from statsmodels.compat.pandas import Appender, is_int_index, to_numpy
from abc import ABC, abstractmethod
import datetime as dt
from typing import Hashable, List, Optional, Sequence, Set, Tuple, Type, Union
import numpy as np
import pandas as pd
from scipy.linalg import qr
from statsmodels.iolib.summary import d_or_f
from statsmodels.tools.validation import (
bool_like,
float_like,
required_int_like,
string_like,
)
from statsmodels.tsa.tsatools import freq_to_period
DateLike = Union[dt.datetime, pd.Timestamp, np.datetime64]
IntLike = Union[int, np.integer]
START_BEFORE_INDEX_ERR = """\
start is less than the first observation in the index. Values can only be \
created for observations after the start of the index.
"""
[docs]class DeterministicTerm(ABC):
"""Abstract Base Class for all Deterministic Terms"""
# Set _is_dummy if the term is a dummy variable process
_is_dummy = False
@property
def is_dummy(self) -> bool:
"""Flag indicating whether the values produced are dummy variables"""
return self._is_dummy
[docs] @abstractmethod
def in_sample(self, index: Sequence[Hashable]) -> pd.DataFrame:
"""
Produce deterministic trends for in-sample fitting.
Parameters
----------
index : index_like
An index-like object. If not an index, it is converted to an
index.
Returns
-------
DataFrame
A DataFrame containing the deterministic terms.
"""
[docs] @abstractmethod
def out_of_sample(
self,
steps: int,
index: Sequence[Hashable],
forecast_index: Optional[Sequence[Hashable]] = None,
) -> pd.DataFrame:
"""
Produce deterministic trends for out-of-sample forecasts
Parameters
----------
steps : int
The number of steps to forecast
index : index_like
An index-like object. If not an index, it is converted to an
index.
forecast_index : index_like
An Index or index-like object to use for the forecasts. If
provided must have steps elements.
Returns
-------
DataFrame
A DataFrame containing the deterministic terms.
"""
@abstractmethod
def __str__(self) -> str:
"""A meaningful string representation of the term"""
def __hash__(self) -> int:
name: Tuple[Hashable, ...] = (type(self).__name__,)
return hash(name + self._eq_attr)
@property
@abstractmethod
def _eq_attr(self) -> Tuple[Hashable, ...]:
"""tuple of attributes that are used for equality comparison"""
@staticmethod
def _index_like(index: Sequence[Hashable]) -> pd.Index:
if isinstance(index, pd.Index):
return index
try:
return pd.Index(index)
except Exception:
raise TypeError("index must be a pandas Index or index-like")
@staticmethod
def _extend_index(
index: pd.Index,
steps: int,
forecast_index: Optional[Sequence[Hashable]] = None,
) -> pd.Index:
"""Extend the forecast index"""
if forecast_index is not None:
forecast_index = DeterministicTerm._index_like(forecast_index)
assert isinstance(forecast_index, pd.Index)
if forecast_index.shape[0] != steps:
raise ValueError(
f"The number of values in forecast_index "
f"({forecast_index.shape[0]}) must match steps ({steps})."
)
return forecast_index
if isinstance(index, pd.PeriodIndex):
return pd.period_range(
index[-1] + 1, periods=steps, freq=index.freq
)
elif isinstance(index, pd.DatetimeIndex) and index.freq is not None:
next_obs = pd.date_range(index[-1], freq=index.freq, periods=2)[1]
return pd.date_range(next_obs, freq=index.freq, periods=steps)
elif isinstance(index, pd.RangeIndex):
assert isinstance(index, pd.RangeIndex)
try:
step = index.step
start = index.stop
except AttributeError:
# TODO: Remove after pandas min ver is 1.0.0+
step = index[-1] - index[-2] if len(index) > 1 else 1
start = index[-1] + step
stop = start + step * steps
return pd.RangeIndex(start, stop, step=step)
elif is_int_index(index) and np.all(np.diff(index) == 1):
idx_arr = np.arange(index[-1] + 1, index[-1] + steps + 1)
return pd.Index(idx_arr)
# default range index
import warnings
warnings.warn(
"Only PeriodIndexes, DatetimeIndexes with a frequency set, "
"RangesIndexes, and Index with a unit increment support "
"extending. The index is set will contain the position relative "
"to the data length.",
UserWarning,
stacklevel=2,
)
nobs = index.shape[0]
return pd.RangeIndex(nobs + 1, nobs + steps + 1)
def __repr__(self) -> str:
