Source code for statsmodels.tsa.holtwinters.model
"""
Notes
-----
Code written using below textbook as a reference.
Results are checked against the expected outcomes in the text book.
Properties:
Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and
practice. OTexts, 2014.
Author: Terence L van Zyl
Modified: Kevin Sheppard
"""
from statsmodels.compat.pandas import deprecate_kwarg
import contextlib
from typing import Any
from collections.abc import Hashable, Sequence
import warnings
import numpy as np
import pandas as pd
from scipy.optimize import basinhopping, least_squares, minimize
from scipy.special import inv_boxcox
from scipy.stats import boxcox
from statsmodels.tools.validation import (
array_like,
bool_like,
dict_like,
float_like,
int_like,
string_like,
)
from statsmodels.tsa.base.tsa_model import TimeSeriesModel
from statsmodels.tsa.exponential_smoothing.ets import (
_initialization_heuristic,
_initialization_simple,
)
from statsmodels.tsa.holtwinters import (
_exponential_smoothers as smoothers,
_smoothers as py_smoothers,
)
from statsmodels.tsa.holtwinters._exponential_smoothers import HoltWintersArgs
from statsmodels.tsa.holtwinters._smoothers import (
to_restricted,
to_unrestricted,
)
from statsmodels.tsa.holtwinters.results import (
HoltWintersResults,
HoltWintersResultsWrapper,
)
from statsmodels.tsa.tsatools import freq_to_period
SMOOTHERS = {
("mul", "add"): smoothers.holt_win_add_mul_dam,
("mul", "mul"): smoothers.holt_win_mul_mul_dam,
("mul", None): smoothers.holt_win__mul,
("add", "add"): smoothers.holt_win_add_add_dam,
("add", "mul"): smoothers.holt_win_mul_add_dam,
("add", None): smoothers.holt_win__add,
(None, "add"): smoothers.holt_add_dam,
(None, "mul"): smoothers.holt_mul_dam,
(None, None): smoothers.holt__,
}
PY_SMOOTHERS = {
("mul", "add"): py_smoothers.holt_win_add_mul_dam,
("mul", "mul"): py_smoothers.holt_win_mul_mul_dam,
("mul", None): py_smoothers.holt_win__mul,
("add", "add"): py_smoothers.holt_win_add_add_dam,
("add", "mul"): py_smoothers.holt_win_mul_add_dam,
("add", None): py_smoothers.holt_win__add,
(None, "add"): py_smoothers.holt_add_dam,
(None, "mul"): py_smoothers.holt_mul_dam,
(None, None): py_smoothers.holt__,
}
def opt_wrapper(func):
def f(*args, **kwargs):
err = func(*args, **kwargs)
if isinstance(err, np.ndarray):
return err.T @ err
return err
return f
class _OptConfig:
alpha: float
beta: float
phi: float
gamma: float
level: float
trend: float
seasonal: np.ndarray
y: np.ndarray
params: np.ndarray
mask: np.ndarray
mle_retvals: Any
def unpack_parameters(self, params) -> "_OptConfig":
self.alpha = params[0]
self.beta = params[1]
self.gamma = params[2]
self.level = params[3]
self.trend = params[4]
self.phi = params[5]
self.seasonal = params[6:]
return self
[docs]
class ExponentialSmoothing(TimeSeriesModel):
"""
Holt Winter's Exponential Smoothing
Parameters
----------
endog : array_like
The time series to model.
trend : {"add", "mul", "additive", "multiplicative", None}, optional
Type of trend component.
damped_trend : bool, optional
Should the trend component be damped.
seasonal : {"add", "mul", "additive", "multiplicative", None}, optional
Type of seasonal component.
seasonal_periods : int, optional
The number of periods in a complete seasonal cycle, e.g., 4 for
quarterly data or 7 for daily data with a weekly cycle.
initialization_method : str, optional
Method for initialize the recursions. One of:
* None
* 'estimated'
* 'heuristic'
* 'legacy-heuristic'
* 'known'
None defaults to the pre-0.12 behavior where initial values
are passed as part of ``fit``. If any of the other values are
passed, then the initial values must also be set when constructing
the model. If 'known' initialization is used, then `initial_level`
must be passed, as well as `initial_trend` and `initial_seasonal` if
applicable. Default is 'estimated'. "legacy-heuristic" uses the same
values that were used in statsmodels 0.11 and earlier.
initial_level : float, optional
The initial level component. Required if estimation method is "known".
If set using either "estimated" or "heuristic" this value is used.
This allows one or more of the initial values to be set while
deferring to the heuristic for others or estimating the unset
parameters.
initial_trend : float, optional
The initial trend component. Required if estimation method is "known".
If set using either "estimated" or "heuristic" this value is used.
This allows one or more of the initial values to be set while
deferring to the heuristic for others or estimating the unset
parameters.
initial_seasonal : array_like, optional
The initial seasonal component. An array of length `seasonal`
or length `seasonal - 1` (in which case the last initial value
is computed to make the average effect zero). Only used if
initialization is 'known'. Required if estimation method is "known".
If set using either "estimated" or "heuristic" this value is used.
This allows one or more of the initial values to be set while
deferring to the heuristic for others or estimating the unset
parameters.
use_boxcox : {True, False, 'log', float}, optional
Should the Box-Cox transform be applied to the data first? If 'log'
then apply the log. If float then use the value as lambda.
bounds : dict[str, tuple[float, float]], optional
An dictionary containing bounds for the parameters in the model,
excluding the initial values if estimated. The keys of the dictionary
are the variable names, e.g., smoothing_level or initial_slope.
The initial seasonal variables are labeled initial_seasonal.<j>
for j=0,...,m-1 where m is the number of period in a full season.
Use None to indicate a non-binding constraint, e.g., (0, None)
constrains a parameter to be non-negative.
dates : array_like of datetime, optional
An array-like object of datetime objects. If a Pandas object is given
for endog, it is assumed to have a DateIndex.
freq : str, optional
The frequency of the time-series. A Pandas offset or 'B', 'D', 'W',
'M', 'A', or 'Q'. This is optional if dates are given.
missing : str
Available options are 'none', 'drop', and 'raise'. If 'none', no nan
checking is done. If 'drop', any observations with nans are dropped.
If 'raise', an error is raised. Default is 'none'.
Notes
-----
This is a full implementation of the holt winters exponential smoothing as
per [1]_. This includes all the unstable methods as well as the stable
methods. The implementation of the library covers the functionality of the
R library as much as possible whilst still being Pythonic.
See the notebook `Exponential Smoothing
<../examples/notebooks/generated/exponential_smoothing.html>`__
for an overview.
References
----------
.. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles
and practice. OTexts, 2014.
