Time Series Analysis - AR Model

hsnyong · May 18, 2014, 2:12pm

Dear all, please advise on points below. Thanks in advance.

An example of AR(2), AR(3) and AR(4) model. I presume we can’t just call it a AR(4) just because the equation has a lag 4 term.
F test, Null hypothesis being R square = zero?

Iconoclasts · May 18, 2014, 3:33pm

Sure we can. AR(4) = 4 lags included.
Not really (even though I understand were you are coming from). R2 is an descriptive statistic and not a theoretical parameter. Generally we only test hypothesis about theoretically expected parameters and not descriptive statistics. Therefore, in the F test is a test of the H0 that all the theoretical parameters included in the regression (like B1, B2, B3 or so) are, jointly, zero versus the alternative hypothesis that they are not.

S2000magician · May 19, 2014, 4:20am

Specifically, we’re testing that all _ slopes _ are zero, not all regression coefficients (which would also include the intercept).

S2000magician · May 19, 2014, 4:23am

Do you mean the F-test in multiple regression, or something (as the title of the thread suggests) involving AR models in time series analysis?

tickersu · May 19, 2014, 9:15pm

S2000magician:

Iconoclasts:

hsnyong:

Dear all, please advise on points below. Thanks in advance.

An example of AR(2), AR(3) and AR(4) model. I presume we can’t just call it a AR(4) just because the equation has a lag 4 term.

F test, Null hypothesis being R square = zero?

Sure we can. AR(4) = 4 lags included.

Not really (even though I understand were you are coming from). R2 is an descriptive statistic and not a theoretical parameter. Generally we only test hypothesis about theoretically expected parameters and not descriptive statistics. Therefore, in the F test is a test of the H0 that all the theoretical parameters included in the regression (like B1, B2, B3 or so) are, jointly, zero versus the alternative hypothesis that they are not.

Specifically, we’re testing that all _ slopes _ are zero, not all regression coefficients (which would also include the intercept).

I would be careful in stating the test is for all slopes (in a techinal sense). Regressions are often run to fit a model with curvature (as long as the model is linear in its parameters), meaning that no slopes are estimated, only rates of curvature and shift parameters. You are right with the catch, though. It is safe to say that global (overall model utility) F-test does not involve testing the intercept, B0, but does involve every other term.

S2000magician · May 19, 2014, 9:22pm

tickersu:

S2000magician:

Iconoclasts:

hsnyong:

Dear all, please advise on points below. Thanks in advance.

An example of AR(2), AR(3) and AR(4) model. I presume we can’t just call it a AR(4) just because the equation has a lag 4 term.

F test, Null hypothesis being R square = zero?

Sure we can. AR(4) = 4 lags included.

Not really (even though I understand were you are coming from). R2 is an descriptive statistic and not a theoretical parameter. Generally we only test hypothesis about theoretically expected parameters and not descriptive statistics. Therefore, in the F test is a test of the H0 that all the theoretical parameters included in the regression (like B1, B2, B3 or so) are, jointly, zero versus the alternative hypothesis that they are not.

Specifically, we’re testing that all _ slopes _ are zero, not all regression coefficients (which would also include the intercept).

I would be careful in stating the test is for all slopes (in a techinal sense). Regressions are often run to fit a model with curvature (as long as the model is linear in its parameters), meaning that no slopes are estimated, only rates of curvature and shift parameters. You are right with the catch, though. It is safe to say that global (overall model utility) F-test does not involve testing the intercept, B0, but does involve every other term.

I was confining my answer to the CFA curriculum, in which we do only multiple _ linear _ regression. For nonlinear regression, you’re correct that it’s not slopes per se.

mission2014 · May 19, 2014, 9:26pm

F-Statistic: H_0: All slope coefficients = 0 H_a: At least one slope coefficient != 0

tickersu · May 19, 2014, 9:53pm

S2000magician:

tickersu:

S2000magician:

Iconoclasts:

hsnyong:

Dear all, please advise on points below. Thanks in advance.

An example of AR(2), AR(3) and AR(4) model. I presume we can’t just call it a AR(4) just because the equation has a lag 4 term.

F test, Null hypothesis being R square = zero?

Sure we can. AR(4) = 4 lags included.

Not really (even though I understand were you are coming from). R2 is an descriptive statistic and not a theoretical parameter. Generally we only test hypothesis about theoretically expected parameters and not descriptive statistics. Therefore, in the F test is a test of the H0 that all the theoretical parameters included in the regression (like B1, B2, B3 or so) are, jointly, zero versus the alternative hypothesis that they are not.

Specifically, we’re testing that all _ slopes _ are zero, not all regression coefficients (which would also include the intercept).

I would be careful in stating the test is for all slopes (in a techinal sense). Regressions are often run to fit a model with curvature (as long as the model is linear in its parameters), meaning that no slopes are estimated, only rates of curvature and shift parameters. You are right with the catch, though. It is safe to say that global (overall model utility) F-test does not involve testing the intercept, B0, but does involve every other term.

I was confining my answer to the CFA curriculum, in which we do only multiple _ linear _ regression. For nonlinear regression, you’re correct that it’s not slopes per se.

Ah, yeah that makes sense! I wasn’t aware (just registered for the first time for L1) that the CFAI didn’t require knowledge beyond a linear estimation. Thanks for clarifying!