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).
- Example(s):
- statsmodels.tsa.arima_model, within statsmodels.tsa.
- statsmodels.tsa.statespace.SARIMAX, withing statsmodels.tsa.
- …
- Counter-Example(s):
- See: ARMA-based System, Box–Jenkins Method, Statistics, Econometrics, Time Series Analysis, Mathematical Model, Autoregressive Moving Average, Time Series, Forecasting, Stationary Process, Order of Integration, Linear Regression, Errors And Residuals in Statistics.
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.
- 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.
- ↑ For further information on Stationarity and Differencing see https://www.otexts.org/fpp/8/1
2020b
- (Duke, 2020b) https://people.duke.edu/~rnau/411arim.htm
- QUOTE: ARIMA models are, in theory, the most general class of models for forecasting a time series which can be made to be “stationary” by differencing (if necessary), perhaps in conjunction with nonlinear transformations such as logging or deflating (if necessary). A random variable that is a time series is stationary if its statistical properties are all constant over time. A stationary series has no trend, its variations around its mean have a constant amplitude, and it wiggles in a consistent fashion, i.e., its short-term random time patterns always look the same in a statistical sense. The latter condition means that its autocorrelations (correlations with its own prior deviations from the mean) remain constant over time, or equivalently, that its power spectrum remains constant over time. A random variable of this form can be viewed (as usual) as a combination of signal and noise, and the signal (if one is apparent) could be a pattern of fast or slow mean reversion, or sinusoidal oscillation, or rapid alternation in sign, and it could also have a seasonal component. An ARIMA model can be viewed as a “filter” that tries to separate the signal from the noise, and the signal is then extrapolated into the future to obtain forecasts.
2003
- (Contreras et al., 2003) ⇒ Javier Contreras, Rosario Espinola, Francisco J. Nogales, and Antonio J. Conejo. "ARIMA Models To Predict Next-Day Electricity Prices". In: IEEE transactions on power systems, 18(3), 1014-1020.
- QUOTE: ARIMA processes are a class of stochastic processes used to analyze time series. The application of the ARIMA methodology for the study of time series analysis is due to Box and Jenkins [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.