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time series forecasting

I have created some artificial data in JMP 17.1 that looks like this:

 

 It has a period of a year with several years worth of data.  When I used a seasonality of 365 days, it did not predict with any periodicity.  Not sure why.  Has anybody seen this before?  Thanks!

@jiancao 

 

 

 

Re: time series forecasting

TSF does not forecast the daily data well.  @peng_liu   please comment. Thanks!

I tried the seasonal ARIMA in the TS platform.  Below is the best mode it finds. (I ran a total of 64 models using the ARIMA Model Group option) 

It seems there are multiple seasonality components in this data according to the spectral density (below).  Seasonal ARIMA models cannot account for multiple seasonal patterns.

I have a data set of daily average temperatures.   Its spectral density:  

The seasonal ARIMA fits this data quite well

 

 

Re: time series forecasting

Thanks, @jiancao I don't have much to add. I couldn't get even close to what you got, until I peeked into your solution.

By looking how the series is simulated, this is a rather complicated process. The foundation include three non-seasonal series, and their squares, then weighted sum of all them together, then add a regime switched sine wave. And the sine wave itself is not a dominant signal either. And look at the ACF, it has rather long memory. ARIMA wins in this round.

Re: time series forecasting

Thanks, @peng_liu  for looking into the TSF. My takeaway is that try TSF first especially when you have multiple series to forecast.  When it fails then go to the TS platform and run the ARIMA Model Group feature.   Fit a group of low order ARIMA modes like this:  (## is the #obs per period; in this case 365): 

 

Re: time series forecasting

I expand the number edit box width in 18, so 365 can show up.

 

Re: time series forecasting

Thanks Jian!  It's nice to know that if things don't work in TSF, then going back to TS is the next best thing to do!

 

Charlie