# Simple concrete example of Wold theorem?

#### JustAengineer

##### New Member
I'm reading the Wold decomposition theorem for time series in http://faculty.chicagobooth.edu/john.cochrane/research/papers/time_series_book.pdf. I've googled this a lot, and I know that there is ample treatment of the subject online. However, the above book seems to be unique in that page 44 provides a simple concrete example of Wold's theorem. Unfortunately, I don't follow it, with the theta's and the phi's. These typically represent ARMA coefficients, but the Wold theorem deals with regressing a new time series value against past values. It's not clear to me exactly what is the data set, what are the dependent variable(s), and what are the predictors. I normally think of a regression as a set of records, each one having one or more fields for dependent variable(s) and multiple fields for predictors. In the above book, I can't figure out whether the the set of records are built up one by one with each time step in the time series, what variables correspond to which predictors, whether the regression is done once or repeatedly for each time step, etc.

I've looked high and low online, but can't find document that is so kind as to provide a "dummy's" example such as the one above. Is anyone aware of such an example? I'm not looking for theory. I'm looking for something that makes the theory (abundantly online) real for someone who doesn't a mathmatician (my graduate studies is in engineering).