"""
@deprecate_kwarg("damped", "damped_trend")
def __init__(
self,
endog,
trend=None,
damped_trend=False,
seasonal=None,
*,
seasonal_periods=None,
initialization_method="estimated",
initial_level=None,
initial_trend=None,
initial_seasonal=None,
use_boxcox=False,
bounds=None,
dates=None,
freq=None,
missing="none",
):
super().__init__(endog, None, dates, freq, missing=missing)
self._y = self._data = array_like(
endog, "endog", ndim=1, contiguous=True, order="C"
)
options = ("add", "mul", "additive", "multiplicative")
trend = string_like(trend, "trend", options=options, optional=True)
if trend in ["additive", "multiplicative"]:
trend = {"additive": "add", "multiplicative": "mul"}[trend]
self.trend = trend
self.damped_trend = bool_like(damped_trend, "damped_trend")
seasonal = string_like(
seasonal, "seasonal", options=options, optional=True
)
if seasonal in ["additive", "multiplicative"]:
seasonal = {"additive": "add", "multiplicative": "mul"}[seasonal]
self.seasonal = seasonal
self.has_trend = trend in ["mul", "add"]
self.has_seasonal = seasonal in ["mul", "add"]
if (self.trend == "mul" or self.seasonal == "mul") and not np.all(
self._data > 0.0
):
raise ValueError(
"endog must be strictly positive when using"
"multiplicative trend or seasonal components."
)
if self.damped_trend and not self.has_trend:
raise ValueError("Can only dampen the trend component")
if self.has_seasonal:
self.seasonal_periods = int_like(
seasonal_periods, "seasonal_periods", optional=True
)
if seasonal_periods is None:
try:
self.seasonal_periods = freq_to_period(self._index_freq)
except Exception:
raise ValueError(
"seasonal_periods has not been provided and index "
"does not have a known freq. You must provide "
"seasonal_periods"
)
if self.seasonal_periods <= 1:
raise ValueError("seasonal_periods must be larger than 1.")
assert self.seasonal_periods is not None
else:
self.seasonal_periods = 0
self.nobs = len(self.endog)
options = ("known", "estimated", "heuristic", "legacy-heuristic")
self._initialization_method = string_like(
initialization_method,
"initialization_method",
optional=False,
options=options,
)
self._initial_level = float_like(
initial_level, "initial_level", optional=True
)
self._initial_trend = float_like(
initial_trend, "initial_trend", optional=True
)
self._initial_seasonal = array_like(
initial_seasonal, "initial_seasonal", optional=True
)
estimated = self._initialization_method == "estimated"
self._estimate_level = estimated
self._estimate_trend = estimated and self.trend is not None
self._estimate_seasonal = estimated and self.seasonal is not None
self._bounds = self._check_bounds(bounds)
self._use_boxcox = use_boxcox
self._lambda = np.nan
self._y = self._boxcox()
self._initialize()
self._fixed_parameters = {}
def _check_bounds(self, bounds):
bounds = dict_like(bounds, "bounds", optional=True)
if bounds is None:
return
msg = (
"bounds must be a dictionary of 2-element tuples of the form"
" (lb, ub) where lb < ub, lb>=0 and ub<=1"
)
variables = self._ordered_names()
for key in bounds:
if key not in variables:
supported = ", ".join(variables[:-1])
supported += ", and " + variables[-1]
raise KeyError(
f"{key} does not match the list of supported variables "
f"names: {supported}."
)
bound = bounds[key]
if not isinstance(bound, tuple):
raise TypeError(msg)
lb = bound[0] if bound[0] is not None else -np.inf
ub = bound[1] if bound[1] is not None else np.inf
if len(bound) != 2 or lb >= ub:
raise ValueError(msg)
if ("smoothing" in key or "damp" in key) and (
bound[0] < 0.0 or bound[1] > 1.0
):
raise ValueError(
f"{key} must have a lower bound >= 0.0 and <= 1.0"
)
return bounds
def _boxcox(self):
if self._use_boxcox is None or self._use_boxcox is False:
self._lambda = np.nan
return self._y
if self._use_boxcox is True:
y, self._lambda = boxcox(self._y)
elif isinstance(self._use_boxcox, (int, float)):
self._lambda = float(self._use_boxcox)
y = boxcox(self._y, self._use_boxcox)
else:
raise TypeError("use_boxcox must be True, False or a float.")
return y
[docs]
@contextlib.contextmanager
def fix_params(self, values):
"""
Temporarily fix parameters for estimation.
Parameters
----------
values : dict
Values to fix. The key is the parameter name and the value is the
fixed value.
Yields
------
None
No value returned.
Examples
--------
>>> from statsmodels.datasets.macrodata import load_pandas
>>> data = load_pandas()
>>> import statsmodels.tsa.api as tsa
>>> mod = tsa.ExponentialSmoothing(data.data.realcons, trend="add",
... initialization_method="estimated")
>>> with mod.fix_params({"smoothing_level": 0.2}):
... mod.fit()
"""
values = dict_like(values, "values")
valid_keys = ("smoothing_level",)
if self.has_trend:
valid_keys += ("smoothing_trend",)
if self.has_seasonal:
valid_keys += ("smoothing_seasonal",)
m = self.seasonal_periods
valid_keys += tuple([f"initial_seasonal.{i}" for i in range(m)])
if self.damped_trend:
valid_keys += ("damping_trend",)
if self._initialization_method in ("estimated", None):
extra_keys = [
key.replace("smoothing_", "initial_")
for key in valid_keys
if "smoothing_" in key
]
valid_keys += tuple(extra_keys)
for key in values:
if key not in valid_keys:
valid = ", ".join(valid_keys[:-1]) + ", and " + valid_keys[-1]
raise KeyError(
f"{key} if not allowed. Only {valid} are supported in "
"this specification."
)
if "smoothing_level" in values:
alpha = values["smoothing_level"]
if alpha <= 0.0:
raise ValueError("smoothing_level must be in (0, 1)")
beta = values.get("smoothing_trend", 0.0)
if beta > alpha:
raise ValueError("smoothing_trend must be <= smoothing_level")
gamma = values.get("smoothing_seasonal", 0.0)
if gamma > 1 - alpha:
raise ValueError(
"smoothing_seasonal must be <= 1 - smoothing_level"
)
try:
self._fixed_parameters = values
yield
finally:
self._fixed_parameters = {}
def _initialize(self):
if self._initialization_method == "known":
return self._initialize_known()
msg = (
f"initialization method is {self._initialization_method} but "
"initial_{0} has been set."
