Assumptions of Log Linear trend

CFA Level II Quant
#1

We have read about the assumptions of a linear regression or linear trend. Are there any assumptions for the log linear trend? Cause in the log linear trend, the error terms are definitely correlated with each other

#2

One of the assumptions of the OLS is that the dependent and independent variables mantain a linear relationship between them. Some times, some variables do not have a linear relationship, but a cuadratic or cubic relationship. So, one way to fix this is to smooth the variables by appying the Log / Ln function to them. After this change, many non-linear variables change to linear behavior, so they can be analysed through OLS models. This change should be totally apart from other OLS assumptions like the “uncorrelated error terms”. Why do you say that log linear models present correlation of errors?

#3

If a log linear trend still presents correlated error terms, you may want to make use of a log-difference or other type that may present as a lenear and no longer have correlation of error terms

#4

One of the main points of that reading is being able to determine what to use to allow the regression to work correctly. A linear, log linear, log difference may be required to make the data work

#5

I mean in previous reading, when they mentioned the serial correlation of the errors, the correction was to use Hansen std errors. why cant we simply apply it to time series?

#6

I believe you don’t use corrected White/Hansen standard errors (as you would in a normal multiple linear regression) in a time series because (when historical time is on your x-axis) the errors usually evolve in some predictive way as your chart progresses rather than a standard regression (aka an econometric model with something like GDP on the x-axis) where the errors are less predictable. With a time series there might even be pockets and clusters of errors that follow a pattern, but average out to roughly 0. So this is where ARCH or even GARCH models come into play. There’s a whole family of modeling and statistics that has evolved around these models and looking at financial data.