time series data and regression

[fffrost]

I'm lost - if we have a timeseries dataset like stock price for some company, why is it unacceptable to take the price as an input variable, lag it n times, and then use those lags of the price as predictors for the future price in a regression model?

I know that this is due to temporal autocorrelation since regressors that were close together in time have a huge covariance, but I can't quite understand what exactly the problem is with this and what to do about it. Isn't the AR model exactly as I suggested?

 

[noetsi]

I spent much of the last decade trying to learn time series regression and I remain lost so don't feel bad

You can do what you suggested but your p values will be wrong because of autocorrelation. Methods such as ARIMA and regression with autoregressive error deal with this. There are time series standard errors (not white's) that can also be used. Note that this involves predicting Y with itself. When you try to use other predictors the situation is a lot worse involving issues like cointegration and structural breaks (where the relationship between X and Y change over time).

There is no simple way to do time series regression with predictors other than Y (a univariate model). Vector Autoregressive models or Vector Error Correction are the state of the art, but not for the faint of heart.