Analytical tools for diagnostics and feature extraction

Time series data is a sequence of values separated by discrete time 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, y(t₁), ..., y(t_T), with one variable for each point in time, t_i , i=1, ..., T. 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, Δt= t_i - t_j, between distinct points in time, t_i, t_j, is called lag, with T-1 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...