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In the statistical analysis of time series, autoregressive–moving-average (ARMA) models are a way to describe of a (weakly) stationary stochastic process using autoregression (AR) and a moving average (MA), each with a polynomial. They are a tool for understanding a series and predicting future values.
Together with the moving-average (MA) model, it is a special case and key component of the more general autoregressive–moving-average (ARMA) and autoregressive integrated moving average (ARIMA) models of time series, which have a more complicated stochastic structure; it is also a special case of the vector autoregressive model (VAR), which ...
Model identification and model selection: making sure that the variables are stationary, identifying seasonality in the dependent series (seasonally differencing it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide which (if any) autoregressive or ...
Non-seasonal ARIMA models are usually denoted ARIMA(p, d, q) where parameters p, d, q are non-negative integers: p is the order (number of time lags) of the autoregressive model, d is the degree of differencing (the number of times the data have had past values subtracted), and q is the order of the moving-average model.
SETAR models were introduced by Howell Tong in 1977 and more fully developed in the seminal paper (Tong and Lim, 1980). They can be thought of in terms of extension of autoregressive models, allowing for changes in the model parameters according to the value of weakly exogenous threshold variable z t, assumed to be past values of y, e.g. y t-d, where d is the delay parameter, triggering the ...
Polynomials of the lag operator can be used, and this is a common notation for ARMA (autoregressive moving average) models. For example, = = = (=) specifies an AR(p) model.A polynomial of lag operators is called a lag polynomial so that, for example, the ARMA model can be concisely specified as
Errors-in-variables model; Instrumental variables regression; Quantile regression; Generalized additive model; Autoregressive model; Moving average model; Autoregressive moving average model; Autoregressive integrated moving average; Autoregressive conditional heteroskedasticity
Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregressive model by allowing for multivariate time series .