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ARMA is appropriate when a system is a function of a series of unobserved shocks (the MA or moving average part) as well as its own behavior. For example, stock prices may be shocked by fundamental information as well as exhibiting technical trending and mean-reversion effects due to market participants.
In time series analysis, the Box–Jenkins method, [1] named after the statisticians George Box and Gwilym Jenkins, applies autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) models to find the best fit of a time-series model to past values of a time series.
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 ...
Specifically, ARMA assumes that the series is stationary, that is, its expected value is constant in time. If instead the series has a trend (but a constant variance/autocovariance), the trend is removed by "differencing", [1] leaving a stationary series. This operation generalizes ARMA and corresponds to the "integrated" part of ARIMA ...
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.
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An ARMA(p, q) model's partial autocorrelation geometrically decays to 0 but only after lags greater than p. The behavior of the partial autocorrelation function mirrors that of the autocorrelation function for autoregressive and moving-average models.
If you've been having trouble with any of the connections or words in Saturday's puzzle, you're not alone and these hints should definitely help you out. Plus, I'll reveal the answers further down