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I'm trying to do multivariate time series forecasting using the forecast package in R. The data set contains one dependent and independent variable. From the cross-correlation the 0 day lag of the independent variable seems to have better correlation with dependent variable.

The time series data is weekly and I have only two and half years of data. Since the data is weekly and have a very high seasonal length. Does auto.arima or Arimax capture the seasonality.

This is my approach to this problem

  1. Use stl decomposition to measure the seasonal strength
  2. If seasonal strength is higher then i intend to go with Dynamic harmonic regression on the independent variable using Fourier coeff(selected based on minimized Aicc values) and use this harmonics matrix to predict the future values of independent variable.(using auto.arima() and harmonics matix on the xreg parameter) 3.And then I intend to use this forecasted values of independent variable to predict the dependent variable using auto.arima( here on the xreg i will use forecasted values of indpendent variable from step 2)
  3. If there is no strong seasonality i would just use auto.arima with xreg parameter to forecast dependent variable

Please advise on this

Thank you

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  • $\begingroup$ See these threads on modeling seasonal data with a long seasonal period such as yours. $\endgroup$
    – Richard Hardy
    Nov 18, 2021 at 14:25
  • $\begingroup$ Thank you Richard for the threads. I have acquired great deal of insights from these threads. Still I couldn't find an answer if its right to use co-variate(x) + Fourier values of y to predict the variable y. I have asked this question a new thread (stats.stackexchange.com/q/552768/289500) with the sample code. Hope will get the right guidance. Thank you so much $\endgroup$
    – Arvind Menon
    Nov 18, 2021 at 17:17

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