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I am trying to write a prediction algorithm for a set of temperature data. I settled on Holt-Winters since it seemed to be a simple time series prediction algorithm and I can easily code it up in python to understand what is going on with it.

When I am plotting the smoothing function as it learns this is how it looks. As you can see, it follows the original curve pretty well.

enter image description here

But when I try to plot a future curve for one year (365 days) -- it really falls down and dies.

enter image description here

And to me intuitively it makes sense why it dies like that. Because if you see the last prediction equation of Holt-Winters it really only makes use of the very very last point in both the curve smoothing and the trend smoothing. And we know that exponential smoothing has a very short memory because of the whole exponential thing.

So I am wondering how does one actually go about using Holt-Winters for prediction (specifically for 365 day seasonal data like this).

If you know of any other methods which I can look at for this domain (temperature prediction) please let me know. I come from python, so it would be very useful if you can point me to resources such as libraries etc to get the job done.

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  • $\begingroup$ Are you confusing Holt with Holt-Winters? Holt-Winters adds a seasonality equation which reflects a time offset of $s$ (the seasonality), which in your case would be 365. At least that's how I understand Holt-Winters. $\endgroup$ – Wayne Dec 20 '11 at 18:24
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Jason,

Holt-Winters is a particular model form, normally additive or multiplicative and apparently may not be applicable to your particular time series. In general a Transfer Function incorporating both stochastic and deterministic structure has been found to a powerful way of handling problems like this. The problem you face I believe may be better handled with a mixed frequency model that might include one or more trends and/or level shifts and perhaps either weekly or monthly effects to deal with the "seasonal component" . Furthermore the model might exclude any identifiable anomalies so as to get a more robust "signal". I suggest that you post your original data to the web and have some of the readers use their methods/software to try to model the data. I will try and do the same. It might make for a very interesting comparison !

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  • $\begingroup$ thank you for the answer. I don't want to post the data yet since I am doing this as a class assignment. Give me pointers to articles/papers that I can read and implement for now. I will be posting the data when I am done with the assignment. I am open to other methods other than holt-winters too, infact like you said holt-winters may not be the best way for this problem. $\endgroup$ – user4280 Apr 21 '11 at 20:19
  • $\begingroup$ @jason,You might consider constructing an equation which incorporates dummies to handle the "seasonal effect" and to create a set of tentative model residuals.These "residuals" may then be used to determine how many trends there are in the data or how many level shifts i.e.intercept changes. This might requires either significant analysis on your part or the programming the algorithms of R.Tsay (Journal of Forecasting Vol pp 1-20,1988 ) or investing in commercially available software. I have been involved in developing these fairly proprietary procedures for AUTOBOX. $\endgroup$ – IrishStat Apr 21 '11 at 20:49

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