Seasonality Lags No of observations

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abeshak sindhi

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Just wanted to clarify one thing if we keep on adding lags we keep on losing one additional no of observation?For eg if my collected data is for 40 quarters and if i run an AR1 model my n becomes 39 AR2 38 and so on?what if i run an AR1 model and seasonality is there so now if add 4th lag my no of observations goes from 40 to 36 or 39 to 35?
 
Is a degree of freedom for each independent variable you add.
For an AR(1) you use 38 df
For and AR with Lag 1 and Lag 4 you use 37 df
For an AR(4) Xt = b0 + b1Xt-1 + b2Xt-2 + b3Xt-3 + b4Xt-4 + e(t) you would use 35 df
Remember that slope coefficients estimators have n - k - 1 df, so an AR(4) like above would be 40 - 4 - 1 = 35
Also remember that the regression has k degrees of freedom (4 for AR(4))
And the whole regression has n - 1 degrees of freedom (39), which are 35 + 4 = 39
Hope this helps!
 
Ok this concept is same as Anova table where k + n-k-1=n-1 where k =no of independent variables.for AR1 and AR4 they are 2 independent variables therefore k=2 and n-k-1 =37 ?
 
abeshak sindhi wrote:
Ok this concept is same as Anova table where k + n-k-1=n-1 where k =no of independent variables.for AR1 and AR4 they are 2 independent variables therefore k=2 and n-k-1 =37 ?
Click to expand...
Exactly.
However, note that an AR4 has 4 variables. Sometimes, not all variables used, so don’t call it AR4 anymore, just AR with lag1 and lag4 (only 2 variables).
 
Harrogath wrote:
abeshak sindhi wrote:
Ok this concept is same as Anova table where k + n-k-1=n-1 where k =no of independent variables.for AR1 and AR4 they are 2 independent variables therefore k=2 and n-k-1 =37 ?
Click to expand...
Exactly.
However, note that an AR4 has 4 variables. Sometimes, not all variables used, so don’t call it AR4 anymore, just AR with lag1 and lag4 (only 2 variables).
Click to expand...
Great.Thanks for the help!!
 
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