How do I find all the independent variables for a time series regression model?

Question

Suppose I have a single time-dependent variable $y_{t}$ (e.g. stock price) and a few hundred independent variables $X_{it}$ with data available for the same time frame as $y_{t}$ (e.g. company revenue, total market sales, interest rates, value of $y_{t-1}$ etc.) I want to identify a model to use for forecasting using this data.

1. How do I know which of the independent variables to include?

2. What is the problem with including all the variables?

My superficial ideas for identification are to use AIC/BIC/R^2 comparison between every single combination of variables in a simple ARIMA and build on that(would be thousands of model calculations) or do Granger causality for every $y_t / x_{it}$ pair. There must be an easier way, surely?

• whuber: Re "every single combination:" there are 2ドル^\text{several hundred}$ such combinations!

Answer 1

There has been work on selecting variables using the lasso and similar methods in a time series context; see here for some pointers to literature.

Alternatively, you could also consider a PCA.