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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.
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 .
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 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.
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.
In statistics, a moving average (rolling average or running average or moving mean [1] or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. Variations include: simple, cumulative, or weighted forms. Mathematically, a moving average is a type of convolution.
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 ...
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