)
if self._initial_level is not None:
raise ValueError(msg.format("level"))
if self._initial_trend is not None:
raise ValueError(msg.format("trend"))
if self._initial_seasonal is not None:
raise ValueError(msg.format("seasonal"))
if self._initialization_method == "legacy-heuristic":
return self._initialize_legacy()
elif self._initialization_method == "heuristic":
return self._initialize_heuristic()
elif self._initialization_method == "estimated":
if self.nobs < 10 + 2 * (self.seasonal_periods // 2):
return self._initialize_simple()
else:
return self._initialize_heuristic()
def _initialize_simple(self):
trend = self.trend if self.has_trend else False
seasonal = self.seasonal if self.has_seasonal else False
lvl, trend, seas = _initialization_simple(
self._y, trend, seasonal, self.seasonal_periods
)
self._initial_level = lvl
self._initial_trend = trend
self._initial_seasonal = seas
def _initialize_heuristic(self):
trend = self.trend if self.has_trend else False
seasonal = self.seasonal if self.has_seasonal else False
lvl, trend, seas = _initialization_heuristic(
self._y, trend, seasonal, self.seasonal_periods
)
self._initial_level = lvl
self._initial_trend = trend
self._initial_seasonal = seas
def _initialize_legacy(self):
lvl, trend, seasonal = self.initial_values(force=True)
self._initial_level = lvl
self._initial_trend = trend
self._initial_seasonal = seasonal
def _initialize_known(self):
msg = "initialization is 'known' but initial_{0} not given"
if self._initial_level is None:
raise ValueError(msg.format("level"))
excess = "initial_{0} set but model has no {0} component"
if self.has_trend and self._initial_trend is None:
raise ValueError(msg.format("trend"))
elif not self.has_trend and self._initial_trend is not None:
raise ValueError(excess.format("trend"))
if self.has_seasonal and self._initial_seasonal is None:
raise ValueError(msg.format("seasonal"))
elif not self.has_seasonal and self._initial_seasonal is not None:
raise ValueError(excess.format("seasonal"))
[docs]
def predict(self, params, start=None, end=None):
"""
In-sample and out-of-sample prediction.
Parameters
----------
params : ndarray
The fitted model parameters.
start : int, str, or datetime
Zero-indexed observation number at which to start forecasting, ie.,
the first forecast is start. Can also be a date string to
parse or a datetime type.
end : int, str, or datetime
Zero-indexed observation number at which to end forecasting, ie.,
the first forecast is start. Can also be a date string to
parse or a datetime type.
Returns
-------
ndarray
The predicted values.
"""
if start is None:
freq = getattr(self._index, "freq", 1)
if isinstance(freq, int):
start = self._index.shape[0]
else:
start = self._index[-1] + freq
start, end, out_of_sample, _ = self._get_prediction_index(
start=start, end=end
)
if out_of_sample > 0:
res = self._predict(h=out_of_sample, **params)
else:
res = self._predict(h=0, **params)
return res.fittedfcast[start : end + out_of_sample + 1]
def _enforce_bounds(self, p, sel, lb, ub):
initial_p = p[sel]
# Ensure strictly inbounds
loc = initial_p <= lb
upper = ub[loc].copy()
upper[~np.isfinite(upper)] = 100.0
eps = 1e-4
initial_p[loc] = lb[loc] + eps * (upper - lb[loc])
loc = initial_p >= ub
lower = lb[loc].copy()
lower[~np.isfinite(lower)] = -100.0
eps = 1e-4
initial_p[loc] = ub[loc] - eps * (ub[loc] - lower)
return initial_p
@staticmethod
def _check_blocked_keywords(
d: dict, keys: Sequence[Hashable], name="kwargs"
):
for key in keys:
if key in d:
raise ValueError(f"{name} must not contain '{key}'")
def _check_bound_feasibility(self, bounds):
if bounds[1][0] > bounds[0][1]:
raise ValueError(
"The bounds for smoothing_trend and smoothing_level are "
"incompatible since smoothing_trend <= smoothing_level."
)
if bounds[2][0] > (1 - bounds[0][1]):
raise ValueError(
"The bounds for smoothing_seasonal and smoothing_level "
"are incompatible since smoothing_seasonal <= "
"1 - smoothing_level."
)
@staticmethod
def _setup_brute(sel, bounds, alpha):
# More points when fewer parameters
ns = 87 // sel[:3].sum()
if not sel[0]:
# Easy case since no cross-constraints
nparams = int(sel[1]) + int(sel[2])
args = []
for i in range(1, 3):
if sel[i]:
bound = bounds[i]
step = bound[1] - bound[0]
lb = bound[0] + 0.005 * step
if i == 1:
ub = min(bound[1], alpha) - 0.005 * step
else:
ub = min(bound[1], 1 - alpha) - 0.005 * step
args.append(np.linspace(lb, ub, ns))
points = np.stack(np.meshgrid(*args))
points = points.reshape((nparams, -1)).T
return np.ascontiguousarray(points)
bound = bounds[0]
step = 0.005 * (bound[1] - bound[0])
points = np.linspace(bound[0] + step, bound[1] - step, ns)
if not sel[1] and not sel[2]:
return points[:, None]
combined = []
b_bounds = bounds[1]
g_bounds = bounds[2]
if sel[1] and sel[2]:
for a in points:
b_lb = b_bounds[0]
b_ub = min(b_bounds[1], a)
g_lb = g_bounds[0]
g_ub = min(g_bounds[1], 1 - a)
if b_lb > b_ub or g_lb > g_ub:
# infeasible point
continue
nb = int(np.ceil(ns * np.sqrt(a)))
ng = int(np.ceil(ns * np.sqrt(1 - a)))
b = np.linspace(b_lb, b_ub, nb)
g = np.linspace(g_lb, g_ub, ng)
both = np.stack(np.meshgrid(b, g)).reshape(2, -1).T
final = np.empty((both.shape[0], 3))
final[:, 0] = a
final[:, 1:] = both
combined.append(final)
elif sel[1]:
for a in points:
b_lb = b_bounds[0]
b_ub = min(b_bounds[1], a)
if b_lb > b_ub:
# infeasible point
continue
nb = int(np.ceil(ns * np.sqrt(a)))
final = np.empty((nb, 2))
final[:, 0] = a
final[:, 1] = np.linspace(b_lb, b_ub, nb)
combined.append(final)
else: # sel[2]
for a in points:
g_lb = g_bounds[0]
g_ub = min(g_bounds[1], 1 - a)
if g_lb > g_ub:
# infeasible point
continue
ng = int(np.ceil(ns * np.sqrt(1 - a)))
final = np.empty((ng, 2))
final[:, 1] = np.linspace(g_lb, g_ub, ng)
final[:, 0] = a
combined.append(final)
return np.vstack(combined)
def _ordered_names(self):
names = (
"smoothing_level",
"smoothing_trend",
"smoothing_seasonal",
"initial_level",
"initial_trend",
"damping_trend",
)
m = self.seasonal_periods
names += tuple([f"initial_seasonal.{i}" for i in range(m)])
return names
def _update_for_fixed(self, sel, alpha, beta, gamma, phi, l0, b0, s0):
if self._fixed_parameters:
fixed = self._fixed_parameters
names = self._ordered_names()
