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Concept
Moving-average model
Résumé
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. The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable.
Together with the autoregressive (AR) model, the moving-average model is a special case and key component of the more general ARMA and ARIMA models of time series, which have a more complicated stochastic structure. Contrary to the AR model, the finite MA model is always stationary.
The moving-average model should not be confused with the moving average, a distinct concept despite some similarities.
The notation MA(q) refers to the moving average model of order q:
where is the mean of the series, the are the parameters of the model and the are white noise error terms. The value of q is called the order of the MA model. This can be equivalently written in terms of the backshift operator B as
Thus, a moving-average model is conceptually a linear regression of the current value of the series against current and previous (observed) white noise error terms or random shocks. The random shocks at each point are assumed to be mutually independent and to come from the same distribution, typically a normal distribution, with location at zero and constant scale.
The moving-average model is essentially a finite impulse response filter applied to white noise, with some additional interpretation placed on it. The role of the random shocks in the MA model differs from their role in the autoregressive (AR) model in two ways. First, they are propagated to future values of the time series directly: for example, appears directly on the right side of the equation for . In contrast, in an AR model does not appear on the right side of the equation, but it does appear on the right side of the equation, and appears on the right side of the equation, giving only an indirect effect of on .
Source officielle
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Proximité ontologique
Concepts associés (8)
Autoregressive integrated moving average
In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. To better comprehend the data or to forecast upcoming series points, both of these models are fitted to time series data. ARIMA models are applied in some cases where data show evidence of non-stationarity in the sense of mean (but not variance/autocovariance), where an initial differencing step (corresponding to the "integrated" part of the model) can be applied one or more times to eliminate the non-stationarity of the mean function (i.
Partial autocorrelation function
In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values, regressed the values of the time series at all shorter lags. It contrasts with the autocorrelation function, which does not control for other lags. This function plays an important role in data analysis aimed at identifying the extent of the lag in an autoregressive (AR) model.
Vecteur Autoregressif (VAR)
Le modèle à Vecteur Autoregressif (VAR) est un modèle économique qui permet de capturer les interdépendances entre plusieurs séries temporelles. Il s'agit de la principale catégorie de modèle statistique. Dans un modèle VAR, les variables sont traitées symétriquement de manière que chacune d'entre elles soit expliquée par ses propres valeurs passées et par les valeurs passées des autres variables. De ce fait, les modèles VAR mobilisent des bases de données importantes.