[WIP] Double Exponentially Smoothed Model (Holt linear model) #36
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A couple of simple changes to get started: corrected
added EWMA functionality and tests
…on. Started work on gradient descent approach as well
…amples Issue sryza#23: Rename toSamples to toInstants
…evant tests), added missing type to EasyPlot functions
ACF and PACF
added scaladoc comments for up/down sampling
…_label_to_key sryza#24: Renamed labels to keys in TimeSeries
josepablocam
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We implement a holt linear model (additive variant), which allows us to capture trend and level. Estimation of parameters implemented with 2 different optimization methods: BOBYQA (bounded optimization by quadratic optimization, derivative-free), and conjugate gradient descent.
The one point I want to highlight, in case I'm missing something obvious, or we want to leave as "unsupported operation" for this model: removeTimeDependentEffects seems to me to be a bit different here. The smoothed values t are a function of the original values at time t - 1, so given a series of length n, if we apply removeTimeDependentEffects, we can only really arrive at series of length n - 1. In this case, I'm simply filling in the last position with an estimate based off of the trend and levels (the components of Holt). Additionally, I've worked through the algebra various times, but the removeTimeDependentEffects, when solving for original values, seem to be slightly off and that error compounds. I believe I did the algebra correctly (and checked various times), but perhaps an extra set of eyes on this one wouldn't hurt.