Time series forecasting with multiple seasonal cycles is the subject of my scientific interests. I use methods based on patterns of seasonal cycles. The patterns used as input and output variables simplify the forecasting problem filtering out the trend and seasonal variations of periods longer that the basic one. The nonstationarity in mean and variance is also eliminated. Using patterns and different models like similarity-based models, neural networks and linear regression I got better results than using standard ARIMA and exponential smoothing. My articles on this topic can be found on my website: http://gdudek.el.pcz.pl/publications.
I am curious what are your experience in forecasting time series with multiple seasonal cycles. What methods do you recommend and why?
You could try some fuzzy inference system (i.e. TSK/ Mamdani-Assilian) and try automated rule extraction. That worked best for me on various benchmark databases. I was also experimenting with NN to forecast financial market (WIG, NASDAQ, Forex) but the result was just about 50% to 60%, so no luck here (paper is on it's way).
Thanks Piotr for your suggestions. I have tried ANFIS model, but results were not better than other approaches. The weak point of fuzzy inference systems in time series forecasting is too many parameters to estimate. Now I am using simpler, local approaches for times series preprocessed using patterns.
I guess that depends on the problem to be solved ;-). I used to compare result with ANFIS and in some combinations of parameters, automated rule extraction was far better but indeed there was clear correlation between the method parameter set and the problem solved (unfortunately). You're welcome to see my Ph.D. Thesis - there are detailed results and comparisons on methods and parameters also regarding comparison with ANFIS and others. You're absolutely right that the amount of parameters is huge but what about employing some heuristic methods, i.e. Evolutionary Strategies to evolve the FIS iteratively rule by rule or even at once?
Where can I find your PhD thesis? I suppose that employing Evolutionary Algorithms we do not reduce the training time in comparison to standard algorithms for ANFIS learning such as gradient or hybrid methods. May be using EA to complexity reduction of the model brings good results. I have not experiences with this.
Here it is - you're welcome: http://www.piotrczekalski.pl/papers/phdpc%20-%20druk%20jednostronny.pdf
and on RG:
https://www.researchgate.net/publication/262171474_Systemy_ewolucyjno-rozmyte_z_parametrycznymi_konkluzjami_w_reguach_if-then?ev=prf_pub
Thesis Systemy ewolucyjno-rozmyte z parametrycznymi konkluzjami w r...
Thank you Piotr. Nice work. I am carious if fuzzy systems with moving consequents could decrease the forecasting error in my problem, i.e. short-term load forecasting.
Thank you!
By the system, you've got an extra degree of freedom for each rule (the conclusion linear combination parameters) that is the gain here. It brings possibilities but also computation cost, particularly when extracting the rules and parameters. I used to differentiate the global model and find its minimum but the problem is that the matrix to be inverted is usually the degenerate one.
Have you thought about using Gaussian Processes? For example, the attached publication looks at a problem that seems similar to yours, and the link below is to a general introductory paper about Gaussian Processes for Time Series Modelling, in which they describe some quasi-periodic kernel (covariance) functions.
http://www.robots.ox.ac.uk/~sjrob/Pubs/philTransA_2012.pdf
Article Gaussian process for nonstationary time series prediction
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