not_fixed = np.array([name not in fixed for name in names])
if (~sel[~not_fixed]).any():
invalid = []
for name, s, nf in zip(names, sel, not_fixed):
if not s and not nf:
invalid.append(name)
invalid_names = ", ".join(invalid)
raise ValueError(
"Cannot fix a parameter that is not being "
f"estimated: {invalid_names}"
)
sel &= not_fixed
alpha = fixed.get("smoothing_level", alpha)
beta = fixed.get("smoothing_trend", beta)
gamma = fixed.get("smoothing_seasonal", gamma)
phi = fixed.get("damping_trend", phi)
l0 = fixed.get("initial_level", l0)
b0 = fixed.get("initial_trend", b0)
for i in range(self.seasonal_periods):
s0[i] = fixed.get(f"initial_seasonal.{i}", s0[i])
return sel, alpha, beta, gamma, phi, l0, b0, s0
def _construct_bounds(self):
trend_lb = 0.0 if self.trend == "mul" else None
season_lb = 0.0 if self.seasonal == "mul" else None
lvl_lb = None if trend_lb is None and season_lb is None else 0.0
bounds = [
(0.0, 1.0), # alpha
(0.0, 1.0), # beta
(0.0, 1.0), # gamma
(lvl_lb, None), # level
(trend_lb, None), # trend
(0.8, 0.995), # phi
]
bounds += [(season_lb, None)] * self.seasonal_periods
if self._bounds is not None:
assert isinstance(self._bounds, dict)
for i, name in enumerate(self._ordered_names()):
bounds[i] = self._bounds.get(name, bounds[i])
# Update bounds to account for fixed parameters
fixed = self._fixed_parameters
if "smoothing_level" in fixed:
# Update bounds if fixed alpha
alpha = fixed["smoothing_level"]
# beta <= alpha
if bounds[1][1] > alpha:
bounds[1] = (bounds[1][0], alpha)
# gamma <= 1 - alpha
if bounds[2][1] > (1 - alpha):
bounds[2] = (bounds[2][0], 1 - alpha)
# gamma <= 1 - alpha
if "smoothing_trend" in fixed:
# beta <= alpha
beta = fixed["smoothing_trend"]
bounds[0] = (max(beta, bounds[0][0]), bounds[0][1])
if "smoothing_seasonal" in fixed:
gamma = fixed["smoothing_seasonal"]
# gamma <= 1 - alpha => alpha <= 1 - gamma
bounds[0] = (bounds[0][0], min(1 - gamma, bounds[0][1]))
# Ensure bounds are feasible
for i, name in enumerate(self._ordered_names()):
lb = bounds[i][0] if bounds[i][0] is not None else -np.inf
ub = bounds[i][1] if bounds[i][1] is not None else np.inf
if lb >= ub:
raise ValueError(
"After adjusting for user-provided bounds fixed values, "
f"the resulting set of bounds for {name}, {bounds[i]}, "
"are infeasible."
)
self._check_bound_feasibility(bounds)
return bounds
def _get_starting_values(
self,
params,
start_params,
use_brute,
sel,
hw_args,
bounds,
alpha,
func,
):
if start_params is None and use_brute and np.any(sel[:3]):
# Have a quick look in the region for a good starting place for
# alpha, beta & gamma using fixed values for initial
m = self.seasonal_periods
sv_sel = np.array([False] * (6 + m))
sv_sel[:3] = True
sv_sel &= sel
hw_args.xi = sv_sel.astype(int)
hw_args.transform = False
# Setup the grid points, respecting constraints
points = self._setup_brute(sv_sel, bounds, alpha)
opt = opt_wrapper(func)
best_val = np.inf
best_params = points[0]
for point in points:
val = opt(point, hw_args)
if val < best_val:
best_params = point
best_val = val
params[sv_sel] = best_params
elif start_params is not None:
if len(start_params) != sel.sum():
msg = "start_params must have {0} values but has {1}."
nxi, nsp = len(sel), len(start_params)
raise ValueError(msg.format(nxi, nsp))
params[sel] = start_params
return params
def _optimize_parameters(
self, data: _OptConfig, use_brute, method, kwargs
) -> _OptConfig:
# Prepare starting values
alpha = data.alpha
beta = data.beta
phi = data.phi
gamma = data.gamma
y = data.y
start_params = data.params
has_seasonal = self.has_seasonal
has_trend = self.has_trend
trend = self.trend
seasonal = self.seasonal
damped_trend = self.damped_trend
m = self.seasonal_periods
params = np.zeros(6 + m)
l0, b0, s0 = self.initial_values(
initial_level=data.level, initial_trend=data.trend
)
init_alpha = alpha if alpha is not None else 0.5 / max(m, 1)
init_beta = beta
if beta is None and has_trend:
init_beta = 0.1 * init_alpha
init_gamma = gamma
if has_seasonal and gamma is None:
init_gamma = 0.05 * (1 - init_alpha)
init_phi = phi if phi is not None else 0.99
# Selection of parameters to optimize
sel = np.array(
[
alpha is None,
has_trend and beta is None,
has_seasonal and gamma is None,
self._estimate_level,
self._estimate_trend,
damped_trend and phi is None,
]
+ [has_seasonal and self._estimate_seasonal] * m,
)
(
sel,
init_alpha,
init_beta,
init_gamma,
init_phi,
l0,
b0,
s0,
) = self._update_for_fixed(
sel, init_alpha, init_beta, init_gamma, init_phi, l0, b0, s0
)
func = SMOOTHERS[(seasonal, trend)]
params[:6] = [init_alpha, init_beta, init_gamma, l0, b0, init_phi]
if m:
params[-m:] = s0
if not np.any(sel):
from statsmodels.tools.sm_exceptions import EstimationWarning
message = (
"Model has no free parameters to estimate. Set "
"optimized=False to suppress this warning"
)
warnings.warn(message, EstimationWarning, stacklevel=3)
data = data.unpack_parameters(params)
data.params = params
data.mask = sel
return data
orig_bounds = self._construct_bounds()
bounds = np.array(orig_bounds[:3], dtype=float)
hw_args = HoltWintersArgs(
sel.astype(int), params, bounds, y, m, self.nobs
)
params = self._get_starting_values(
params,
start_params,
use_brute,
sel,
hw_args,
bounds,
init_alpha,
func,
)
# We always use [0, 1] for a, b and g and handle transform inside
mod_bounds = [(0, 1)] * 3 + orig_bounds[3:]
relevant_bounds = [bnd for bnd, flag in zip(mod_bounds, sel) if flag]
bounds = np.array(relevant_bounds, dtype=float)
lb, ub = bounds.T
lb[np.isnan(lb)] = -np.inf
ub[np.isnan(ub)] = np.inf
hw_args.xi = sel.astype(int)
# Ensure strictly inbounds
initial_p = self._enforce_bounds(params, sel, lb, ub)
# Transform to unrestricted space
params[sel] = initial_p
params[:3] = to_unrestricted(params, sel, hw_args.bounds)
initial_p = params[sel]
# Ensure parameters are transformed internally
hw_args.transform = True
if method in ("least_squares", "ls"):
# Least squares uses a different format for bounds
ls_bounds = lb, ub
self._check_blocked_keywords(kwargs, ("args", "bounds"))
res = least_squares(
func, initial_p, bounds=ls_bounds, args=(hw_args,), **kwargs
)
success = res.success
elif method in ("basinhopping", "bh"):
