In the curriculum, we are given the example with AR(1), s.e. = 1/sqrt(T) t-stat = cov(t, t-k) / s.e with (T-2) degrees of freedom (Ref: Schweser B1 p.231, CFAI V1 p.376) I would like to confirm the DF to be used for the cases AR(2) … AR(n). I’m trying to compile the checklist for the DFs covered in L2, here’s my starting list: 1) Simple Regression - coefficient t-test: df = n-2 - F-stat: df = (2, n-2) 2) Multiple Regression - coefficient t-test: df = n-k-1 - F-stat: df = (k, n-k-1) 3) t-test for correlation coefficient: - t-test: df = n-2 4) Heteroskedasticity test - BP chi-square test: df = # of indep variables 5) Autocorrelation Test in AR - (question above) Appreciate any comments from anyone to make it complete!
- Simple Regression - coefficient t-test: df = n-2 - F-stat: df = (2, n-2) I think for F-stat: df=(1,n-2) cause the numerator df should be equal to the number of indenpendent variables (which is 1 in simple linear regression) 2) For Auto-correlation, it is (number of obervations-number of lags-2). So if you have 40 oberservations and AR (1) model, than 1 oberservation is lost because of the lag (39). So df=39-2=37. therefore, for AR(2), it should be (40-2-2=36)
oh~ thanks. I made a mistake in (1). for auto-correlation, I double checked Schweser and CFAI and they both used (n-2) in their examples. Could you point me to more reference for this formula: df = (number of obervations-number of lags-2) I think I definitely missed sth here …
Also the df for simple linear regression is actually n-k-1, but since k=1 (there is one variable) its also n-2. For Fstat DF is always k on the top and n-k-1 on the bottom or Fstat(k, n-k-1). You can follow this into the anova table for MSSr and MSSe. It looks as though the curriclum uses T as k and K as n. is you see what I mean. Good idea summarising all the different ones, it can get really confusing.
any reference for the following? Thx! df = (number of obervations-number of lags-2)
krykry, the formula i mentioned; i havn’t read it in this form anywhere in schewer. However, the numbers I have mentioned are from schewer’s example in the Time series chapter where the test on significance of Auto-corelations is mentioned. Sorry, i do not have my book with me now…so i cannot tell you what page number this is…but this is definitely in the time series section of Schwser