Suppose I have quite a large time series (e.g., daily car accident rates in London for the past 20 years) and I also have further datasets for the same time period (e.g., daily precipitation, wind speeds, visibility, etc.). I would like to investigate whether there is any relationship between these variables (rain, winds, visibility, either taken individually, or as a multidimensional dataset) and my original variable (accident rates). In particular, I would like to deduce results such as:
- If precipitation increases over some value $x$, car accidents will increase with probability $p_1$
- If precipitation increases over some value $x$, and visibility decreases below some value $y$, car accidents will increase with probability $p_2$
Generalizing, given an $n$-dimensional dataset, how can I study the relationship between this multidimensional dataset and any other data? I am talking specifically about time series (although accident rates were just an example, it could really be anything). I suppose one could start by just considering one dimension, and then slowly adding more and more dimensions to see how they affect the results. What kind of tools can be used in this case? Can anybody also suggest some references on this topic?