I have a series with double seasonality, one daily and one weekly. I modelled the daily seasonality with SARIMA, and I want to include weekly dummy variables.

I only included weekday variables for the times when spikes occur in my data, and dropped the rest. That's how a long term forecast looks with this model:

enter image description here

Now my problem: it isn't supposed to have an upward trend like that.
If I don't include the weekday dummies, it stays on the same level (which I want), but with weekday dummies, the above happens and I have an upward trend (in the spikes).

I don't know why that happens. Any clue why that happens/how I can fix that?


Regardless of the exact SARIMA specification, there is always no trend without dummies, and always a trend when i include "variablewochentag" (German for weekday variable). There are 2 spikes per day in my data, and my data is Mo-Fr, so i have 10 weekday variables. There is also a seasonal difference (65 = daily seasonality) in my estimation, and i have no constant. I have 2080 observations which i used for estimation, added weekday dummies for future observations and then have run the forecast which results in the above picture.

Estimation Output: enter image description here


http://www.filedropper.com/data_10 Here is my data. Note: the first 2080 data points are my actual observations, the rest are just zeros + the relevant variables to do the long term forecast. Seasonality is 65 for daily, 325 for weekly.

  • $\begingroup$ Could you include the estimated model coefficients? $\endgroup$ Dec 5, 2015 at 18:51
  • 1
    $\begingroup$ please provide the data ...... and all meaningful output . You probably have a differenced model with a steady state positive constant $\endgroup$
    – IrishStat
    Dec 5, 2015 at 18:54
  • $\begingroup$ @Richardhardy i included the estimation output. $\endgroup$
    – Jariel
    Dec 5, 2015 at 23:05
  • $\begingroup$ @IrishStat i included the estimation output. The model is differenced (seasonally), but it doesn't have a constant. The trend doesn't exist if i don't include my dummy variables. $\endgroup$
    – Jariel
    Dec 5, 2015 at 23:06
  • $\begingroup$ also added my data. $\endgroup$
    – Jariel
    Dec 6, 2015 at 1:31

1 Answer 1


Your model is way over-specified (kitchen-sink modelling) probably because of your reliance on a simple statistic like AIC/BIC which premises no outliers/level shifts/time trends/constant parameters/constant error variance and many other things. If you have redundant/cancelling parameters like AR(65) and MA(65) as you do all bets are off with the normal expectation of stable (i.e.non-trending) forecasts. Furthermore if your coefficients are non-invertible or nearly non-invertible like your AR(1) and AR(2) this can lead to "explosive forecasts" . Consider an AR(2) model with coefficients .6 and .5 ....which is non-invertible because the coefficients sum to more than 1.0 , you get explosive forecasts . KISS is the order of the day. Model identification is important.

  • $\begingroup$ even if i only include Ma(1) and SMA(65), i still get an "explosive forecast" if i also include my dummy variables. $\endgroup$
    – Jariel
    Dec 7, 2015 at 9:17
  • $\begingroup$ If i include a constant in my model (together with my seasonal differencing), i also get a trend. Why is described here: robjhyndman.com/hyndsight/arimaconstants Could there be the same problem with dummies? $\endgroup$
    – Jariel
    Dec 7, 2015 at 10:34
  • $\begingroup$ I think i know now why i get a trend. I need to difference my dummy variables which i haven't done. $\endgroup$
    – Jariel
    Dec 7, 2015 at 10:55
  • $\begingroup$ That is possible .... $\endgroup$
    – IrishStat
    Dec 7, 2015 at 13:24
  • $\begingroup$ Any luck ... I doubt it .. $\endgroup$
    – IrishStat
    Dec 8, 2015 at 9:48

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