# Take a deeper look in the local minimum we are in to find the
# best solution to parameters, maybe hop around to try escape the
# local minimum we may be in.
minimizer_kwargs = {"args": (hw_args,), "bounds": relevant_bounds}
kwargs = kwargs.copy()
if "minimizer_kwargs" in kwargs:
self._check_blocked_keywords(
kwargs["minimizer_kwargs"],
("args", "bounds"),
name="kwargs['minimizer_kwargs']",
)
minimizer_kwargs.update(kwargs["minimizer_kwargs"])
del kwargs["minimizer_kwargs"]
default_kwargs = {
"minimizer_kwargs": minimizer_kwargs,
"stepsize": 0.01,
}
default_kwargs.update(kwargs)
obj = opt_wrapper(func)
res = basinhopping(obj, initial_p, **default_kwargs)
success = res.lowest_optimization_result.success
else:
obj = opt_wrapper(func)
self._check_blocked_keywords(kwargs, ("args", "bounds", "method"))
res = minimize(
obj,
initial_p,
args=(hw_args,),
bounds=relevant_bounds,
method=method,
**kwargs,
)
success = res.success
# finally transform to restricted space
params[sel] = res.x
params[:3] = to_restricted(params, sel, hw_args.bounds)
res.x = params[sel]
if not success:
from statsmodels.tools.sm_exceptions import ConvergenceWarning
warnings.warn(
"Optimization failed to converge. Check mle_retvals.",
ConvergenceWarning,
)
params[sel] = res.x
data.unpack_parameters(params)
data.params = params
data.mask = sel
data.mle_retvals = res
return data
[docs]
@deprecate_kwarg("smoothing_slope", "smoothing_trend")
@deprecate_kwarg("initial_slope", "initial_trend")
@deprecate_kwarg("damping_slope", "damping_trend")
def fit(
self,
smoothing_level=None,
smoothing_trend=None,
smoothing_seasonal=None,
damping_trend=None,
*,
optimized=True,
remove_bias=False,
start_params=None,
method=None,
minimize_kwargs=None,
use_brute=True,
use_boxcox=None,
use_basinhopping=None,
initial_level=None,
initial_trend=None,
):
"""
Fit the model
Parameters
----------
smoothing_level : float, optional
The alpha value of the simple exponential smoothing, if the value
is set then this value will be used as the value.
smoothing_trend : float, optional
The beta value of the Holt's trend method, if the value is
set then this value will be used as the value.
smoothing_seasonal : float, optional
The gamma value of the holt winters seasonal method, if the value
is set then this value will be used as the value.
damping_trend : float, optional
The phi value of the damped method, if the value is
set then this value will be used as the value.
optimized : bool, optional
Estimate model parameters by maximizing the log-likelihood.
remove_bias : bool, optional
Remove bias from forecast values and fitted values by enforcing
that the average residual is equal to zero.
start_params : array_like, optional
Starting values to used when optimizing the fit. If not provided,
starting values are determined using a combination of grid search
and reasonable values based on the initial values of the data. See
the notes for the structure of the model parameters.
method : str, default "L-BFGS-B"
The minimizer used. Valid options are "L-BFGS-B" , "TNC",
"SLSQP" (default), "Powell", "trust-constr", "basinhopping" (also
"bh") and "least_squares" (also "ls"). basinhopping tries multiple
starting values in an attempt to find a global minimizer in
non-convex problems, and so is slower than the others.
minimize_kwargs : dict[str, Any]
A dictionary of keyword arguments passed to SciPy's minimize
function if method is one of "L-BFGS-B", "TNC",
"SLSQP", "Powell", or "trust-constr", or SciPy's basinhopping
or least_squares functions. The valid keywords are optimizer
specific. Consult SciPy's documentation for the full set of
options.
use_brute : bool, optional
Search for good starting values using a brute force (grid)
optimizer. If False, a naive set of starting values is used.
use_boxcox : {True, False, 'log', float}, optional
Should the Box-Cox transform be applied to the data first? If 'log'
then apply the log. If float then use the value as lambda.
.. deprecated:: 0.12
Set use_boxcox when constructing the model
use_basinhopping : bool, optional
Deprecated. Using Basin Hopping optimizer to find optimal values.
Use ``method`` instead.
.. deprecated:: 0.12
Use ``method`` instead.
initial_level : float, optional
Value to use when initializing the fitted level.
.. deprecated:: 0.12
Set initial_level when constructing the model
initial_trend : float, optional
Value to use when initializing the fitted trend.
.. deprecated:: 0.12
Set initial_trend when constructing the model
or set initialization_method.
Returns
-------
HoltWintersResults
See statsmodels.tsa.holtwinters.HoltWintersResults.
Notes
-----
This is a full implementation of the holt winters exponential smoothing
as per [1]. This includes all the unstable methods as well as the
stable methods. The implementation of the library covers the
functionality of the R library as much as possible whilst still
being Pythonic.
The parameters are ordered
[alpha, beta, gamma, initial_level, initial_trend, phi]
which are then followed by m seasonal values if the model contains
a seasonal smoother. Any parameter not relevant for the model is
omitted. For example, a model that has a level and a seasonal
component, but no trend and is not damped, would have starting
values
[alpha, gamma, initial_level, s0, s1, ..., s<m-1>]
where sj is the initial value for seasonal component j.
References
----------
[1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles
and practice. OTexts, 2014.
"""
# Variable renames to alpha,beta, etc as this helps with following the
# mathematical notation in general
alpha = float_like(smoothing_level, "smoothing_level", True)
beta = float_like(smoothing_trend, "smoothing_trend", True)
gamma = float_like(smoothing_seasonal, "smoothing_seasonal", True)
phi = float_like(damping_trend, "damping_trend", True)
initial_level = float_like(initial_level, "initial_level", True)
initial_trend = float_like(initial_trend, "initial_trend", True)
start_params = array_like(start_params, "start_params", optional=True)
minimize_kwargs = dict_like(
minimize_kwargs, "minimize_kwargs", optional=True
)
minimize_kwargs = {} if minimize_kwargs is None else minimize_kwargs
use_basinhopping = bool_like(
use_basinhopping, "use_basinhopping", optional=True
)
supported_methods = ("basinhopping", "bh")
supported_methods += ("least_squares", "ls")
supported_methods += (
"L-BFGS-B",
"TNC",
"SLSQP",
"Powell",
"trust-constr",
)
method = string_like(
method,
"method",
options=supported_methods,
lower=False,
optional=True,
)
# TODO: Deprecate initial_level and related parameters from fit
if initial_level is not None or initial_trend is not None:
raise ValueError(
"Initial values were set during model construction. These "
"cannot be changed during fit."
)
if use_boxcox is not None:
raise ValueError(
"use_boxcox was set at model initialization and cannot "
"be changed"
)
elif self._use_boxcox is None:
use_boxcox = False
else:
use_boxcox = self._use_boxcox
if use_basinhopping is not None:
raise ValueError(
"use_basinhopping is deprecated. Set optimization method "
"using 'method'."
