FourierFeatures#

class FourierFeatures(sp_list: List[Union[int, float]], fourier_terms_list: List[int], freq: Optional[str] = None, keep_original_columns: Optional[bool] = True)[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 number of time steps elapsed from the beginning of the time series.

The output of the trasform is a pandas DataFrame that includes the fourier terms as additional columns with the naming convention stated above (sin_sp_k and cos_sp_k). For instance for sp_list = [12, 3] and fourier_terms_list = [2, 1] the transformed series will have the additional columns: “cos_12_1”, “sin_12_1”, “cos_12_2”, “sin_12_2”, “cos_3_1”, “sin_3_1”

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

Parameters
sp_listList[Union[int, float]]

list of seasonal periods

fourier_terms_listList[int]

list of number of fourier terms (K) for each seasonal period. Each K matches to the sp (seasonal period) of the sp_list. For example, if sp_list = [7, 365] and fourier_terms_list = [3, 9], the seasonal frequency of 7 will have 3 fourier terms and the seasonal frequency of 365 will have 9 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=True

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.series.fourier import FourierFeatures
>>> transformer = FourierFeatures(sp_list=[12], fourier_terms_list=[4])
>>> y_hat = transformer.fit_transform(y)


Methods

 Check if the estimator has been fitted. Obtain a clone of the object with same hyper-parameters. clone_tags(estimator[, tag_names]) clone/mirror tags from another estimator as dynamic override. create_test_instance([parameter_set]) Construct Estimator instance if possible. 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 tag value from estimator class (only class tags). Get class tags from estimator class and all its parent classes. get_fitted_params([deep]) Get fitted parameters. Get parameter defaults for the object. Get parameter names for the object. get_params([deep]) Get parameters for this estimator. get_tag(tag_name[, tag_value_default, …]) Get tag value from estimator class and dynamic tag overrides. Get tags from estimator class and dynamic tag 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. Check if the object is composite. load_from_path(serial) Load object from file location. load_from_serial(serial) Load object from serialized memory container. Reset the object to a clean post-init state. save([path]) Save serialized self to bytes-like object or to (.zip) file. set_params(**params) Set the parameters of this object. set_tags(**tag_dict) Set dynamic tags to given values. transform(X[, y]) Transform X and return a transformed version. update(X[, y, update_params]) Update transformer with X, optionally y.
classmethod get_test_params(parameter_set='default')[source]#

Return testing parameter settings for the estimator.

Parameters
parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set. There are currently no reserved values for transformers.

Returns
paramsdict or list of dict, default = {}

Parameters to create testing instances of the class Each dict are parameters to construct an “interesting” test instance, i.e., MyClass(**params) or MyClass(**params[i]) creates a valid test instance. create_test_instance uses the first (or only) dictionary in params

check_is_fitted()[source]#

Check if the estimator has been fitted.

Raises
NotFittedError

If the estimator has not been fitted yet.

clone()[source]#

Obtain a clone of the object with same hyper-parameters.

A clone is a different object without shared references, in post-init state. This function is equivalent to returning sklearn.clone of self. Equal in value to type(self)(**self.get_params(deep=False)).

Returns
instance of type(self), clone of self (see above)
clone_tags(estimator, tag_names=None)[source]#

clone/mirror tags from another estimator as dynamic override.

Parameters
estimatorestimator inheriting from :class:BaseEstimator
tag_namesstr or list of str, default = None

Names of tags to clone. If None then all tags in estimator are used as tag_names.

Returns
Self

Reference to self.

Notes

Changes object state by setting tag values in tag_set from estimator as dynamic tags in self.

classmethod create_test_instance(parameter_set='default')[source]#

Construct Estimator instance if possible.

Parameters
parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns
instanceinstance of the class with default parameters

Notes

get_test_params can return dict or list of dict. This function takes first or single dict that get_test_params returns, and constructs the object with that.

classmethod create_test_instances_and_names(parameter_set='default')[source]#

Create list of all test instances and a list of names for them.

Parameters
parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns
objslist of instances of cls

i-th instance is cls(**cls.get_test_params()[i])

nameslist of str, same length as objs

i-th element is name of i-th instance of obj in tests convention is {cls.__name__}-{i} if more than one instance otherwise {cls.__name__}

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

fit(X, y=None)[source]#

Fit transformer to X, optionally to y.

State change:

Changes state to “fitted”.

