I have to forecast daily page views of a web portal. We have the daily page views of the data for the last 2 years. We have to forecast for next 90 days. I am using a multi-seasonal (with season values weekly (7) and annual (365.25)) TBATS model in R to forecast the data set. Is this the best model or any other model can be considered ?


1 Answer 1


A good place to start is here .. where a simple question is answered in a thorough fashion / When you have a complicated problem/opportunity sometimes simple is simply not good enough. In my opinion your choice for analysis is way too simple as it doesn't often treat the opportunities ( as listed below ) that may exist in order for a forecasting model to be useful.

.. Simple method of forecasting number of guests given current and historical data

Then might want to review https://stats.stackexchange.com/search?q=user%3A3382+daily+data as they detail the advantage of actually analyzing and detecting evidented structure in daily data which may include:

1) Daily deterministic effects AND/OR Daily memory effects

2) Day-of-the-month-effects and changes in day-of-the-month effects

3) Week=of-the-month effects

4) Month=of-the-year effects

5) lead and lag effects of each type of holiday

6) multiple level shifts

7) multiple time trends

8) changes in parameters over time

9) changes in error variance over time

10) long weekend effects

11) arima structure in a thorough manner

12) lead and lag effects of user-specified causals e.g. price of the paper

Software is available in R to accomplish these things .

Are you satisfied that your current approach is capturing all the information ?. This can be confirmed if tour model's residuals are free of structure .. if not then there is work to be done ! If you wish you can post your data and I will try and help further .


enter image description here

Clearly not white noise as there are huge outliers and visually obvious variance changes . Your test for randomness i.e. a series free of both arima structure , outliers and or variance/parameter changes is simply not performing what you think it should perform. Note that untreated outliers often deflate the acf ! See Ord's citation here Determining parameters (p, d, q) for ARIMA modeling reflecting on Alice-in-Wonderland.


This is a plot of the original 1090 daily values ... enter image description here . The model that was automatically developed was (1,1,0)(0,0,0)7 is here enter image description here and here enter image description here. With pulse indicators representing points of inflection/unusual data points given the arima model.

The Actual/Fit and Forecast is here enter image description here with forecasts here for the next 21 days enter image description here

A partial listing of the data shows that it is primarily a deterministic process enter image description here .

The plot of the model residuals is here [enter image description here]suggesting even more anomalies. I would have to say that this residual plot is better/cleaner than your residual plot.

You the OP have some explaining to do as to how this series was recorded as it is primarily a step up and down function not readily amenable to even the best analytical program for time series data.

  • $\begingroup$ Thanks for the quick response. These 12 points you mentioned are mostly relevant for shop floor production. For web page views weekends, holidays and level shifts etc might not be that relevant. $\endgroup$
    – webstat
    Commented Mar 18, 2019 at 11:40
  • $\begingroup$ Also i checked the residual white noise test and it is free of noise. So is that enough to stay with tbats model ? $\endgroup$
    – webstat
    Commented Mar 18, 2019 at 11:41
  • $\begingroup$ Dataset has 1090 days of daily data. I can't paste it here due to length constraint. Please send an email ID to mail the data. $\endgroup$
    – webstat
    Commented Mar 18, 2019 at 12:34
  • $\begingroup$ [email protected] .. what country is involved ... what is the starting date $\endgroup$
    – IrishStat
    Commented Mar 18, 2019 at 12:36
  • $\begingroup$ if the noise is free of anomalies such as pulses , level shifts , local time trends and also has non-significant autocorrelation and constant error variance over time .. that is a good sign ! $\endgroup$
    – IrishStat
    Commented Mar 18, 2019 at 12:39

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