return self.__str__() + f" at 0x{id(self):0x}"
def __eq__(self, other: object) -> bool:
if isinstance(other, type(self)):
own_attr = self._eq_attr
oth_attr = other._eq_attr
if len(own_attr) != len(oth_attr):
return False
return all([a == b for a, b in zip(own_attr, oth_attr)])
else:
return False
[docs]class TimeTrendDeterministicTerm(DeterministicTerm, ABC):
"""Abstract Base Class for all Time Trend Deterministic Terms"""
def __init__(self, constant: bool = True, order: int = 0) -> None:
self._constant = bool_like(constant, "constant")
self._order = required_int_like(order, "order")
@property
def constant(self) -> bool:
"""Flag indicating that a constant is included"""
return self._constant
@property
def order(self) -> int:
"""Order of the time trend"""
return self._order
@property
def _columns(self) -> List[str]:
columns = []
trend_names = {1: "trend", 2: "trend_squared", 3: "trend_cubed"}
if self._constant:
columns.append("const")
for power in range(1, self._order + 1):
if power in trend_names:
columns.append(trend_names[power])
else:
columns.append(f"trend**{power}")
return columns
def _get_terms(self, locs: np.ndarray) -> np.ndarray:
nterms = int(self._constant) + self._order
terms = np.tile(locs, (1, nterms))
power = np.zeros((1, nterms), dtype=int)
power[0, int(self._constant) :] = np.arange(1, self._order + 1)
terms **= power
return terms
def __str__(self) -> str:
terms = []
if self._constant:
terms.append("Constant")
if self._order:
terms.append(f"Powers 1 to {self._order + 1}")
if not terms:
terms = ["Empty"]
terms_str = ",".join(terms)
return f"TimeTrend({terms_str})"
[docs]class TimeTrend(TimeTrendDeterministicTerm):
"""
Constant and time trend determinstic terms
Parameters
----------
constant : bool
Flag indicating whether a constant should be included.
order : int
A non-negative int containing the powers to include (1, 2, ..., order).
See Also
--------
DeterministicProcess
Seasonality
Fourier
CalendarTimeTrend
Examples
--------
>>> from statsmodels.datasets import sunspots
>>> from statsmodels.tsa.deterministic import TimeTrend
>>> data = sunspots.load_pandas().data
>>> trend_gen = TimeTrend(True, 3)
>>> trend_gen.in_sample(data.index)
"""
def __init__(self, constant: bool = True, order: int = 0) -> None:
super().__init__(constant, order)
[docs] @classmethod
def from_string(cls, trend: str) -> "TimeTrend":
"""
Create a TimeTrend from a string description.
Provided for compatibility with common string names.
Parameters
----------
trend : {"n", "c", "t", "ct", "ctt"}
The string representation of the time trend. The terms are:
* "n": No trend terms
* "c": A constant only
* "t": Linear time trend only
* "ct": A constant and a time trend
* "ctt": A constant, a time trend and a quadratic time trend
Returns
-------
TimeTrend
The TimeTrend instance.
"""
constant = trend.startswith("c")
order = 0
if "tt" in trend:
order = 2
elif "t" in trend:
order = 1
return cls(constant=constant, order=order)
[docs] @Appender(DeterministicTerm.in_sample.__doc__)
def in_sample(
self, index: Union[Sequence[Hashable], pd.Index]
) -> pd.DataFrame:
index = self._index_like(index)
nobs = index.shape[0]
locs = np.arange(1, nobs + 1, dtype=np.double)[:, None]
terms = self._get_terms(locs)
return pd.DataFrame(terms, columns=self._columns, index=index)
[docs] @Appender(DeterministicTerm.out_of_sample.__doc__)
def out_of_sample(
self,
steps: int,
index: Union[Sequence[Hashable], pd.Index],
forecast_index: Optional[Sequence[Hashable]] = None,
) -> pd.DataFrame:
index = self._index_like(index)
nobs = index.shape[0]
fcast_index = self._extend_index(index, steps, forecast_index)
locs = np.arange(nobs + 1, nobs + steps + 1, dtype=np.double)[:, None]
terms = self._get_terms(locs)
return pd.DataFrame(terms, columns=self._columns, index=fcast_index)
@property
def _eq_attr(self) -> Tuple[Hashable, ...]:
return self._constant, self._order
[docs]class Seasonality(DeterministicTerm):
"""
Seasonal dummy deterministic terms
Parameters
----------
period : int
The length of a full cycle. Must be >= 2.
initial_period : int
The seasonal index of the first observation. 1-indexed so must
be in {1, 2, ..., period}.
