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The model is usually denoted ARMA(p, q), where p is the order of AR and q is the order of MA. The general ARMA model was described in the 1951 thesis of Peter Whittle , Hypothesis testing in time series analysis , and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins .
In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. [ 1 ] [ 2 ] The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable.
Moving average model, order identified by where plot becomes zero. Decay, starting after a few lags Mixed autoregressive and moving average model. All zero or close to zero Data are essentially random. High values at fixed intervals Include seasonal autoregressive term. No decay to zero (or it decays extremely slowly) Series is not stationary.
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.
Moving average; Moving-average model; Moving average representation – redirects to Wold's theorem; Moving least squares; Multi-armed bandit; Multi-vari chart; Multiclass classification; Multiclass LDA (linear discriminant analysis) – redirects to Linear discriminant analysis; Multicollinearity; Multidimensional analysis; Multidimensional ...
The acronyms "ARFIMA" or "FARIMA" are often used, although it is also conventional to simply extend the "ARIMA(p, d, q)" notation for models, by simply allowing the order of differencing, d, to take fractional values.
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The autoregressive fractionally integrated moving-average (ARFIMA) model generalizes the former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector ...