def mase_loss(y_test, y_pred, y_train, sp=1):
"""Mean absolute scaled error.
This scale-free error metric can be used to compare forecast methods on
a single
series and also to compare forecast accuracy between series. This metric
is well
suited to intermittent-demand series because it never gives infinite or
undefined
values.
Parameters
----------
y_test : pandas Series of shape = (fh,) where fh is the forecasting horizon
Ground truth (correct) target values.
y_pred : pandas Series of shape = (fh,)
Estimated target values.
y_train : pandas Series of shape = (n_obs,)
Observed training values.
sp : int
Seasonal periodicity of training data.
Returns
-------
loss : float
MASE loss
References
----------
..[1] Hyndman, R. J. (2006). "Another look at measures of forecast
accuracy", Foresight, Issue 4.
"""
# input checks
y_test = check_y(y_test)
y_pred = check_y(y_pred)
y_train = check_y(y_train)
check_equal_time_index(y_test, y_pred)
# check if training set is prior to test set
if y_train is not None:
check_time_index(y_train.index)
if y_train.index.max() >= y_test.min():
raise ValueError("Found `y_train` with time index which is not "
"before time index of `y_pred`")
# naive seasonal prediction
y_train = np.asarray(y_train)
y_pred_naive = y_train[:-sp]
# mean absolute error of naive seasonal prediction
mae_naive = np.mean(np.abs(y_train[sp:] - y_pred_naive))
# if training data is flat, mae may be zero,
# return np.nan to avoid divide by zero error
# and np.inf values
if mae_naive == 0:
return np.nan
else:
return np.mean(np.abs(y_test - y_pred)) / mae_naive
def remove_trend(x, coefs, time_index=None):
"""Remove trend from an array with a trend of given order along axis 0 or 1
Parameters
----------
x : array_like, shape=[n_samples, n_obs]
Time series data, each sample is de-trended separately
coefs : ndarray, shape=[n_samples, order + 1]
Fitted coefficients for each sample, single column means order zero,
two columns mean order 1
(linear), three columns mean order 2 (quadratic), etc
time_index : array-like, shape=[n_obs], optional (default=None)
Time series index for which to add the trend components
Returns
-------
xt : ndarray
The de-trended series is the residual of the linear regression of the
data on the trend of given order.
See Also
--------
fit_trend
add_trend
References
----------
Adapted from statsmodels (0.9.0), see
https://www.statsmodels.org/dev/_modules/statsmodels/tsa/tsatools.html
#detrend
"""
x = check_array(x)
# infer order from shape of given coefficients
order = coefs.shape[1] - 1
# special case, remove mean
if order == 0:
xt = x - coefs
return xt
else:
if time_index is None:
# if no time index is given, create range index
n_obs = x.shape[1]
time_index = np.arange(n_obs)
else:
# validate given time index
time_index = check_time_index(time_index)
if len(time_index) != x.shape[1]:
raise ValueError(
'Length of passed index does not match length of passed x')
poly_terms = np.vander(time_index, N=order + 1)
xt = x - np.dot(poly_terms, coefs.T).T
return xt
def add_trend(x, coefs, time_index=None):
"""Add trend to array for given fitted coefficients along axis 0 or 1,
inverse function to `remove_trend()`
Parameters
----------
x : array_like, shape=[n_samples, n_obs]
Time series data, each sample is treated separately
coefs : array-like, shape=[n_samples, order + 1]
fitted coefficients of polynomial order for each sample, one column
means order zero, two columns mean order 1
(linear), three columns mean order 2 (quadratic), etc
time_index : array-like, shape=[n_obs], optional (default=None)
Time series index for which to add the trend components
Returns
-------
xt : ndarray
The series with added trend.
See Also
-------
fit_trend
remove_trend
"""
x = check_array(x)
# infer order from shape of given coefficients
order = coefs.shape[1] - 1
# special case, add mean
if order == 0:
xt = x + coefs
else:
if time_index is None:
n_obs = x.shape[1]
time_index = np.arange(n_obs)
else:
# validate given time index
time_index = check_time_index(time_index)
if not len(time_index) == x.shape[1]:
raise ValueError(
'Length of passed index does not match length of passed x')
poly_terms = np.vander(time_index, N=order + 1)
xt = x + np.dot(poly_terms, coefs.T).T
return xt
def _get_duration(x, y=None, coerce_to_int=False, unit=None):
"""Compute duration of time index `x` or durations between time
points `x` and `y` if `y` is given
Parameters
----------
x : pd.Index, pd.Timestamp, pd.Period, int
y : pd.Timestamp, pd.Period, int, optional (default=None)
coerce_to_int : bool
If True, duration is returned as integer value for given unit
unit : str
Time unit
Returns
-------
ret : duration type
Duration
"""
if y is None:
x = check_time_index(x)
duration = x[-1] - x[0]
else:
assert isinstance(x, (int, np.integer, pd.Period, pd.Timestamp))
# check types allowing (np.integer, int) combinations to pass
assert type(x) is type(y) or (isinstance(x, (np.integer, int))
and isinstance(x, (np.integer, int)))
duration = x - y
# coerce to integer result for given time unit
if coerce_to_int and isinstance(
x, (pd.PeriodIndex, pd.DatetimeIndex, pd.Period, pd.Timestamp)):
if unit is None:
# try to get the unit from the data if not given
unit = _get_unit(x)
duration = _coerce_duration_to_int(duration, unit=unit)
return duration
def _check_y(y):
# allow for pd.Series
if isinstance(y, pd.Series):
y = y.index
return check_time_index(y)
def _set_oh_index(self, y):
self._oh_index = check_time_index(y.index)
