Function and Seasonal Component Forecast

Synopsis

这个操作符的火车一个函数和季节性排版onent Forecast model.

Description

The model contains of a polynomial function which describes the trend of a time series and a seasonal component with length seasonality which describes the seasonal effects of a time series.

A forecast for a time series is created by evaluating the polynomial function to determine the trend values and adding or multiplying (depending on thedecomposition modeof the performed decomposition) the corresponding values of the seasonal component.

这个操作符火车一个函数和季节性混合涂料nent Forecast model by first performing a decomposition (for the type of decomposition see parameterdecomposition method) on thetime seriesto determine trend and seasonal component. The seasonal component is directly used for the Forecast model. A polynomial fit (degree specified by the parameterdegree) is performed on the trend values. The fitted function is provided to the Forecast model.

Ifno decompositionis selected, no decomposition is performed on the time series. The seasonal component will have a length of 1 and a value of 0. The polynomial fit is then performed on the original time series values and not on the decomposed trend values.

Ifno fitis selected, the polynomial function is not fitted and a constant with value 0 (in case thedecomposition modeisadditive) or 1 (in case thedecomposition modeismultiplicative) is used for the function.

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 Function and Seasonal Component Forecast model) and creates the forecast for the time series it was trained on.

ARIMA

This operator trains an ARIMA model (Autoregressive Integrated Moving Average) on time series data to perform a forecast.

Default Forecast

This operator trains a Default Forecast model (predicting single value) 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 Function and Seasonal Forecast model fitted to the specified time series attribute. It also contains the original time series values.

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 Function and Seasonal Component Forecast 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.

Indices attribute

The attribute holding the indices values of the time series. 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 know

Decomposition method

This parameter defines the kind of decomposition used to determine the trend and seasonal components of the time series. The seasonal component is directly used for the Function and Seasonal Forecast model, the trend component is used to fit the polynomial function to it.

no decomposition: No decomposition is performed. The seasonal component will have a length of 1 and a value of 0. The polynomial fit will be performed on the original time series values
经典的分解: A Classic Decomposition is performed (see operator Classic Decomposition).
STL decomposition: : A STL Decomposition is performed (see operator STL Decomposition). Thedecomposition modeis set toadditive.

Function fitting method

This parameter defines the method to fit the function for the Forecast model. The function is fitted on the decomposed trend values, if thedecomposition methodis notno decomposition. Then the fit is performed on the original time seires values.

no fit: The function is not fitted and a constant with value 0 (in case thedecomposition modeisadditive) or 1 (in case thedecomposition modeismultiplicative) is used for the function of the Forecast model.
polynomial function: A polynomial function of the degree specified by thedegreeparameter is fitted. Invalid values are ignored by this fit. See operator Extract Coefficients (Polynomial Fit) for more details.

Degree

This parameter is only visible iffunction fitting methodispolynomial fit. This parameter defines the degree of the polynomial function fitted to the time series.

Decomposition mode

This parameter is only visible ifdecomposition methodis经典的分解. The mode, how the different components are combined.

additive: Trend, seasonal and remainder component are added to build the time series: Y = T + S + R. Used if seasonal and remainder component are independent of the trend level.
multiplicative: Trend, seasonal and remainder component are multiplied to build the time series: Y = T x S x R. Used if the magnitude of seasonal and remainder component depends on the trend level.

Seasonality

This parameter is only visible ifdecomposition methodis经典的分解orSTL decomposition. The length of one seasonal pattern of the seasonal component. For example for a seasonal pattern which occurs every year the seasonality is 4 (for quartely data), 12 (for montly data) or 52 (for weekly data). Or for a pattern which occurs every hour the seasonality is 60 (for minutely data) or 3600 (for secondly data).

Ignore invalid values

This parameter is only visible ifdecomposition methodis经典的分解. If this parameter is set to true invalid values (missing, positive and negative infinity) are ignored in the computation of the trend component of the classic decomposition.

Default robust calculations

This parameter is only visible ifdecomposition methodisSTL decomposition. This parameter defines if the decomposition includes default settings for robust iterations to handle outliers. The number of inner iterations is set to 1 and the number of robust iterations to 15.

Inner iterations

This parameter is only visible ifdecomposition methodisSTL decomposition. This parameter defines the number of inner iterations performed to improve the accuracy of the estimation of the decomposition components.

Robust iterations

This parameter is only visible ifdecomposition methodisSTL decomposition. This parameter defines the number of robust (outer) iterations peformed to reduce the effect of outliers on the estimation of the trend and the seasonal component. Can be set to 0, if no outliers are expected in the data.

