# Quant Gurus Help

one of the regression assumptions is - they should be independently distributed (no auto correlation) and the mean is constant But later in time series stuff, if the residuals or correlated and mean is non constant, use log linear model (Per Schweser) or if it exhibits a trend. Does time series does not follow any regression assumptions? Does this also mean it is not necessary to be covariance stationary (Mean is not constant and Variance is not constant). Is covariance stationary only applicable to AR models?

You are talking about serial correlation. Here is what you need to know about this assumption and autoregressions. First, Durbin Watson test statistic does NOT work for AR models. To test for serial correlation, you run a test to see if the correlation of the error term’s on a lagged error term. You use the test statistic t = p(1/sqrt(T)). If it is significant from 0, serial correlation exists and you need to add a lag term to adjust for seasonality.

i assume you meant to say “Durbin Watson statistic does NOT work for AR models.”

I am more talking about log linear model But by the way. Schweser says do not use DW test for testing Serial correlation for AR models. use T-tests. I think I also saw this in one of the samples

Opps. Thanks for catching that. I edited to not confuse anyone.

You are getting covariance stationarity confused with using log linear models I think. If the mean and variance is not constant, the model is covariance unstationarity. To solve, you take the first differences which basically means instead of predicting the level of X, you predict the amount X will change from the last value. The only thing you need to remember about logs vs. linear, is if something increases by constant amount each period, use linear model. If it increases by constant rate, you log model. Nothing else should really change.

You can use DW on a time series model if it is a linear or logniear model. You cannot use DW on a time series model that use lagged dependent variables.

To summarize, I do not need to worry about Covariance stationary for log linear models. But need to check for AR models. Cannot test using DW and use t-tests. Thanks

drk Wrote: ------------------------------------------------------- > To summarize, I do not need to worry about > Covariance stationary for log linear models. > > But need to check for AR models. Cannot test using > DW and use t-tests. > > Thanks After you convert it to a log linear model, it should be covariance stationary. If it isn’t, then you have a problem.

Still unclear to me. Are you saying that all log linear models are covariance stationary?

Schweser says “The log linear model more accurately captures the behavior of time series, the impact of correlation in the error terms is minimized”. This is so fricking confusing.

hope these points below help you understand better. 1. growth is exponential. 2. just having a linear model for b0+b1t - if you plot it - will be a curve, when t increases. 3. e^(b0+b1t) ==> which is the log linear model - will be a straight line. 4. the linear in t model will not be covariance stationary. If you got a regression line - there is going to be a lot of variance. 5. log linear model on the other hand - will be cov. stationary - since the line is going to be closer to the points.

Beautiful…This clears up my mind. Thanks.

cpk: are you sure that loglinear models must be covariance statoinary? that would be saying that all loglinear lines have a constant mean and variance, and im not so sure thats the case.

page 227 schweser book 1 shows a loglinear trend line. no way that is covariance stationary.

2nd picture on the right… in the absence of supporting data evidence - it does not seem non-covariance stationary either. (constant mean, constant variance, constant covariance). also the fact that the model is used to predict a variable (as indicated in the paragraph immeidately below) - allows me to believe it is covariance stationary. but continuing this argument is not required any longer.

sighs of non stationary include linear and exponential trends~~

if a log linear model displays an upward trend, it migt have a unit root, hence may not covarianve stationary.