How do you choose the timeframe for a prediction to be tested?

Question

To (hopefully) clarify the question a bit more if you have a broad working hypothesis that x influences y, on a causal/predictive basis (e.g. if x goes up in time t, then you would expect y to go up in time t+1, assuming the working hypothesis is true).

In traditional time-series analysis the length of time that the period t represents for t and t+1 tends to be equal. Can alterations in the periods that each represents, be easily altered for the purposes of analysis?

Also if we take the example of t to be a day, is it possible to distinguish differences in predictivity for various time frames, e.g. x goes up today, and over the course of the next 3 days y goes up, or over the course of the next 5 days y goes down (what happens if they are both significant?).

How does one go about detecting the time-frame of prediction appart from brute-forcing every possible combination of before and after timeframes (e.g. testing if x has gone up over the course of the last m days what happens to y over the next 1 to n days).

Answer 1

The time frame of prediction i.e. the size of the "bucket" is set by you. You select whether tou wish to react/respond to hourly data or daily data or other frequencies. Data arrives as transactions and is hen bucketed to time intervals. This time interval is your choice. We are developing forecats at 15 minute intervals for major food chains and others while incorporating daily trends/factors that are driven by promotions/events. THe quality of the predictivity can be measured for different size buckets for different lead times.