See Also
--------
DeterministicProcess
TimeTrend
Fourier
CalendarSeasonality
Examples
--------
Solar data has an 11-year cycle
>>> from statsmodels.datasets import sunspots
>>> from statsmodels.tsa.deterministic import Seasonality
>>> data = sunspots.load_pandas().data
>>> seas_gen = Seasonality(11)
>>> seas_gen.in_sample(data.index)
To start at a season other than 1
>>> seas_gen = Seasonality(11, initial_period=4)
>>> seas_gen.in_sample(data.index)
"""
_is_dummy = True
def __init__(self, period: int, initial_period: int = 1) -> None:
self._period = required_int_like(period, "period")
self._initial_period = required_int_like(
initial_period, "initial_period"
)
if period < 2:
raise ValueError("period must be >= 2")
if not 1 <= self._initial_period <= period:
raise ValueError("initial_period must be in {1, 2, ..., period}")
@property
def period(self) -> int:
"""The period of the seasonality"""
return self._period
@property
def initial_period(self) -> int:
"""The seasonal index of the first observation"""
return self._initial_period
[docs] @classmethod
def from_index(
cls, index: Union[Sequence[Hashable], pd.DatetimeIndex, pd.PeriodIndex]
) -> "Seasonality":
"""
Construct a seasonality directly from an index using its frequency.
Parameters
----------
index : {DatetimeIndex, PeriodIndex}
An index with its frequency (`freq`) set.
Returns
-------
Seasonality
The initialized Seasonality instance.
"""
index = cls._index_like(index)
if isinstance(index, pd.PeriodIndex):
freq = index.freq
elif isinstance(index, pd.DatetimeIndex):
freq = index.freq if index.freq else index.inferred_freq
else:
raise TypeError("index must be a DatetimeIndex or PeriodIndex")
if freq is None:
raise ValueError("index must have a freq or inferred_freq set")
period = freq_to_period(freq)
return cls(period=period)
@property
def _eq_attr(self) -> Tuple[Hashable, ...]:
return self._period, self._initial_period
def __str__(self) -> str:
return f"Seasonality(period={self._period})"
@property
def _columns(self) -> List[str]:
period = self._period
columns = []
for i in range(1, period + 1):
columns.append(f"s({i},{period})")
return columns
[docs] @Appender(DeterministicTerm.in_sample.__doc__)
def in_sample(
self, index: Union[Sequence[Hashable], pd.Index]
) -> pd.DataFrame:
index = self._index_like(index)
nobs = index.shape[0]
period = self._period
term = np.zeros((nobs, period))
offset = self._initial_period - 1
for i in range(period):
col = (i + offset) % period
term[i::period, col] = 1
return pd.DataFrame(term, columns=self._columns, index=index)
[docs] @Appender(DeterministicTerm.out_of_sample.__doc__)
def out_of_sample(
self,
steps: int,
index: Union[Sequence[Hashable], pd.Index],
forecast_index: Optional[Sequence[Hashable]] = None,
) -> pd.DataFrame:
index = self._index_like(index)
fcast_index = self._extend_index(index, steps, forecast_index)
nobs = index.shape[0]
period = self._period
term = np.zeros((steps, period))
offset = self._initial_period - 1
for i in range(period):
col_loc = (nobs + offset + i) % period
term[i::period, col_loc] = 1
return pd.DataFrame(term, columns=self._columns, index=fcast_index)
[docs]class FourierDeterministicTerm(DeterministicTerm, ABC):
"""Abstract Base Class for all Fourier Deterministic Terms"""
def __init__(self, order: int) -> None:
self._order = required_int_like(order, "terms")
@property
def order(self) -> int:
"""The order of the Fourier terms included"""
return self._order
def _get_terms(self, locs: np.ndarray) -> np.ndarray:
locs = 2 * np.pi * locs.astype(np.double)
terms = np.empty((locs.shape[0], 2 * self._order))
for i in range(self._order):
for j, func in enumerate((np.sin, np.cos)):
terms[:, 2 * i + j] = func((i + 1) * locs)
return terms
[docs]class Fourier(FourierDeterministicTerm):
r"""
Fourier series deterministic terms
Parameters
----------
period : int
The length of a full cycle. Must be >= 2.
order : int
The number of Fourier components to include. Must be <= 2*period.
