Tools for diagnostics and feature extraction
A time series is a sequence of values separated by discrete intervals that are typically even spaced (except for missing values). A time series is often modeled as a stochastic process consisting of a collection of random variables, , with one variable for each point in time, . A univariate time series consists of a single value, y, at each point in time, whereas a multivariate time series consists of several observations that can be represented by a vector.
The number of periods, , between distinct points in time, ti, tj, is called lag, with T-1 distinct lags for each time series. Just as relationships between different variables at a given point in time is key for cross-sectional models, relationships between data points separated by a given lag are fundamental to analyzing and exploiting patterns in time series.
For cross-sectional models, we distinguished between input and output variables, or target and predictors...