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I want to test how many quantization levels (discretizing levels) are the best for the given data(time series) set I have. Therefore I am applying different levels of binning (like discretisize data to 4,5 and 6 levels) and calculate the log likelihood and AIC and BIC score. However I am observing the pattern that as the number of quantization level is increased like from 4 levels to 5 levels the log likelihood, AIC and BIC get worse (log likelihood getting smaller) Is there any reason behind that ?

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