# Autoregressive Model

This is confusing me: In AR model what determines the order; the lags or the number of independant variables?

i guess both as the lags are the independent variables

I think its just the number of independent variables. AR(1) will have one independent variable and AR§ will have p number of independent variables please correct me

a lag acts as an independent variable x (t) = b0 + b1x(t-1) + e The lagged variable x(t-1) is an independent variable

Lags are only independent if no serial correlation

kochunni69 Wrote: ------------------------------------------------------- > I think its just the number of independent > variables. AR(1) will have one independent > variable and AR§ will have p number of > independent variables > > please correct me I had the same question because one of the books mentioned that a AR model x (t) = b0 + b1x(t-1) + b2x(t-4) +e was AR(1) My interpretation from this website is that the AR(“number”) is the number of ind vars of immediately preceding periods, not just the total number of independent vars. http://economics.about.com/cs/economicsglossary/g/ar.htm So A(3) would have the three immediately preceding periods as ind vars, BUT you could have and AR(1) with three ind vars if you used t-1, t-3 and t-4…that is, if you skipped past t-2… Hope this helps

mbc Wrote: ------------------------------------------------------- > kochunni69 Wrote: > -------------------------------------------------- > ----- > > I think its just the number of independent > > variables. AR(1) will have one independent > > variable and AR§ will have p number of > > independent variables > > > > please correct me > > > I had the same question because one of the books > mentioned that a AR model x (t) = b0 + b1x(t-1) + > b2x(t-4) +e was AR(1) > > My interpretation from this website is that the > AR(“number”) is the number of ind vars of > immediately preceding periods, not just the total > number of independent vars. > > > > http://economics.about.com/cs/economicsglossary/g/ > ar.htm > > So A(3) would have the three immediately preceding > periods as ind vars, BUT you could have and AR(1) > with three ind vars if you used t-1, t-3 and > t-4…that is, if you skipped past t-2… > > Hope this helps Was confused by this to. according to the book, that is an AR(1) model with a seasonal lag which is not an AR(2) model. Can someone explain!!!

This is great my friend. This is exacly what I was looking for. Thanks a lot

mcf Wrote: ------------------------------------------------------- > mbc Wrote: > -------------------------------------------------- > ----- > > kochunni69 Wrote: > > > -------------------------------------------------- > > > ----- > > > I think its just the number of independent > > > variables. AR(1) will have one independent > > > variable and AR§ will have p number of > > > independent variables > > > > > > please correct me > > > > > > I had the same question because one of the > books > > mentioned that a AR model x (t) = b0 + b1x(t-1) > + > > b2x(t-4) +e was AR(1) > > > > My interpretation from this website is that the > > AR(“number”) is the number of ind vars of > > immediately preceding periods, not just the > total > > number of independent vars. > > > > > > > > > http://economics.about.com/cs/economicsglossary/g/ > > > ar.htm > > > > So A(3) would have the three immediately > preceding > > periods as ind vars, BUT you could have and > AR(1) > > with three ind vars if you used t-1, t-3 and > > t-4…that is, if you skipped past t-2… > > > > Hope this helps > > Was confused by this to. according to the book, > that is an AR(1) model with a seasonal lag which > is not an AR(2) model. Can someone explain!!! Seasonal Lags are an exception to the AR(#) convention. Do not include them if you are counting how many lags an AR model has. For example if a monthly model is xt-1 + xt-2 +xt-12 it is an AR(2) model. Excuse the poor notation.

So are we saying that the actual lags needs to be sequential. That is xt-1 + xt-2 + xt-5 + xt-12 would actually be an AR(2) model with 2 seasonal lags?

mcf Wrote: ------------------------------------------------------- > mbc Wrote: > -------------------------------------------------- > ----- > > kochunni69 Wrote: > > > -------------------------------------------------- > > > ----- > > > I think its just the number of independent > > > variables. AR(1) will have one independent > > > variable and AR§ will have p number of > > > independent variables > > > > > > please correct me > > > > > > I had the same question because one of the > books > > mentioned that a AR model x (t) = b0 + b1x(t-1) > + > > b2x(t-4) +e was AR(1) > > > > My interpretation from this website is that the > > AR(“number”) is the number of ind vars of > > immediately preceding periods, not just the > total > > number of independent vars. > > > > > > > > > http://economics.about.com/cs/economicsglossary/g/ > > > ar.htm > > > > So A(3) would have the three immediately > preceding > > periods as ind vars, BUT you could have and > AR(1) > > with three ind vars if you used t-1, t-3 and > > t-4…that is, if you skipped past t-2… > > > > Hope this helps > > Was confused by this to. according to the book, > that is an AR(1) model with a seasonal lag which > is not an AR(2) model. Can someone explain!!! I know someone can word this better… the AR(number) is the number of consecutive periods going back in time …t minus 1, 2, 3, 4, 5 the number stops “counting” when you skip a period going back so t minus 1,2,3, 5,6,7,9… would be AR(3)

I think this statement is correct, rest are all BS I think its just the number of independent variables. AR(1) will have one independent variable and AR§ will have p number of independent variables please correct me

This reminds me: Do you lose an observation for each lag you add? Like if you have 25 observations, and an AR(1) with a 4th quarter lag, do you now have 23 observations?