FourierFeatures

FourierFeatures

class FourierFeatures(sp_list: list[float], fourier_terms_list: list[int], freq: str | None = None, keep_original_columns: bool | None = False)[source]

Fourier Features for time series seasonality.

Fourier Series terms can be used as explanatory variables for the cases of multiple seasonal periods and or complex / long seasonal periods [1], [2]. For every seasonal period, \(sp\) and fourier term \(k\) pair there are 2 fourier terms sin_sp_k and cos_sp_k:

• sin_sp_k = \(sin(\frac{2 \pi k t}{sp})\)

• cos_sp_k = \(cos(\frac{2 \pi k t}{sp})\)

Where \(t\) is the elapsed time since the beginning of the seasonal period and \(sp\) the total time of the seasonal period.

The transformed output is a series that contains all requested Fourier terms.

Warning: the output will contain only the Fourier terms under default settings, and discard the original columns of the input data, to avoid multiplication of the original data in a pipeline or FeatureUnion. To keep the original columns, set keep_original_columns=True.

Names of the columns are generated as follows: additional columns with the naming convention stated above (sin_sp_k and cos_sp_k). The numbers of Fourier terms \(K\) in the fourier_terms_list determines the number of Fourier terms that will be used for each seasonal period, i.e., Fourier terms \(k = 1\dots K\) (integers), cos and sine, will be generated for the seasonality \(sp\) at the same list index. For example, consider sp_list = [12, “Y”] and fourier_terms_list = [2, 1]. This says that we compute 2 (2 cos, 2 sine) Fourier terms for seasonality 12 periods, and 1 Fourier term (1 cos and 1 sine) for seasonality 1 year. The transformed series will then have columns with the following names: “cos_12_1”, “sin_12_1”, “cos_12_2”, “sin_12_2”, “cos_Y_1”, “sin_Y_1”

The implementation is based on the fourier function from the R forecast package [3]

Parameters:

sp_listList[float and/or str]

List of seasonal periods. Can be defined with the following options:

• float : Periodicity defined as number of timesteps since the beginning of the data seen in fit.
• string : Periodicity defined as a column name in X that contains the \(t/sp\) values.
• string : Periodicity defined as a pandas period alias: https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#period-aliases

fourier_terms_listList[int]

List of number of fourier terms (\(K\)) per corresponding (\(sp\)); each \(K\) matches to one \(sp\) of the sp_list. For example, if sp_list = [7, “Y”] and fourier_terms_list = [3, 9], the seasonality of 7 timesteps will have 3 sin_sp_k and 3 cos_sp_k fourier terms and the yearly seasonality “Y” will have 9 sin_sp_k and 9 cos_sp_k fourier terms.

freqstr, optional, default = None

Only used when X has a pd.DatetimeIndex without a specified frequency. Specifies the frequency of the index of your data. The string should match a pandas offset alias:

https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#offset-aliases

keep_original_columnsboolean, optional, default=False

Keep original columns in X passed to .transform()

Attributes:

is_fitted

Whether fit has been called.

References

[1]

Hyndsight - Forecasting with long seasonal periods: https://robjhyndman.com/hyndsight/longseasonality/

[2]

Hyndman, R.J., & Athanasopoulos, G. (2021) Forecasting: principles and practice, 3rd edition, OTexts: Melbourne, Australia. OTexts.com/fpp3. Accessed on August 14th 2022.

[3]

https://pkg.robjhyndman.com/forecast/reference/fourier.html

Examples

>>> from sktime.transformations.fourier import FourierFeatures
>>> from sktime.datasets import load_airline
>>> y = load_airline()
>>> transformer = FourierFeatures(sp_list=[12, "Y"], fourier_terms_list=[4, 1])
>>> y_hat = transformer.fit_transform(y)

Methods

check_is_fitted([method_name])	Check if the estimator has been fitted.
clone()	Obtain a clone of the object with same hyper-parameters and config.
clone_tags(estimator[, tag_names])	Clone tags from another object as dynamic override.
create_test_instance([parameter_set])	Construct an instance of the class, using first test parameter set.
create_test_instances_and_names([parameter_set])	Create list of all test instances and a list of names for them.
fit(X[, y])	Fit transformer to X, optionally to y.
fit_transform(X[, y])	Fit to data, then transform it.
get_class_tag(tag_name[, tag_value_default])	Get class tag value from class, with tag level inheritance from parents.
get_class_tags()	Get class tags from class, with tag level inheritance from parent classes.
get_config()	Get config flags for self.
get_fitted_params([deep])	Get fitted parameters.
get_param_defaults()	Get object's parameter defaults.
get_param_names([sort])	Get object's parameter names.
get_params([deep])	Get a dict of parameters values for this object.
get_tag(tag_name[, tag_value_default, ...])	Get tag value from instance, with tag level inheritance and overrides.
get_tags()	Get tags from instance, with tag level inheritance and overrides.
get_test_params([parameter_set])	Return testing parameter settings for the estimator.
inverse_transform(X[, y])	Inverse transform X and return an inverse transformed version.
is_composite()	Check if the object is composed of other BaseObjects.
load_from_path(serial)	Load object from file location.
load_from_serial(serial)	Load object from serialized memory container.
reset()	Reset the object to a clean post-init state.
save([path, serialization_format])	Save serialized self to bytes-like object or to (.zip) file.
set_config(**config_dict)	Set config flags to given values.
set_params(**params)	Set the parameters of this object.
set_random_state([random_state, deep, ...])	Set random_state pseudo-random seed parameters for self.
set_tags(**tag_dict)	Set instance level tag overrides to given values.
transform(X[, y])	Transform X and return a transformed version.
update(X[, y, update_params])	Update transformer with X, optionally y.