I'm working on 2D time series data where two attributes are depth and temperature. When I plotted depth-vs-temp curve and saw its variation over time, the fluctuation occurs at few places only.
I'm not saying temperature is dependent on depth. But given these data, what should I look into to establish relationships between depth, temperature, time?
Ideas:
Look for depth regions where fluctuation in temperatures occurs over time. And develop time series prediction for these given regions.
What models/papers should I study to get insights out of the data? I want to understand and study what are the various methods that could be tested and visualizations built over these data. It's a data exploration problem.
Data shape: (2000,2,100) (samples,depth-temperature,time-sample) .i.e 2000 depth,temperature samples for each of 100 time stamps.
Thanks.
Best Answer
The general solution to your problem is Vector ARIMA (VARIMA) where the 2 endogenous variables that you specify can be related not only to their past values BUT past errors in both series. VAR is a special case of VARIMA as it doesn't assume a specific structure. In both cases VAR and VARIMA one must be concerned with anomalies such as Pulses/Level Shifts/Seasonal Pulses and Local Time Trends. If one doesn't treat these four kinds of omitted deterministic structure your results might be seriously flawed. Furthermore changes in parameters and/or the variance of the error processes need to be considered as the t/F tests are not robust to these violations. Unfortunately VARIMA solutions which don't deal with the pre-mentioned caveats are not very useful. If you find that primarily Y responds to X rather than X responding to Y , one could use a Dynamic Regression (a.k.a' Transfer Function) approach where all of the pre-mentioned conditions can be considered.