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I'm trying to forecast daily data (I have 15 years of historical data) with complex seasonality: weekly, monthly, annual and also irregular seasonality due to moving events like Easter. As suggested by Hyndman, I tried to use the auto.arima() function with covariates (Fourier Terms for regular seasonality; dummy variables for moving events). However, the multiple step-ahead forecasts for out of sample data are not good. Besides the auto.arima() function is very slow when including covariates.

I tried another approach:

  1. Heuristically choose maximum lag orders for $p$, $q$, and the dummy variables for moving events;
  2. Penalise the size of the coefficients (potentially all the way to zero) using LASSO.

The out of sample forecasts, both one-step ahead and multiple-steps ahead, are way better, and my code is running faster. But I'm not sure whether this approach make sense?

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    $\begingroup$ I believe you'll find your answer here stats.stackexchange.com/q/152202/240024 $\endgroup$
    – Ryan Volpi
    Commented Jun 5, 2020 at 15:50
  • $\begingroup$ How do you implement LASSO ($L_1$) penalization for ARIMA with exogenous regressors or regression with ARMA errors? I am curious, because given that the error terms in the MA part of the model are unobserved, the problem is not a typical regression problem for which several LASSO algorithms exist. $\endgroup$
    – Richard Hardy
    Commented Jun 5, 2020 at 16:05
  • $\begingroup$ @RichardHardy my mistake I posted to quickly => indeed in my alternative atempt I just have lags and dummy. $\endgroup$
    – Eds
    Commented Jun 5, 2020 at 16:39
  • $\begingroup$ @Nutle, as far as I know, no one has done that, and given how simple/intuitive this is, there must be good reasons for that... See also my question linked in the comment above. $\endgroup$
    – Richard Hardy
    Commented Jun 5, 2020 at 17:07
  • $\begingroup$ Please register &/or merge your accounts (you can find information on how to do this in the My Account section of our help center), then you will be able to edit & comment on your own question. $\endgroup$
    – gung - Reinstate Monica
    Commented Jun 5, 2020 at 17:13

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