I have a multivariate time series dataset. For each timestep, there are 11 features and 1 output. I am going to use supervised ML to predect the output. I understand that in univariate cases, if I am going to use the past 3 days to predict the t-th day, the dataset will be formatted as

x(t-3) | x(t-2) | x(t-1) | x(t)

, where x(t) is the output to predict. 

How should I format the dataset when it is a multivariate problem?

I saw that in some kernels, the problem is formatted as

x12(t-3) | x12(t-2) | x12(t-1) | x1(t), x2(t), ..., x12(t)

, where x12(t) is the output to predict. 

In this case, variables x1 to x11 for the past 3 days are ignored.

However, these variables may be important in my case. Can I format the problem into

x1(t-3),...,x12(t-3) | x1(t-2), ..., x12(t-2) | x1(t-1),..., x12(t-1) | x1(t), x2(t), ..., x12(t) 


(some of the features are just day, month, day of week, etc. created from the datetime index)


With only 11 features, is it necessary to conduct feature selection?


Regarding how to handle multivariate time series problem, I believe that GitHub link Timeseries multivariate will be helpful.

You have to change n_inputs and n_outputs as 12 and 1 respectively.


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