Writes to self: _is_fitted : flag is set to True. _X : X, coerced copy of X, if remember_data tag is True

possibly coerced to inner type or update_data compatible type by reference, when possible

model attributes (ending in “_”) : dependent on estimator

Parameters
XSeries or Panel, any supported mtype
Data to fit transform to, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to sktime mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

Returns
selfa fitted instance of the estimator
fit_transform(X, y=None)[source]#

Fit to data, then transform it.

Fits the transformer to X and y and returns a transformed version of X.

State change:

Changes state to “fitted”.

Writes to self: _is_fitted : flag is set to True. _X : X, coerced copy of X, if remember_data tag is True

possibly coerced to inner type or update_data compatible type by reference, when possible

model attributes (ending in “_”) : dependent on estimator

Parameters
XSeries or Panel, any supported mtype
Data to be transformed, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to sktime mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

Returns
transformed version of X
type depends on type of X and scitype:transform-output tag:
X | tf-output | type of return |

|----------|————–|------------------------| | Series | Primitives | pd.DataFrame (1-row) | | Panel | Primitives | pd.DataFrame | | Series | Series | Series | | Panel | Series | Panel | | Series | Panel | Panel |

instances in return correspond to instances in X
combinations not in the table are currently not supported
Explicitly, with examples:
if X is Series (e.g., pd.DataFrame) and transform-output is Series

then the return is a single Series of the same mtype Example: detrending a single series

if X is Panel (e.g., pd-multiindex) and transform-output is Series
then the return is Panel with same number of instances as X

(the transformer is applied to each input Series instance)

Example: all series in the panel are detrended individually

if X is Series or Panel and transform-output is Primitives

then the return is pd.DataFrame with as many rows as instances in X Example: i-th row of the return has mean and variance of the i-th series

if X is Series and transform-output is Panel

then the return is a Panel object of type pd-multiindex Example: i-th instance of the output is the i-th window running over X

classmethod get_class_tag(tag_name, tag_value_default=None)[source]#

Get tag value from estimator class (only class tags).

Parameters
tag_namestr

Name of tag value.

tag_value_defaultany type

Returns
tag_value

Value of the tag_name tag in self. If not found, returns tag_value_default.

classmethod get_class_tags()[source]#

Get class tags from estimator class and all its parent classes.

Returns
collected_tagsdict

Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance. NOT overridden by dynamic tags set by set_tags or mirror_tags.

get_fitted_params(deep=True)[source]#

Get fitted parameters.

State required:

Requires state to be “fitted”.

Parameters
deepbool, default=True

Whether to return fitted parameters of components.

• If True, will return a dict of parameter name : value for this object, including fitted parameters of fittable components (= BaseEstimator-valued parameters).

• If False, will return a dict of parameter name : value for this object, but not include fitted parameters of components.

Returns
fitted_paramsdict with str-valued keys

Dictionary of fitted parameters, paramname : paramvalue keys-value pairs include:

• always: all fitted parameters of this object, as via get_param_names values are fitted parameter value for that key, of this object

• if deep=True, also contains keys/value pairs of component parameters parameters of components are indexed as [componentname]__[paramname] all parameters of componentname appear as paramname with its value

• if deep=True, also contains arbitrary levels of component recursion, e.g., [componentname]__[componentcomponentname]__[paramname], etc

classmethod get_param_defaults()[source]#

Get parameter defaults for the object.

Returns
default_dict: dict with str keys

keys are all parameters of cls that have a default defined in __init__ values are the defaults, as defined in __init__

classmethod get_param_names()[source]#

Get parameter names for the object.

Returns
param_names: list of str, alphabetically sorted list of parameter names of cls
get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns
paramsdict

Parameter names mapped to their values.

get_tag(tag_name, tag_value_default=None, raise_error=True)[source]#

Get tag value from estimator class and dynamic tag overrides.

Parameters
tag_namestr

Name of tag to be retrieved

tag_value_defaultany type, optional; default=None

raise_errorbool

Returns
tag_value

Value of the tag_name tag in self. If not found, returns an error if raise_error is True, otherwise it returns tag_value_default.

Raises
ValueError if raise_error is True i.e. if tag_name is not in self.get_tags(
).keys()
get_tags()[source]#

Get tags from estimator class and dynamic tag overrides.

Returns
collected_tagsdict

Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance and then any overrides and new tags from _tags_dynamic object attribute.

inverse_transform(X, y=None)[source]#

Inverse transform X and return an inverse transformed version.

Currently it is assumed that only transformers with tags

“scitype:transform-input”=”Series”, “scitype:transform-output”=”Series”,

have an inverse_transform.

State required:

Requires state to be “fitted”.

