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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.
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models are a way to describe 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.
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.
Plotting the partial autocorrelation function and drawing the lines of the confidence interval is a common way to analyze the order of an AR model. To evaluate the order, one examines the plot to find the lag after which the partial autocorrelations are all within the confidence interval. This lag is determined to likely be the AR model's order ...
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.
The moving ranges involved are serially correlated so runs or cycles can show up on the moving average chart that do not indicate real problems in the underlying process. [ 2 ] : 237 In some cases, it may be advisable to use the median of the moving range rather than its average, as when the calculated range data contains a few large values ...
This test is sometimes known as the Ljung–Box Q test, and it is closely connected to the Box–Pierce test (which is named after George E. P. Box and David A. Pierce). In fact, the Ljung–Box test statistic was described explicitly in the paper that led to the use of the Box–Pierce statistic, [ 1 ] [ 2 ] and from which that statistic takes ...