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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 ...
The notation ARMA(p, q) refers to the model with p autoregressive terms and q moving-average terms.This model contains the AR(p) and MA(q) models, [5]= + = + =. The general ARMA model was described in the 1951 thesis of Peter Whittle, who used mathematical analysis (Laurent series and Fourier analysis) and statistical inference.
Box–Jenkins method. 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 .
In statistics, autoregressive fractionally integrated moving average models are time series models that generalize ARIMA ( autoregressive integrated moving average) models by allowing non-integer values of the differencing parameter. These models are useful in modeling time series with long memory —that is, in which deviations from the long ...
Autoregressive model. In statistics, econometrics, and signal processing, an autoregressive ( AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own ...
[1] [2] 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, [3] which have a more complicated stochastic ...
Exponential smoothing. Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to ...