# Vector Autoregression (VAR)

The vector autoregression (VAR) method uses an AR model to model the next step in each time series. It is a generalization of AR to multiple parallel time series. Multivariate time series: Model notation involves specifying the order of the AR(p) model as a parameter to the VAR function, e.g. VAR(p). This method is suitable for multivariate time series without trend and seasonal components.

# Vector Autoregressive Moving Average (VARMA)

The vector autoregressive moving-average (VARMA) method uses an ARMA model to model the next step in each time series. It is a generalization of ARMA to multiple parallel time series. Multivariate time series: Model notation involves specifying the order of the AR (p) and MA (q) models as parameters to the VARMA function - VARMA (p, q). You can also use VARMA models to develop VAR and VMA models. This method is suitable for multivariate time series without trend and seasonal components.

# Vector Autoregression Moving-Average with Exogenous Regressors (VARMAX)

The vector autoregression moving-average with exogenous regressors (VARMAX) is an extension of the VARMA model that also includes the modeling of exogenous variables. It is a multivariate version of the ARMAX method. Exogenous variables are also tabbed covariates and can be thought of as parallel input sequences that have observations at the same time steps as the original series. The primary series(es) are referred to as endogenous data to distinguish from the exogenous sequence(s). The observations for exogenous variables are included in the model directly at each time step and are not modeled in the same way as the primary endogenous sequence (e.g. AR and MA processes). The VARMAX method can also be used to model the subsumed models with exogenous variables, such as VARX and VMAX. The method is suitable for multivariate time series without trend and seasonal components and exogenous variables.

# Simple Exponential Smoothing (SES)

The simple exponential smoothing (SES) method models the next time step as an exponentially weighted linear function of observations at prior time steps. The method is suitable for univariate time series without trend and seasonal components.

# Holt–Winters Exponential Smoothing (HWES)

The Holt-Winters Exponential Smoothing method comprising of the forecast equation and three smoothing equations models the next time step as an exponentially weighted linear function of observations at prior time steps, taking trends and seasonality into account. The method is suitable for univariate time series with trend and/or seasonal components.