# multivariate time series: selecting a predictive model

I have a time series dataset that looks like this

                      x       y     z
t
2017-10-28 00:00:01   0.18    0.01  0.55
2017-10-28 00:00:02   0.20    0.01  0.56
2017-10-28 00:00:03   0.24    0.01  0.57
2017-10-28 00:00:04   0.23    0.02  0.58
2017-10-28 00:00:05   0.26    0.01  0.59
...                   ...     ...   ...
2017-10-28 12:59:08   0.53   -0.03  0.9
2017-10-28 12:59:09   0.56   -0.04  0.89
2017-10-28 01:00:00   0.57   -0.04  ???


give (x) & (y) at time (t) I want a chose a model that will best predict the next value in the sequence (z)

notes:
• the time series is stationary - i have detrended, deaseasonlized, and minmax scaled each feature

• What have you tried? – Demetri Pananos Jul 15 at 2:10
• @DemetriPananos k-nearest neighbor to extrapolate z using n-number of past observations of z. no additional features. got less than satisfactory results – Logarithm Jul 15 at 2:13
• This might be helpful – Demetri Pananos Jul 15 at 2:33
• A VAR (Vector AutoRegression) model could be used. – user2974951 Jul 15 at 6:04

You have a multivariate data set with one dependent series (multivariate-single equation). VAR is inappropriate when you have only 1 dependent series i.e. equation because you only have have 1 endogenous variable to predict. You might find the following tutorial interesting reading https://autobox.com/pdfs/regvsbox-old.pdf .

The solution for this problem is called ARMAX or sometimes SARMAX or sometimes Transfer Function . It is essentially a multiple regression solution that may incorporate the history of the dependent series and possible current and previous values of the user-suggested predictor series. One should identify and include any latent deterministic structure such as level shifts in z or deterministic time trends in z or seasonal pulses.

https://autobox.com/pdfs/SARMAX.pdf

This Using lagged explanatory variables to forecast future value of depended recent post in SE might help and Exploring relation between time series .

De-seasonalizing and detrending or adjusting unusual values or differencing or power transforming is not needed as these kinds of structures are part of the the final model. In order to make forecasts and generate confidence intervals , one equation is the suggested method.