Fast Fourier Transform and Clustering of Time Series

Question

I'm making a project connected with identifying dynamic of sales. That's how the piece of my database looks like http://imagizer.imageshack.us/a/img854/1958/zlco.jpg. There are three columns:

Product - present the group of product

Week - time since launch the product (week), first 26 weeks

Sales_gain - how the sales of product change by week

In the database there is 3302 observations = 127 time series

My aim is to cluster time series in groups which are going to show me different dynamic of sales. Before clustering I want to use Fast Fourier Transform to change time series on vectors and take into consideration amplitude etc and then use a distance algorithm and group products.

It's my first time I deal with FFT and clustering, so I would be grateful if anybody would point steps, which I have to do before/after using FFT to group dynamics of sales. I want to do all steps in R, so it would be wonderful if somebody type which procedures should I use to do all steps.

That's how my time series look like now http://imageshack.com/a/img703/6726/sru7.jpg

Please note that I am relatively new to time series analysis (that's why I cannot put here my code) so any clarity you could provide in R or any package you could recommend that would accomplish this task efficiently would be appreciated.

P.S. Instead of FFT I found the code for DWT here -> www.rdatamining.com/examples/time-series-clustering-classification but cannot use it on my data base and time series (suggest R to analyze new time series after 26 weeks). Can sb explain it to me?

Answer 1

You may have too little data for FFT/DWT to make sense. DTW may be better, but I also don't think it makes sense for sales data - why would there be a x-week temporal offset from one location to another? It's not as if the data were captured at unknown starting weeks.

FFT and DWT are good when your data will have interesting repetitive patterns, and you have A) a good temporal resolution (for audio data, e.g. 16000 Hz - I am talking about thousands of data points!) and B) you have no idea of what frequencies to expect. If you know e.g. you will have weekly patterns (e.g. no sales on sundays) then you should filter them with other algorithms instead.

DTW (dynamic time-warping) is good when you don't know when the event starts and how they align. Say you are capturing heart measurements. You cannot expect to have the hearts of two subjects to beat in synchronization. DTW will try to align this data, and may (or may not) succeed in matching e.g. an anomaly in the heart beat of two subjects. In theory...

Maybe you don't need specialized time methods here at all.

A) your data has too low temporal resolution

B) your data is already perfectly aligned

Maybe all you need is spend more time in preprocessing your data, in particular normalization, to be able to capture similarity.