Accesses in self: _is_fitted : must be True _X : optionally accessed, only available if remember_data tag is True fitted model attributes (ending in “_”) : accessed by _inverse_transform

Parameters
XSeries or Panel, any supported mtype
Data to be inverse transformed, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to sktime mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

Returns
inverse transformed version of X

of the same type as X, and conforming to mtype format specifications

is_composite()[source]#

Check if the object is composite.

A composite object is an object which contains objects, as parameters. Called on an instance, since this may differ by instance.

Returns
composite: bool, whether self contains a parameter which is BaseObject
property is_fitted[source]#

Whether fit has been called.

Parameters
serialresult of ZipFile(path).open(“object)
Returns
deserialized self resulting in output at path, of cls.save(path)

Load object from serialized memory container.

Parameters
serial1st element of output of cls.save(None)
Returns
deserialized self resulting in output serial, of cls.save(None)
reset()[source]#

Reset the object to a clean post-init state.

Equivalent to sklearn.clone but overwrites self. After self.reset() call, self is equal in value to type(self)(**self.get_params(deep=False))

Detail behaviour: removes any object attributes, except:

hyper-parameters = arguments of __init__ object attributes containing double-underscores, i.e., the string “__”

runs __init__ with current values of hyper-parameters (result of get_params)

Not affected by the reset are: object attributes containing double-underscores class and object methods, class attributes

save(path=None)[source]#

Save serialized self to bytes-like object or to (.zip) file.

Behaviour: if path is None, returns an in-memory serialized self if path is a file location, stores self at that location as a zip file

saved files are zip files with following contents: _metadata - contains class of self, i.e., type(self) _obj - serialized self. This class uses the default serialization (pickle).

Parameters
pathNone or file location (str or Path)

if None, self is saved to an in-memory object if file location, self is saved to that file location. If:

path=”estimator” then a zip file estimator.zip will be made at cwd. path=”/home/stored/estimator” then a zip file estimator.zip will be stored in /home/stored/.

Returns
if path is None - in-memory serialized self
if path is file location - ZipFile with reference to the file
set_params(**params)[source]#

Set the parameters of this object.

The method works on simple estimators as well as on nested objects. The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters
**paramsdict

BaseObject parameters

Returns
selfreference to self (after parameters have been set)
set_tags(**tag_dict)[source]#

Set dynamic tags to given values.

Parameters
tag_dictdict

Dictionary of tag name : tag value pairs.

Returns
Self

Reference to self.

Notes

Changes object state by settting tag values in tag_dict as dynamic tags in self.

transform(X, y=None)[source]#

Transform X and return a transformed version.

State required:

Requires state to be “fitted”.

Accesses in self: _is_fitted : must be True _X : optionally accessed, only available if remember_data tag is True fitted model attributes (ending in “_”) : must be set, accessed by _transform

Parameters
XSeries or Panel, any supported mtype
Data to be transformed, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to sktime mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

Returns
transformed version of X
type depends on type of X and scitype:transform-output tag:

transform

X

-output

type of return

Series

Primitives

pd.DataFrame (1-row)

Panel

Primitives

pd.DataFrame

Series

Series

Series

Panel

Series

Panel

Series

Panel

Panel

instances in return correspond to instances in X
combinations not in the table are currently not supported
Explicitly, with examples:
if X is Series (e.g., pd.DataFrame) and transform-output is Series

then the return is a single Series of the same mtype Example: detrending a single series

if X is Panel (e.g., pd-multiindex) and transform-output is Series
then the return is Panel with same number of instances as X

(the transformer is applied to each input Series instance)

Example: all series in the panel are detrended individually

if X is Series or Panel and transform-output is Primitives

then the return is pd.DataFrame with as many rows as instances in X Example: i-th row of the return has mean and variance of the i-th series

if X is Series and transform-output is Panel

then the return is a Panel object of type pd-multiindex Example: i-th instance of the output is the i-th window running over X

update(X, y=None, update_params=True)[source]#

Update transformer with X, optionally y.

State required:

Requires state to be “fitted”.

Accesses in self: _is_fitted : must be True _X : accessed by _update and by update_data, if remember_data tag is True fitted model attributes (ending in “_”) : must be set, accessed by _update

Writes to self: _X : updated by values in X, via update_data, if remember_data tag is True fitted model attributes (ending in “_”) : only if update_params=True

type and nature of update are dependent on estimator

Parameters
XSeries or Panel, any supported mtype
Data to fit transform to, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to sktime mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

update_paramsbool, default=True

whether the model is updated. Yes if true, if false, simply skips call. argument exists for compatibility with forecasting module.

Returns
selfa fitted instance of the estimator