Suppose I have a set of observational data as a time series where the observations are collected at uniform interval over the course of several years. The data exhibits seasonality over the course of both the day and the seasons of the year (it's environmental data). I am interested in examining the data stream over several time scales: seasons, day v. night, months, and year.
I am not interested in comparing those time scales against one another but perhaps to want to create a best-fit model for each period (e.g., January's observational values typically contain values that have a given set of summary statistic attributes like mean, median, spread, and modality). I see reason to believe some of the data series will be multimodal in some cases. The data is continuous and floating point.
I'm not particularly interested in creating a forecast model for the underlying time series data set but rather applying density functions on each time period to reduce the data into a summary. I'm interested in seeing if I can create a model for each density function. For instance, the density function for January observations look typically like X, and there is a degree of confidence attached to it.
What model or corpus of knowledge would I need to learn to build such an estimate? I'd be interested in doing this for both the df and cdf of the time windows. Is there any past research I should consider?
Again, I am interested in solely the reduced representation of the series — its df and cdf — and trying to infer what the true df or cdf look like with only having samples over several years and not eternity.
I am a little bit familiar with forecasting and confidence intervals for underlying time series with Holt-Winters, but I wouldn't know where to begin with the above.
