A very important topic… Regression model problems.
There are many regression problem that are hard to conceptualize. Lets start with the simpler ones:
The easiest is definitely Heteroskedasticity where the standard errors increase as the dependant variable X increase. This cause the small X value to have small errors but biggerX value to have large error. Thus model become invalid as time series becomes bigger. Use Breush-Pagen to test (have no clue of the formula…)
Autocorrelation or also serial correlation/ lagged correlation: Patterns within a linear regression lines which causes additional errors. Use Durbin-Watson to test If DW = 2 then no problem, if DW is higher than 2, the standard error is overstated if lesser than 2, standard deviation is understated. Correct with Hansen Method.
Multicollinearity : Only applicable to multiple regression. High correlation between X. High R Square so indicate a nice correlation but, F stat and T stat are very low thus making the whole equation insignificant (F stat) or the regression insignificant (T stat). Solution would be to decrease a few regression parameters (Xs).
Cointegration : Tested on the CFAI 12AM and apparantly some scientist called Engle-Granger found the solution. (have no clue what this is). Dont remeber seeing this in Schweser12 or Stalla 2011.
Problem with non-linear models :
Covariance stationary : VAR is constant across time (isnt this a good thing(, perform Dickey fuller test.
Unit root : what the hell is that anyways?