)
data = self._data
damped = self.damped_trend
phi = phi if damped else 1.0
if self._use_boxcox is None:
if use_boxcox == "log":
lamda = 0.0
y = boxcox(data, lamda)
elif isinstance(use_boxcox, float):
lamda = use_boxcox
y = boxcox(data, lamda)
elif use_boxcox:
y, lamda = boxcox(data)
# use_boxcox = lamda
else:
y = data.squeeze()
else:
y = self._y
self._y = y
res = _OptConfig()
res.alpha = alpha
res.beta = beta
res.phi = phi
res.gamma = gamma
res.level = initial_level
res.trend = initial_trend
res.seasonal = None
res.y = y
res.params = start_params
res.mle_retvals = res.mask = None
method = "SLSQP" if method is None else method
if optimized:
res = self._optimize_parameters(
res, use_brute, method, minimize_kwargs
)
else:
l0, b0, s0 = self.initial_values(
initial_level=initial_level, initial_trend=initial_trend
)
res.level = l0
res.trend = b0
res.seasonal = s0
if self._fixed_parameters:
fp = self._fixed_parameters
res.alpha = fp.get("smoothing_level", res.alpha)
res.beta = fp.get("smoothing_trend", res.beta)
res.gamma = fp.get("smoothing_seasonal", res.gamma)
res.phi = fp.get("damping_trend", res.phi)
res.level = fp.get("initial_level", res.level)
res.trend = fp.get("initial_trend", res.trend)
res.seasonal = fp.get("initial_seasonal", res.seasonal)
hwfit = self._predict(
h=0,
smoothing_level=res.alpha,
smoothing_trend=res.beta,
smoothing_seasonal=res.gamma,
damping_trend=res.phi,
initial_level=res.level,
initial_trend=res.trend,
initial_seasons=res.seasonal,
use_boxcox=use_boxcox,
remove_bias=remove_bias,
is_optimized=res.mask,
)
hwfit._results.mle_retvals = res.mle_retvals
return hwfit
[docs]
def initial_values(
self, initial_level=None, initial_trend=None, force=False
):
"""
Compute initial values used in the exponential smoothing recursions.
Parameters
----------
initial_level : {float, None}
The initial value used for the level component.
initial_trend : {float, None}
The initial value used for the trend component.
force : bool
Force the calculation even if initial values exist.
Returns
-------
initial_level : float
The initial value used for the level component.
initial_trend : {float, None}
The initial value used for the trend component.
initial_seasons : list
The initial values used for the seasonal components.
Notes
-----
Convenience function the exposes the values used to initialize the
recursions. When optimizing parameters these are used as starting
values.
Method used to compute the initial value depends on when components
are included in the model. In a simple exponential smoothing model
without trend or a seasonal components, the initial value is set to the
first observation. When a trend is added, the trend is initialized
either using y[1]/y[0], if multiplicative, or y[1]-y[0]. When the
seasonal component is added the initialization adapts to account for
the modified structure.
"""
if self._initialization_method is not None and not force:
return (
self._initial_level,
self._initial_trend,
self._initial_seasonal,
)
y = self._y
trend = self.trend
seasonal = self.seasonal
has_seasonal = self.has_seasonal
has_trend = self.has_trend
m = self.seasonal_periods
l0 = initial_level
b0 = initial_trend
if has_seasonal:
l0 = y[np.arange(self.nobs) % m == 0].mean() if l0 is None else l0
if b0 is None and has_trend:
# TODO: Fix for short m
lead, lag = y[m : m + m], y[:m]
if trend == "mul":
b0 = np.exp((np.log(lead.mean()) - np.log(lag.mean())) / m)
else:
b0 = ((lead - lag) / m).mean()
s0 = list(y[:m] / l0) if seasonal == "mul" else list(y[:m] - l0)
elif has_trend:
l0 = y[0] if l0 is None else l0
if b0 is None:
b0 = y[1] / y[0] if trend == "mul" else y[1] - y[0]
s0 = []
else:
if l0 is None:
l0 = y[0]
b0 = None
s0 = []
return l0, b0, s0
@deprecate_kwarg("smoothing_slope", "smoothing_trend")
@deprecate_kwarg("damping_slope", "damping_trend")
def _predict(
self,
h=None,
smoothing_level=None,
smoothing_trend=None,
smoothing_seasonal=None,
initial_level=None,
initial_trend=None,
damping_trend=None,
initial_seasons=None,
use_boxcox=None,
lamda=None,
remove_bias=None,
is_optimized=None,
):
"""
Helper prediction function
Parameters
----------
h : int, optional
The number of time steps to forecast ahead.
"""
# Variable renames to alpha, beta, etc as this helps with following the
# mathematical notation in general
alpha = smoothing_level
beta = smoothing_trend
gamma = smoothing_seasonal
phi = damping_trend
# Start in sample and out of sample predictions
data = self.endog
damped = self.damped_trend
has_seasonal = self.has_seasonal
has_trend = self.has_trend
trend = self.trend
seasonal = self.seasonal
m = self.seasonal_periods
phi = phi if damped else 1.0
if use_boxcox == "log":
lamda = 0.0
y = boxcox(data, 0.0)
elif isinstance(use_boxcox, float):
lamda = use_boxcox
y = boxcox(data, lamda)
elif use_boxcox:
y, lamda = boxcox(data)
else:
lamda = None
y = data.squeeze()
if np.ndim(y) != 1:
raise NotImplementedError("Only 1 dimensional data supported")
y_alpha = np.zeros((self.nobs,))
y_gamma = np.zeros((self.nobs,))
alphac = 1 - alpha
y_alpha[:] = alpha * y
betac = 1 - beta if beta is not None else 0
gammac = 1 - gamma if gamma is not None else 0
if has_seasonal:
y_gamma[:] = gamma * y
lvls = np.zeros((self.nobs + h + 1,))
b = np.zeros((self.nobs + h + 1,))
s = np.zeros((self.nobs + h + m + 1,))
lvls[0] = initial_level
b[0] = initial_trend
s[:m] = initial_seasons
phi_h = (
np.cumsum(np.repeat(phi, h + 1) ** np.arange(1, h + 1 + 1))
if damped
else np.arange(1, h + 1 + 1)
)
trended = {"mul": np.multiply, "add": np.add, None: lambda l, b: l}[
trend
]
detrend = {"mul": np.divide, "add": np.subtract, None: lambda l, b: 0}[
