TripleExponentialSmoothing

class hana_ml.algorithms.pal.tsa.exponential_smoothing.TripleExponentialSmoothing(alpha=None, beta=None, gamma=None, seasonal_period=None, forecast_num=None, seasonal=None, initial_method=None, phi=None, damped=None, accuracy_measure=None, ignore_zero=None, expost_flag=None, level_start=None, trend_start=None, season_start=None, prediction_confidence_1=None, prediction_confidence_2=None)

Triple exponential smoothing is used to handle the time series data containing a seasonal component.

Parameters:
alphafloat, optional

Weight for smoothing. Value range: 0 < alpha < 1.

Defaults to 0.1.

betafloat, optional

Weight for the trend component. Value range: 0 <= beta < 1.

Defaults to 0.1.

gammafloat, optional

Weight for the seasonal component. Value range: 0 < gamma < 1.

Defaults to 0.1.

seasonal_periodint, optional

Length of a seasonal_period(should be greater than 1).

For example, the seasonal_period of quarterly data is 4, and the seasonal_period of monthly data is 12.

Defaults to 2.

forecast_numint, optional

Number of values to be forecast.

Defaults to 0.

seasonal{'multiplicative', 'additive'}, optional

Specifies the type of model for triple exponential smoothing.

  • 'multiplicative': Multiplicative triple exponential smoothing.

  • 'additive': Additive triple exponential smoothing.

When seasonal is set to 'additive', the default value of initial_method is 1; When seasonal is set to 'multiplicative', the default value of initial_method is 0.

Defaults to 'multiplicative'.

initial_methodint, optional

Initialization method for the trend and seasonal components.

Defaults to 0 or 1, depending the setting of seasonal.

phifloat, optional

Value of the damped smoothing constant phi (0 < phi < 1).

Defaults to 0.1.

dampedbool, optional

Specifies whether or not to use damped trend method.

  • False: No, uses the Holt's linear trend method.

  • True: Yes, use damped trend method.

Defaults to False.

accuracy_measurestr or list of str, optional

The metric to quantify how well a model fits input data. Options: "mpe", "mse", "rmse", "et", "mad", "mase", "wmape", "smape", "mape".

No default value.

Note

Specify a measure name if you want the corresponding measure value to be reflected in the output statistics self.stats_.

ignore_zerobool, optional
  • False: Uses zero values in the input dataset when calculating "mpe" or "mape".

  • True: Ignores zero values in the input dataset when calculating "mpe" or "mape".

Only valid when accuracy_measure is "mpe" or "mape".

Defaults to False.

expost_flagbool, optional
  • False: Does not output the expost forecast, and just outputs the forecast values.

  • True: Outputs the expost forecast and the forecast values.

Defaults to True.

level_startfloat, optional

The initial value for level component S.

If this value is not provided, it will be calculated in the way as described in Triple Exponential Smoothing.

level_start cannot be zero. If it is set to zero, 0.0000000001 will be used instead.

trend_startfloat, optional

The initial value for trend component B.

season_startlist of tuple/float, optional

A list of initial values for seasonal component C. If specified, the list must be of the length specified in seasonal_period, i.e. start values must be provided for a whole seasonal period.

We can simply give out the start values in a list, where the cycle index of each value is determined by its index in the list; or we can give out the start values together with their cycle indices in a list of tuples.

For example, suppose the seasonal period is 4, with starting values \(x_i, 1 \leq i \leq 4\) indexed by their cycle ID. Then the four season start values can be specified in a list as \([x_1, x_2, x_3, x_4]\), or equivalently in a list of tuples as \([(1, x_1), (2, x_2), (3, x_3), (4, x_4)]\).

If not provided, start values shall be computed by a default scheme.

prediction_confidence_1float, optional

Prediction confidence for interval 1.

Only valid when the upper and lower columns are provided in the result table.

Defaults to 0.8.

prediction_confidence_2float, optional

Prediction confidence for interval 2.

Only valid when the upper and lower columns are provided in the result table.

Defaults to 0.95.

Examples

Input Dataframe df for TripleExponentialSmoothing:

>>> df.collect()
ID    RAW_DATA
 1       362.0
 2       385.0
 3       432.0
 4       341.0
 5       382.0
...
18       707.0
19       773.0
20       592.0
21       627.0
22       725.0
23       854.0
24       661.0

Create a TripleExponentialSmoothing instance:

>>> tesm = TripleExponentialSmoothing(alpha=0.822,
                                      beta=0.055,
                                      gamma=0.055,
                                      seasonal_period=4,
                                      forecast_num=6,
                                      seasonal=0,
                                      initial_method=0,
                                      phi=None,
                                      damped=None,
                                      accuracy_measure='mse',
                                      ignore_zero=None,
                                      expost_flag=True,
                                      level_start=None,
                                      trend_start=None,
                                      season_start=None,
                                      prediction_confidence_1=0.8,
                                      prediction_confidence_2=0.95)

Perform fit_predict() on the given data:

>>> tesm.fit_predict(data=df)

Output:

>>> tesm.forecast_.collect().set_index('TIMESTAMP').head(3)
TIMESTAMP           VALUE   PI1_LOWER    PI1_UPPER   PI2_LOWER    PI2_UPPER
       5       371.288158         NaN          NaN         NaN          NaN
       6       414.636207         NaN          NaN         NaN          NaN
       7       471.431808         NaN          NaN         NaN          NaN
>>> tesm.stats_.collect()
STAT_NAME        STAT_VALUE
      MSE        616.541542
Attributes:
forecast_DataFrame

Forecast values.

stats_DataFrame

Statistics analysis content.

Methods

fit_predict(data[, key, endog])

Fit and predict based on the given time series.

fit_predict(data, key=None, endog=None)

Fit and predict based on the given time series.

Parameters:
dataDataFrame

Input data. At least two columns, one is ID column, the other is raw data.

keystr, optional

The ID column.

Defaults to the first column of data if the index column of data is not provided. Otherwise, defaults to the index column of data.

endogstr, optional

The column of series to be fitted and predicted.

Defaults to the first non-ID column.

Returns:
DataFrame

Forecast values.

Inherited Methods from PALBase

Besides those methods mentioned above, the TripleExponentialSmoothing class also inherits methods from PALBase class, please refer to PAL Base for more details.