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# Classical time series methods (+cheat sheet)

Autoregression (AR): The autoregression (AR) method models the next step in the sequence as a linear function of the observations at prior time steps. The method is suitable for univariate time series without trend and seasonal components.

Moving Average (MA): The moving average (MA) method models the next step in the sequence as a linear function of the residual errors from a mean process at prior time steps. The method is suitable for univariate time series without trend and seasonal components.

Autoregressive Moving Average (ARMA): The Autoregressive Moving Average (ARMA) method models the next step in the sequence as a linear function of the observations and resiudal errors at prior time steps. The method is suitable for univariate time series without trend and seasonal components.

Autoregressive Integrated Moving Average (ARIMA): The Autoregressive Integrated Moving Average (ARIMA) method models the next step in the sequence as a linear function of the differenced observations and residual errors at prior time steps. The method is suitable for univariate time series with trend and without seasonal components.

Seasonal Autoregressive Integrated Moving-Average (SARIMA): The Seasonal Autoregressive Integrated Moving Average (SARIMA) method models the next step in the sequence as a linear function of the differenced observations, errors, differenced seasonal observations, and seasonal errors at prior time steps. The method is suitable for univariate time series with trend and/or seasonal components.

Seasonal Autoregressive Integrated Moving-Average with Exogenous Regressors (SARIMAX): The Seasonal Autoregressive Integrated Moving-Average with Exogenous Regressors (SARIMAX) is an extension of the SARIMA model that also includes the modeling of exogenous variables. The method is suitable for univariate time series with trend and/or seasonal components and exogenous variables.

Vector Autoregression (VAR): The Vector Autoregression (VAR) method models the next step in each time series using an AR model. It is the generalization of AR to multiple parallel time series, e.g. multivariate time series. The method is suitable for multivariate time series without trend and seasonal components.

Vector Autoregression Moving-Average (VARMA): The Vector Autoregression Moving-Average (VARMA) method models the next step in each time series using an ARMA model. It is the generalization of ARMA to multiple parallel time series, e.g. multivariate time series. The 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. 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 Winter’s Exponential Smoothing (HWES): The Holt Winter’s Exponential Smoothing (HWES) also called the Triple Exponential Smoothing method 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.

Source:

11 Classical Time Series Forecasting Methods in Python (Cheat Sheet)