But I’ll do it anyway. Does autocorrelation (or serial correlation, is it really always the same?) automatically mean the independent variable is also correlated with the error term, because the error term is a product of the independent variable in the first place? I haven’t found a single statistics textbook which explicitly states this, but that is the way I keep telling it to myself. Maybe it is so obvious from the formulas, but I was never great with formulas. Please, help me to find some sleep again…
from what I know, autocorrelation and serial correlation are the same. Autocorrelation means correlation among the error terms. Multicollinearity means correlation betn. the independent variables.
Hmm…put another way: does autocorrelation inevitably lead to the the independent variable being correlated with the error term, which is a violation of the linear regression assumptions? Related to that, Schweser says this is a regression assumption violation, whereas in, my opinion, I cannot find this stated explicitly as a regression violation in the CFAI literature.
No, not always. When the independent term is a lag of the dependent variable, then what you said is possible. I remember reading something similar in the CFAI text. I would advise you to open that bit and read it.
It is important to note that there are different assumptions for time series v. cross sectional regressions. Many are overlapping assumtpions but some are type specifc. Autocorrelation and serial correlation are only present in time series regressions. This stuff is pure econometrics, thats the type of textbook you should check out if you want to learn more. My guess is this stuff will not be in a general stats book
So: 1) if we have a cross-sectional regression, the violation that the independent variable is correlated with the error term is probably irrelevant/not existent. 2) if we have a time series regression where we regress a variable against its lagged value, the above violation would be very likely and we have to test for it. 3) if we have a time series where we regress a variable against another variable, the above violation could be there, but it could be not, and we have to test for it. Testing for serial correlation we obviously use Durbin Watson, but how do we test for correlation between independent variable and error term? Sorry for being so stubborn…just have to understand this.
the 3 violations level 2 deal with are: 1. heteros…: correlation between VARIANCE of error term and independent variable 2. autocorrelation: correlation between the error terms 3. multico…: correlation between independent variables So, the correlation between error term and independent variable is not my business.
Ok, since nobody is really concerned about this, this will be my last post. Schweser explicitly states that one of the assumptions is “The independent variable is uncorrelated with the residuals.” And it doesn’t mention that it refers only to the variance between them… From Q-Bank: Session 3 | Reading 11 | LOS e, (Part 1) CFA Institute Area 3: Quantitative Analysis Session 3: Investment Tools: Quantitative Methods for Valuation Reading 11: Correlation and Regression LOS e, (Part 1): Explain the assumptions underlying linear regression. LOS Explanation A linear relationship exists between the dependent and independent variable. The independent variable is uncorrelated with the residuals. The expected value of the residual term is zero. The variance of the residual term is constant for all observations. The residual term is independently distributed; that is, the residual for one observation is not correlated with that of another observation. The residual term is normally distributed.
Man, if you have started looking at ‘out of syllabus’ stuff like this: correlation between error term and independent variable, then I am assuming you are already good with Serial correlation/autocorrelation, multicollearity, heteroskadicity, Breusch Pagan , Durban Watson, Chi-Squares and tonnes of other concepts in SS3???
You can never be good enough with the concepts…and this daliy reminder to me comes from survived pain. Anyway, there is a little nasty footnote in CFAI Vol. 1 on page 234 which clears it all up. Thank you for the discussion, though, I appeciated it and it helped me find a solution! Great members here.