Predictions Using Time Series Data

General Phenological Model for Seasonality

In business, time series data $f(t)$ usually carries information about trend $g(t)$ ($g$ is used since trend is usually growth), seasonalities (periodical effects) $p(t)$, holiday effects (structural effects) $s(t)$, etc. We will decompose a time series $f(t)$ into four components

$$ \begin{equation} f(t) = g(t) + p(t) + s(t) + \epsilon(t). \end{equation} $$

To train a model for the predictions, we need to write down the exact models of these three predictable components.