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ARIMA

Synopsis​

This operator trains an ARIMA model for a selected time series attribute.

Description​

ARIMA stands for Autoregressive Integrated Moving Average. Typically an ARIMA model is used for forecasting time series.

An ARIMA model is defined by its three order parameters, p, d, q. p specifies the number of Autoregressive terms in the model. d specifies the number of differentations applied on the time series values. q specifies the number of Moving Average terms in the model.

An ARIMA model is an integrated ARMA model. The ARMA model describes a time series by a weighted sum of lagged time series values (the Autoregressive terms) and a weighted sum of lagged residuals. These residuals originates from a normal distributed noise process. The "integrated" indicates that the values of the ARMA model are integrated, which is equal to that the original time series values which the ARMA model describes are differentiated.

The ARIMA operator fits an ARIMA model with given p,d,q to a time series by finding the p+q coefficients (and if estimate constant is true, the constant) which maximize the conditional loglikelihood of the model describing the time series. For the optimization the LBFGS (Limited-memory Broyden-Fletcher-Foldfarb-Shanno) algorithm is used.

If chosing values for p,d,q, it is important that the conditional loglikelihood is only a good estimation for the exact loglikelihood if the number of parameters (sum of p,d,q) is not in the order of the length of the time series. Hence the number of parameters should be way smaller than the length of the time series.

How well a trained ARIMA model describes a given time series is often calculated with the Akaikes Information Criterion (AIC), the Bayesian Information Criterion (BIC) or a corrected Akaikes Information Criterion (AICC). The ArimaTrainer operator calculates these performance measures and outputs a Performance Vector containing the calculated values. An ARIMA model which describes a time series well has small information criteria.

This operator works only on numerical time series.

Differentiation​

This operator is similar to other modeling operators, but is specifically designed to work on time series data. One of the implications of this is, that the forecast model should be applied on the same data it was trained on.

Apply Forecast​

This operator receives a trained Forecast Model (e.g. the ARIMA model) and creates the forecast for the time series it was trained on.

Default Forecast​

This operator trains a Default Forecast model (predicting single value) on time series data to perform a forecast.

Function and Seasonal Component Forecast​

This operator trains a Function and Seasonal Forecast model (combining fitted function and seasonal component values) on time series data to perform a forecast.

Holt-Winters​

This operator trains a Holt-Winters model (triple exponential smoothing) on time series data to perform a forecast.

Input​

example set​

The ExampleSet which contains the time series data as an attribute.

Output​

forecast model​

The ARIMA model (forecast model) fitted to the specified time series attribute. It also contains the original time series values.

performance​

This port delivers a performance vector of the fitted ARIMA model. The calculated performances are the AIC (Akaike information criterion), BIC ( Bayesian information criterion) and AICC (Akaike information criterion, corrected).

original​

The ExampleSet that was given as input is passed through without changes.

Parameters​

Time series attribute​

The time series attribute (numerical) for which the ARIMA model should be build. The required attribute can be selected from this option. The attribute name can be selected from the drop down box of the parameter if the meta data is known.

Has indices​

This parameter indicates if there is an index attribute associated with the time series. If this parameter is set to true, the index attribute has to be selected.

Indices attribute​

If the parameter has indices is set to true, this parameter defines the associated index attribute. It can be either a date, date_time or numeric value type attribute. The attribute name can be selected from the drop down box of the parameter if the meta data is known.

P: order of the autoregressive model​

The parameter p specifies the number of lags used by the autoregressive part of the ARIMA model.

D: degree of differencing​

The parameter d specifies how often the time series values are differentiated.

Q: order of the moving-average model​

The parameter q specifies the order of the moving-average part of the model.

Estimate constant​

This parameter indicates if the constant of the ARIMA process should be estimated or not.

Main criterion​

The performance measure which is used as the main criterion in the Performance Vector.

  • aic: Akaikes Information Criterion: Estimator of the relative quality of statistical models for a given set of data. The aic deals with the trade-off betwen the goodness of fit of the model and the simplicity of the model
  • bic: Bayesian Information Criterion: Similar to the aic, but with a larger penalty term for the number of parameters in the model.
  • aicc: corrected Akaikes Information Criterion: The aicc performance measure is the aic with a correction for small sample sizes, to prevent overfitting.