Seasonal smoothing settings

This parameter is only visible ifdecomposition methodisSTL decomposition. This parameter defines which settings of the seasonal smoothing are set by the user and which are set to default values by the operator. The seasonal smoothing has 3 parameters, theseasonal width,seasonal degreeand theseasonal jump. See the description of the individual parameters on their effects and their default settings.

default: Onlyseasonal widthhas to be specified.
periodic: This option contrains the seasonal component to be exactly periodic. All three parameters are set by the operator.
width and degree**seasonal widthandseasonal degreehave to be specified,seasonal jump** is set to the default value.
width and jump**seasonal widthandseasonal jumphave to be specified,seasonal degree** is set to the default value.
all: All three parameters have to be specified.

Seasonal width

This parameter is only visible ifdecomposition methodisSTL decomposition. The width of the Loess smoother to determine the seasonal components. Has to be larger than 2 and uneven. Ifseasonal widthis even, it is automatically increased by one. A largeseasonal widthreduce the rate of change of the seasonal component over time. Has always to be specified, except theseasonal smoothing settingsis set toperiodic. In this case theseasonal widthis set to 100 times the length of the time series.

Seasonal degree

This parameter is only visible ifdecomposition methodisSTL decomposition. The degree of the polynomial used in the Loess smoothing. Has to be 0, 1, or 2 and defaults to 1. If theseasonal smoothing settingsis set toperiodicthe degree is set to 0.

Seasonal jump

This parameter is only visible ifdecomposition methodisSTL decomposition. The number of points skipped between the Loess smoothing. Has to be larger than 0 and defaults to 10% of theseasonal width(ceiled).

Trend smoothing settings

This parameter is only visible ifdecomposition methodisSTL decomposition. This parameter defines which settings of the trend smoothing are set by the user and which are set to default values by the operator. The trend smoothing has 3 parameters, thetrend width,trend degreeand thetrend jump. See the description of the individual parameters on their effects and their default settings.

default: For all three parameters the default values are used.
flat: The trend component is forced to be flat. All three parameters are set by the operator.
linear: The trend component is forced to be linear. All three parameters are set by the operator.
width: Onlytrend widthhas to be specified.
degree: Onlytrend degreehas to be specified.
jump: Onlytrend jumphas to be specified.
width and degree**trend widthandtrend degreehave to be specified,trend jump** is set to the default value.
width and jump**trend widthandtrend jumphave to be specified,trend degree** is set to the default value.
degree and jump**trend degreeandtrend jumphave to be specified,trend width** is set to the default value.
all: All three parameters have to be specified.

Trend width

This parameter is only visible ifdecomposition methodisSTL decomposition. The width of the Loess smoother to determine the trend components. Has to be larger than 2 and uneven. Iftrend widthis even, it is automatically increased by one. Thetrend widthincreases the smoothing effect on the trend component. If thetrend smoothing settingsis set toflatorlinearthetrend widthis automatically set to 100 timesseasonalitytimes length of time series. If it is not specified by the user, thetrend widthdefaults to floor(1.5 xseasonality/ (1 - 1.5 /seasonal width) + 0.5).

Trend degree

This parameter is only visible ifdecomposition methodisSTL decomposition. The degree of the polynomial used in the Loess smoothing. Has to be 0, 1, or 2 and defaults to 1. If thetrend smoothing settingsis set toflatorlinearthetrend widthis automatically set 0 (flat) or 1 (linear).

Trend jump

Lowpass smoothing settings

This parameter is only visible ifdecomposition methodisSTL decomposition. This parameter defines which settings of the lowpass smoothing are set by the user and which are set to default values by the operator. The lowpass smoothing has 3 parameters, thelowpass width,低通的程度and thelowpass jump. See the description of the individual parameters on their effects and their default settings.

default: For all three parameters the default values are used.
width: Onlylowpass widthhas to be specified.
degree: Only低通的程度has to be specified.
jump: Onlylowpass jumphas to be specified.
width and degree**lowpass widthand低通的程度have to be specified,lowpass jump** is set to the default value.
width and jump**lowpass widthandlowpass jumphave to be specified,低通的程度** is set to the default value.
degree and jump**低通的程度andlowpass jumphave to be specified,lowpass width** is set to the default value.
all: All three parameters have to be specified.

Lowpass width

This parameter is only visible ifdecomposition methodisSTL decomposition. The width of the Loess smoother to smooth (and with that remove) the seasonal components from the time series data. Has to be larger than 2 and uneven. Iflowpass widthis even, it is automatically increased by one. If it is not specified by the user, thelowpass widthdefaults toseasonality.

Lowpass degree

This parameter is only visible ifdecomposition methodisSTL decomposition. The degree of the polynomial used in the Loess smoothing. Has to be 0, 1, or 2 and defaults to 1.