We know that correlation assumes stationary time series data. On the other hand we know that convolution principally does the same job as cross-correlation (the only difference is that convolution rotates the kernel function by 180 degrees.) Does convolution have a same assumption? Can we use convolution for measuring similarity or finding patterns in non stationary time series data?
I like this idea! So to my understanding, the convolving matrix can do all kinds of things, from detecting edges in images to sensing certain features. So it seems like it would have the flexibility to find other types of patterns in other types of data. . . I think this would be worth exploring.
Warren Baker Yes, in fact the whole deep learning buzz is about convoluting small filter kernels with neighborhoods of the same size within a stationary data set--e.g., a picture. However, I think a non-stationary time series is more like a movie i.e., the average intensity of pixels is a random walk and does not converge to a number. That is what makes me hesitant in using convolution for non-stationary time series. It might be possible though...
Right - the convolutions are used for images. But the "images" are just numerical summaries of pixels - so they COULD be any numerical data whatever. I have been playing with employing Tensorflow to use convolutions on numerical data sets. I only started on this a few weeks ago after reading that others are doing this. It's a great idea and I hope to hear more of your thoughts on this!
About what you said - maybe not exactly a RANDOM walk. . . and besides it depends on what features you are attempting to emphasize. You could even use correlation within the matrix used for convolving. With the "pixels" as states over time with the convolving matrix being some summary of those states, including correlation with something. So the features you generate could even be indications of evolution in a positive or negative direction or becoming larger or smaller. . .
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