trend
]
dampen = {"mul": np.power, "add": np.multiply, None: lambda b, phi: 0}[
trend
]
nobs = self.nobs
if seasonal == "mul":
for i in range(1, nobs + 1):
lvls[i] = y_alpha[i - 1] / s[i - 1] + (
alphac * trended(lvls[i - 1], dampen(b[i - 1], phi))
)
if has_trend:
b[i] = (beta * detrend(lvls[i], lvls[i - 1])) + (
betac * dampen(b[i - 1], phi)
)
s[i + m - 1] = y_gamma[i - 1] / trended(
lvls[i - 1], dampen(b[i - 1], phi)
) + (gammac * s[i - 1])
_trend = b[1 : nobs + 1].copy()
season = s[m : nobs + m].copy()
lvls[nobs:] = lvls[nobs]
if has_trend:
b[:nobs] = dampen(b[:nobs], phi)
b[nobs:] = dampen(b[nobs], phi_h)
trend = trended(lvls, b)
s[nobs + m - 1 :] = [
s[(nobs - 1) + j % m] for j in range(h + 1 + 1)
]
fitted = trend * s[:-m]
elif seasonal == "add":
for i in range(1, nobs + 1):
lvls[i] = (
y_alpha[i - 1]
- (alpha * s[i - 1])
+ (alphac * trended(lvls[i - 1], dampen(b[i - 1], phi)))
)
if has_trend:
b[i] = (beta * detrend(lvls[i], lvls[i - 1])) + (
betac * dampen(b[i - 1], phi)
)
s[i + m - 1] = (
y_gamma[i - 1]
- (gamma * trended(lvls[i - 1], dampen(b[i - 1], phi)))
+ (gammac * s[i - 1])
)
_trend = b[1 : nobs + 1].copy()
season = s[m : nobs + m].copy()
lvls[nobs:] = lvls[nobs]
if has_trend:
b[:nobs] = dampen(b[:nobs], phi)
b[nobs:] = dampen(b[nobs], phi_h)
trend = trended(lvls, b)
s[nobs + m - 1 :] = [
s[(nobs - 1) + j % m] for j in range(h + 1 + 1)
]
fitted = trend + s[:-m]
else:
for i in range(1, nobs + 1):
lvls[i] = y_alpha[i - 1] + (
alphac * trended(lvls[i - 1], dampen(b[i - 1], phi))
)
if has_trend:
b[i] = (beta * detrend(lvls[i], lvls[i - 1])) + (
betac * dampen(b[i - 1], phi)
)
_trend = b[1 : nobs + 1].copy()
season = s[m : nobs + m].copy()
lvls[nobs:] = lvls[nobs]
if has_trend:
b[:nobs] = dampen(b[:nobs], phi)
b[nobs:] = dampen(b[nobs], phi_h)
trend = trended(lvls, b)
fitted = trend
level = lvls[1 : nobs + 1].copy()
if use_boxcox or use_boxcox == "log" or isinstance(use_boxcox, float):
fitted = inv_boxcox(fitted, lamda)
err = fitted[: -h - 1] - data
sse = err.T @ err
# (s0 + gamma) + (b0 + beta) + (l0 + alpha) + phi
k = m * has_seasonal + 2 * has_trend + 2 + 1 * damped
aic = self.nobs * np.log(sse / self.nobs) + k * 2
dof_eff = self.nobs - k - 3
if dof_eff > 0:
aicc_penalty = (2 * (k + 2) * (k + 3)) / dof_eff
else:
aicc_penalty = np.inf
aicc = aic + aicc_penalty
bic = self.nobs * np.log(sse / self.nobs) + k * np.log(self.nobs)
resid = data - fitted[: -h - 1]
if remove_bias:
fitted += resid.mean()
self.params = {
"smoothing_level": alpha,
"smoothing_trend": beta,
"smoothing_seasonal": gamma,
"damping_trend": phi if damped else np.nan,
"initial_level": lvls[0],
"initial_trend": b[0] / phi if phi > 0 else 0,
"initial_seasons": s[:m],
"use_boxcox": use_boxcox,
"lamda": lamda,
"remove_bias": remove_bias,
}
# Format parameters into a DataFrame
codes = ["alpha", "beta", "gamma", "l.0", "b.0", "phi"]
codes += [f"s.{i}" for i in range(m)]
idx = [
"smoothing_level",
"smoothing_trend",
"smoothing_seasonal",
"initial_level",
"initial_trend",
"damping_trend",
]
idx += [f"initial_seasons.{i}" for i in range(m)]
formatted = [alpha, beta, gamma, lvls[0], b[0], phi]
formatted += s[:m].tolist()
formatted = list(map(lambda v: np.nan if v is None else v, formatted))
formatted = np.array(formatted)
if is_optimized is None:
optimized = np.zeros(len(codes), dtype=bool)
else:
optimized = is_optimized.astype(bool)
included = [True, has_trend, has_seasonal, True, has_trend, damped]
included += [True] * m
formatted = pd.DataFrame(
[[c, f, o] for c, f, o in zip(codes, formatted, optimized)],
columns=["name", "param", "optimized"],
index=idx,
)
formatted = formatted.loc[included]
hwfit = HoltWintersResults(
self,
self.params,
fittedfcast=fitted,
fittedvalues=fitted[: -h - 1],
fcastvalues=fitted[-h - 1 :],
sse=sse,
level=level,
trend=_trend,
season=season,
aic=aic,
bic=bic,
aicc=aicc,
resid=resid,
k=k,
params_formatted=formatted,
optimized=optimized,
)
return HoltWintersResultsWrapper(hwfit)
[docs]
class SimpleExpSmoothing(ExponentialSmoothing):
"""
Simple Exponential Smoothing
Parameters
----------
endog : array_like
The time series to model.
initialization_method : str, optional
Method for initialize the recursions. One of:
* None
* 'estimated'
* 'heuristic'
* 'legacy-heuristic'
* 'known'
None defaults to the pre-0.12 behavior where initial values
are passed as part of ``fit``. If any of the other values are
passed, then the initial values must also be set when constructing
the model. If 'known' initialization is used, then `initial_level`
must be passed, as well as `initial_trend` and `initial_seasonal` if
applicable. Default is 'estimated'. "legacy-heuristic" uses the same
values that were used in statsmodels 0.11 and earlier.
initial_level : float, optional
The initial level component. Required if estimation method is "known".
If set using either "estimated" or "heuristic" this value is used.
This allows one or more of the initial values to be set while
deferring to the heuristic for others or estimating the unset
parameters.
See Also
--------
ExponentialSmoothing
Exponential smoothing with trend and seasonal components.
Holt
Exponential smoothing with a trend component.
Notes
-----
This is a full implementation of the simple exponential smoothing as
per [1]_. `SimpleExpSmoothing` is a restricted version of
:class:`ExponentialSmoothing`.
See the notebook `Exponential Smoothing
<../examples/notebooks/generated/exponential_smoothing.html>`__
for an overview.
References
----------
.. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles
and practice. OTexts, 2014.
