Quant -- multiple regression and time-series

  1. one of the assumptions of multiple regression model is: the variance of the residual term is constant for all observations. What does ‘variance’ mean here? can i equalize it with ‘squared residuals’? Since one observation only has one residual term, am i right? 2. in time-series analysis, autocorrelation analysis is often conducted on AR models, in which a list of lags will be presented. for example, the autocorrelation of lag 12 is 0.012334. what does lag 12 mean??? i’m so confuesed…
  1. yes variance is squared residual. [(xt - Xbar)^2] xbar = avg (xt). 2. lag 12 -> Observation 12 - Observation 11. Say it is monthly returns data. Lag 12 = Return Month 12 - Return Month 11.

hey CP, that really helps, thanks! a small question tho, by Lag 12 = Return Month 12 - Return Month 11, do you mean ‘the error term of montn 12 - the error term of month 11’?

I believe it is the # of original observations. Remember Error (1) = Observation 2 - Observation 1 … this is the Lagged error. schweser does tend to confuse you a bit without presenting the entire problem. read the text book… your auto-correlation is on the error terms. But the error terms themselves are derived from the original data series.

that cleared things up, many thanks!

Lag = # of periods behind. Lag12 = Obs 12 - Obs 1. (not obs 11 - that would be lag 1). Autocorrelation is measured for residuals. This is to see that the model captures all the timeseries pattern - any pattern still left tells you that the model has failed (to adequately describe the time series).

  1. Actually you can still run multiple variable linear regression even the variance is not constant - you can adjust the variance by some factor(scaler); Make sure you mention linear as in non-linear world,the variance might not apply.