Autoregressive Integrated Moving Average (ARIMA) Modeling System

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An Autoregressive Integrated Moving Average (ARIMA) Modeling System is univariate timeseries modeling system that applies an ARIMA algorithm (to solve an ARIMA-based task that requires an trained ARIMA structure).



References

2020a

  • (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average Retrieved:2020-9-6.
    • 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. Both of these models are fitted to time series data either to better understand the data or to predict future points in the series (forecasting). ARIMA models are applied in some cases where data show evidence of non-stationarity, 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. [1] The part of ARIMA indicates that the evolving variable of interest is regressed on its own lagged (i.e., prior) values. The part indicates that the regression error is actually a linear combination of error terms whose values occurred contemporaneously and at various times in the past. The (for "integrated") indicates that the data values have been replaced with the difference between their values and the previous values (and this differencing process may have been performed more than once). The purpose of each of these features is to make the model fit the data as well as possible. Non-seasonal ARIMA models are generally denoted ARIMA(p,d,q) where parameters p, d, and 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. Seasonal ARIMA models are usually denoted ARIMA(p,d,q)(P,D,Q)m, where m refers to the number of periods in each season, and the uppercase P,D,Q refer to the autoregressive, differencing, and moving average terms for the seasonal part of the ARIMA model.

      When two out of the three terms are zeros, the model may be referred to based on the non-zero parameter, dropping "", "" or "" from the acronym describing the model. For example, is AR(1), is I(1), and is MA(1).

      ARIMA models can be estimated following the Box–Jenkins approach.

  1. For further information on Stationarity and Differencing see https://www.otexts.org/fpp/8/1

2020b

2003

  1. G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, "Time Series Analysis Forecasting and Control", Third ed. Englewood Cliffs, NJ: PrenticeHall, 1994.