"""
def __init__(
self,
endog,
initialization_method=None, # Future: 'estimated',
initial_level=None,
):
super().__init__(
endog,
initialization_method=initialization_method,
initial_level=initial_level,
)
[docs]
def fit(
self,
smoothing_level=None,
*,
optimized=True,
start_params=None,
initial_level=None,
use_brute=True,
use_boxcox=None,
remove_bias=False,
method=None,
minimize_kwargs=None,
):
"""
Fit the model
Parameters
----------
smoothing_level : float, optional
The smoothing_level value of the simple exponential smoothing, if
the value is set then this value will be used as the value.
optimized : bool, optional
Estimate model parameters by maximizing the log-likelihood.
start_params : ndarray, optional
Starting values to used when optimizing the fit. If not provided,
starting values are determined using a combination of grid search
and reasonable values based on the initial values of the data.
initial_level : float, optional
Value to use when initializing the fitted level.
use_brute : bool, optional
Search for good starting values using a brute force (grid)
optimizer. If False, a naive set of starting values is used.
use_boxcox : {True, False, 'log', float}, optional
Should the Box-Cox transform be applied to the data first? If 'log'
then apply the log. If float then use the value as lambda.
remove_bias : bool, optional
Remove bias from forecast values and fitted values by enforcing
that the average residual is equal to zero.
method : str, default "L-BFGS-B"
The minimizer used. Valid options are "L-BFGS-B" (default), "TNC",
"SLSQP", "Powell", "trust-constr", "basinhopping" (also "bh") and
"least_squares" (also "ls"). basinhopping tries multiple starting
values in an attempt to find a global minimizer in non-convex
problems, and so is slower than the others.
minimize_kwargs : dict[str, Any]
A dictionary of keyword arguments passed to SciPy's minimize
function if method is one of "L-BFGS-B" (default), "TNC",
"SLSQP", "Powell", or "trust-constr", or SciPy's basinhopping
or least_squares. The valid keywords are optimizer specific.
Consult SciPy's documentation for the full set of options.
Returns
-------
HoltWintersResults
See statsmodels.tsa.holtwinters.HoltWintersResults.
Notes
-----
This is a full implementation of the simple exponential smoothing as
per [1].
References
----------
[1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles
and practice. OTexts, 2014.
"""
return super().fit(
smoothing_level=smoothing_level,
optimized=optimized,
start_params=start_params,
initial_level=initial_level,
use_brute=use_brute,
remove_bias=remove_bias,
use_boxcox=use_boxcox,
method=method,
minimize_kwargs=minimize_kwargs,
)
[docs]
class Holt(ExponentialSmoothing):
"""
Holt's Exponential Smoothing
Parameters
----------
endog : array_like
The time series to model.
exponential : bool, optional
Type of trend component.
damped_trend : bool, optional
Should the trend component be damped.
initialization_method : str, optional
Method for initialize the recursions. One of:
* None
* 'estimated'
* 'heuristic'
* 'legacy-heuristic'
* 'known'
None defaults to the pre-0.12 behavior where initial values
are passed as part of ``fit``. If any of the other values are
passed, then the initial values must also be set when constructing
the model. If 'known' initialization is used, then `initial_level`
must be passed, as well as `initial_trend` and `initial_seasonal` if
applicable. Default is 'estimated'. "legacy-heuristic" uses the same
values that were used in statsmodels 0.11 and earlier.
initial_level : float, optional
The initial level component. Required if estimation method is "known".
If set using either "estimated" or "heuristic" this value is used.
This allows one or more of the initial values to be set while
deferring to the heuristic for others or estimating the unset
parameters.
initial_trend : float, optional
The initial trend component. Required if estimation method is "known".
If set using either "estimated" or "heuristic" this value is used.
This allows one or more of the initial values to be set while
deferring to the heuristic for others or estimating the unset
parameters.
See Also
--------
ExponentialSmoothing
Exponential smoothing with trend and seasonal components.
SimpleExpSmoothing
Basic exponential smoothing with only a level component.
Notes
-----
This is a full implementation of the Holt's exponential smoothing as
per [1]_. `Holt` is a restricted version of :class:`ExponentialSmoothing`.
See the notebook `Exponential Smoothing
<../examples/notebooks/generated/exponential_smoothing.html>`__
for an overview.
References
----------
.. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles
and practice. OTexts, 2014.
"""
@deprecate_kwarg("damped", "damped_trend")
def __init__(
self,
endog,
exponential=False,
damped_trend=False,
initialization_method=None, # Future: 'estimated',
initial_level=None,
initial_trend=None,
):
trend = "mul" if exponential else "add"
super().__init__(
endog,
trend=trend,
damped_trend=damped_trend,
initialization_method=initialization_method,
initial_level=initial_level,
initial_trend=initial_trend,
)
[docs]
@deprecate_kwarg("smoothing_slope", "smoothing_trend")
@deprecate_kwarg("initial_slope", "initial_trend")
@deprecate_kwarg("damping_slope", "damping_trend")
def fit(
self,
smoothing_level=None,
smoothing_trend=None,
*,
damping_trend=None,
optimized=True,
start_params=None,
initial_level=None,
initial_trend=None,
use_brute=True,
use_boxcox=None,
remove_bias=False,
method=None,
minimize_kwargs=None,
):
"""
Fit the model
Parameters
----------
smoothing_level : float, optional
The alpha value of the simple exponential smoothing, if the value
is set then this value will be used as the value.
smoothing_trend : float, optional
The beta value of the Holt's trend method, if the value is
set then this value will be used as the value.
damping_trend : float, optional
The phi value of the damped method, if the value is
set then this value will be used as the value.
optimized : bool, optional
Estimate model parameters by maximizing the log-likelihood.
start_params : ndarray, optional
Starting values to used when optimizing the fit. If not provided,
starting values are determined using a combination of grid search
and reasonable values based on the initial values of the data.
initial_level : float, optional
Value to use when initializing the fitted level.
.. deprecated:: 0.12
Set initial_level when constructing the model
initial_trend : float, optional
Value to use when initializing the fitted trend.
.. deprecated:: 0.12
Set initial_trend when constructing the model
use_brute : bool, optional
Search for good starting values using a brute force (grid)
optimizer. If False, a naive set of starting values is used.
use_boxcox : {True, False, 'log', float}, optional
Should the Box-Cox transform be applied to the data first? If 'log'
then apply the log. If float then use the value as lambda.
remove_bias : bool, optional
Remove bias from forecast values and fitted values by enforcing
that the average residual is equal to zero.
method : str, default "L-BFGS-B"
The minimizer used. Valid options are "L-BFGS-B" (default), "TNC",
"SLSQP", "Powell", "trust-constr", "basinhopping" (also "bh") and
"least_squares" (also "ls"). basinhopping tries multiple starting
values in an attempt to find a global minimizer in non-convex
problems, and so is slower than the others.
minimize_kwargs : dict[str, Any]
A dictionary of keyword arguments passed to SciPy's minimize
function if method is one of "L-BFGS-B" (default), "TNC",
"SLSQP", "Powell", or "trust-constr", or SciPy's basinhopping
or least_squares. The valid keywords are optimizer specific.
Consult SciPy's documentation for the full set of options.
Returns
-------
HoltWintersResults
See statsmodels.tsa.holtwinters.HoltWintersResults.
Notes
-----
This is a full implementation of the Holt's exponential smoothing as
per [1].
References
----------
[1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles
and practice. OTexts, 2014.
"""
return super().fit(
smoothing_level=smoothing_level,
smoothing_trend=smoothing_trend,
damping_trend=damping_trend,
optimized=optimized,
start_params=start_params,
initial_level=initial_level,
initial_trend=initial_trend,
use_brute=use_brute,
use_boxcox=use_boxcox,
remove_bias=remove_bias,
method=method,
minimize_kwargs=minimize_kwargs,
)
Last update:
Apr 19, 2024