I have a time series with muliple seasonal cycles, which are 24 and 168 hours for my case. I would like to use Double Seasonal Exponential Smoothing method to forecast, which was published by James W. Taylor (http://users.ox.ac.uk/~mast0315/). The link for his article is here

When I check Taylor's paper and all other papers in the literature, I saw that AR(1) adjustment has been implemented to the residuals. Is it a coincidence to make AR(1) correction to residuals of all the time series, that have been used in these papers?

I am using "forecast" package in R by Rob Hyndman, http://cran.r-project.org/web/packages/forecast/forecast.pdf

Firstly, I run the code without using an AR(1) model for the errors.

    data <- scan("data.dat", skip=1)
    datatimeseries <- ts(data)
    dataforecasts <- dshw(datatimeseries, 24, 168, armethod=FALSE)

Below, you can see the ACF and PACF graphs of the residuals. enter image description here enter image description here

As you can see there are some serious non-zera autocorrelation. I can not do AR(1) correction as papers suggest because PACF does not show it.I do not know what to do. I am sorry if it's a silly question however I am so new to time series. Would you please care to explain what to do next step-by-step and elaborately. Thanks in advance


1 Answer 1


The AR(1) error would help a lot. But if you want something more general and flexible, use the tbats function instead.

  • 1
    $\begingroup$ Mr. Hyndman, When I do AR(1), no matter what the graphs depict, I still get non-zero autocorrelations. That means I did not get a perfect model. thus, how I use this tbats function you mentioned and why? $\endgroup$
    – ARAT
    Jun 26, 2013 at 8:05
  • 1
    $\begingroup$ First, you may never get a perfect model. Second, I've already explained why -- it is more general and flexible. Third, if you want to know how to use a function, read the help file. $\endgroup$ Jun 26, 2013 at 13:30

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