. For choice B, we would add one more lag (and make it AR(2)) and recheck autocorrelations of residuals. If none is significant, we stop. Otherwise, we would continue modifying the model until it captures all of the time series properties (relationships) in the data.

I agree with AMCC. B says that you need to add another term. A tells you to add many terms some of which might be unnecessary. Rule of thumb: use as few parameters as possible.

I don’t know that B is even explicitly saying to add just one other term (like AR1 to AR2), i think it’s a little more vague and all encompassing; to me it says “if there’s an autocorrelation, fix the model” which isn’t terribly specific, but fixing it does sound like a good idea. Incidently, going from AR(X) to AR(X+1) would be how you’d do it (and then you’d check again and see if serial correlation is still a problem). A is definitely on the excessive side; if you have 5 autocorrelations, it’s a little crazy to go from AR(X) to AR(X+5). I don’t really like this question, tbh. it’s the type of thing where you can know the concept really well, and still get lost in the wording.

magicskyfairy, presense of statistically significant autocorrelations indicates an issue with the model. Just as you said, something needs to be done. One way of doing that would be examining PACF though I think it’s outside of the scope of the CFA curriculum.

A suggests that by adding a lag, you are removing auto correlation. You cannot fix a problem by just adding something (except glue) B suggests you revise it due to autocorrelation (if so).

I think the fault in A is “add an AR lag for EACH significant autocorrelation.” This means that if we have 3 significant autocorrelations we (as per the answer) shall add 3 lags. This is wrong. You should add one lag at a time and check the autocorrelations again. If significance remains, you continue the same process.