I'm wondering what the best way to estimate the delay and confidence between two non-periodic time series would be.
Specifically, I thought it would be interesting to look at the different economic indicators, say the price of oil and a stock price, and determine whether one predicts the other, with how much confidence and by how far in advance.
Most of the answers I've been able to find so far have described periodic time series and phase difference in radians. It is not clear to me how this type of analysis would convert to non-periodic data and difference in time instead of angle. It may be possible to glean some information from treating the data as periodic, so that's not completely out.
Any reading recommendations?
Thanks!
Best Answer
The most straightforward approach is probably cross-correlation. You may be interested in the answers to this post and the posts linked in the right-hand-side of that post (linked also in my comment to one of the answers).
Another approach is by means of a dynamic regression. You could fit an autoregressive distributed lag model. For a description of this model and some references see for example my answer to this post.
This will allow you to test for the significance of one variable to explain the other and also for the significance of lags of the explanatory variable. The order of the highest significant lag will be a measure of the delay between both variables.
For the kind of data that you mention (economic indicators), you will probably need to fit the model for the differences or growth rates of the variables (not for the original series) in order for them to be stationary and avoid possible spurious results due to stochastic trends in the variables.
A more involved approach would be as follows:
A nice way to look at the estimated cycles is the animated plot used by Statistics Netherlands to track the business cycle. This plot does not reveal exactly by how many periods an economic indicator is ahead or behind other indicators, but it's a nice way to summarize the results.