Forecasting out of sample with Fourier regressors

Question

I'm trying to create a multivariate multi-step-ahead forecast using machine learning (weekly and yearly seasonality). I use some exogenous variables, including Fourier terms. I'm happy with the results of testing the model with in sample data, but now I want to go for production and make real forecasts on completely unseen data. While I can update the other regressors (variables) since they are dummy variables and related to time, I don't know how I will generate new Fourier terms for the N steps ahead. I have an understanding problem here and what to check it with you: when you generate the fourier terms based on periodicity and the number of sin/cos used to decompose the time serie you want to forecast this process should be independent on that values of the time series. Is that right? If so, how do you extend the terms for the N steps? Just for the sake of completeness, I use R.

Thank you

Answer 1

From what I am reading and understanding, you want to get future N terms on the Fourier. To do this, you need to shift your calculated time frame to be some point in the past (say N-1). This is just simple causality, you cannot model the future with Fourier (for example, you cant have (N-1) = a(N+1) + b(N-2) + c(N).