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Table Of Contents
Time Series with PyTorch
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We take a step back and re-think about our time series forecasting problem. Time series forecasting can be formulated as transition probability estimation problems. To understand the concept, we establish a simple stage where we only have 5 time steps,
. We want to estimate the distribution of the time steps
,
, denoted as
, using the given historical values
,
,
, the chain rule of probability tells us

Following the research by K. Rasul et. al. (Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting available), we simplify the calculations, we assume that we can approximate the distributions using the following:

where
and
model the temporal dynamics of the time series data. For example,
can be an RNN hidden state that carries the information of the historical values
,
,
. With these assumptions, we can formulate a time series forecasting problem as a sequence of conditional probability estimations...