See Also
--------
DeterministicProcess
TimeTrend
Seasonality
CalendarFourier
Notes
-----
Both a sine and a cosine term are included for each i=1, ..., order
.. math::
f_{i,s,t} & = \sin\left(2 \pi i \times \frac{t}{m} \right) \\
f_{i,c,t} & = \cos\left(2 \pi i \times \frac{t}{m} \right)
where m is the length of the period.
Examples
--------
Solar data has an 11-year cycle
>>> from statsmodels.datasets import sunspots
>>> from statsmodels.tsa.deterministic import Fourier
>>> data = sunspots.load_pandas().data
>>> fourier_gen = Fourier(11, order=2)
>>> fourier_gen.in_sample(data.index)
"""
_is_dummy = False
def __init__(self, period: float, order: int):
super().__init__(order)
self._period = float_like(period, "period")
if 2 * self._order > self._period:
raise ValueError("2 * order must be <= period")
@property
def period(self) -> float:
"""The period of the Fourier terms"""
return self._period
@property
def _columns(self) -> List[str]:
period = self._period
fmt_period = d_or_f(period).strip()
columns = []
for i in range(1, self._order + 1):
for typ in ("sin", "cos"):
columns.append(f"{typ}({i},{fmt_period})")
return columns
[docs] @Appender(DeterministicTerm.in_sample.__doc__)
def in_sample(
self, index: Union[Sequence[Hashable], pd.Index]
) -> pd.DataFrame:
index = self._index_like(index)
nobs = index.shape[0]
terms = self._get_terms(np.arange(nobs) / self._period)
return pd.DataFrame(terms, index=index, columns=self._columns)
[docs] @Appender(DeterministicTerm.out_of_sample.__doc__)
def out_of_sample(
self,
steps: int,
index: Union[Sequence[Hashable], pd.Index],
forecast_index: Optional[Sequence[Hashable]] = None,
) -> pd.DataFrame:
index = self._index_like(index)
fcast_index = self._extend_index(index, steps, forecast_index)
nobs = index.shape[0]
terms = self._get_terms(np.arange(nobs, nobs + steps) / self._period)
return pd.DataFrame(terms, index=fcast_index, columns=self._columns)
@property
def _eq_attr(self) -> Tuple[Hashable, ...]:
return self._period, self._order
def __str__(self) -> str:
return f"Fourier(period={self._period}, order={self._order})"
[docs]class CalendarDeterministicTerm(DeterministicTerm, ABC):
"""Abstract Base Class for calendar deterministic terms"""
def __init__(self, freq: str) -> None:
try:
index = pd.date_range("2020-01-01", freq=freq, periods=1)
self._freq = index.freq
except ValueError:
raise ValueError("freq is not understood by pandas")
@property
def freq(self) -> str:
"""The frequency of the deterministic terms"""
return self._freq.freqstr
def _compute_ratio(
self, index: Union[pd.DatetimeIndex, pd.PeriodIndex]
) -> np.ndarray:
if isinstance(index, pd.PeriodIndex):
index = index.to_timestamp()
delta = index - index.to_period(self._freq).to_timestamp()
pi = index.to_period(self._freq)
gap = (pi + 1).to_timestamp() - pi.to_timestamp()
return to_numpy(delta) / to_numpy(gap)
def _check_index_type(
self,
index: pd.Index,
allowed: Union[Type, Tuple[Type, ...]] = (
pd.DatetimeIndex,
pd.PeriodIndex,
),
) -> Union[pd.DatetimeIndex, pd.PeriodIndex]:
if isinstance(allowed, type):
allowed = (allowed,)
if not isinstance(index, allowed):
if len(allowed) == 1:
allowed_types = "a " + allowed[0].__name__
else:
allowed_types = ", ".join(a.__name__ for a in allowed[:-1])
if len(allowed) > 2:
allowed_types += ","
allowed_types += " and " + allowed[-1].__name__
msg = (
f"{type(self).__name__} terms can only be computed from "
f"{allowed_types}"
)
raise TypeError(msg)
assert isinstance(index, (pd.DatetimeIndex, pd.PeriodIndex))
return index
[docs]class CalendarFourier(CalendarDeterministicTerm, FourierDeterministicTerm):
r"""
Fourier series deterministic terms based on calendar time
Parameters
----------
freq : str
A string convertible to a pandas frequency.
order : int
The number of Fourier components to include. Must be <= 2*period.
See Also
--------
DeterministicProcess
CalendarTimeTrend
CalendarSeasonality
Fourier
Notes
-----
Both a sine and a cosine term are included for each i=1, ..., order
.. math::
f_{i,s,t} & = \sin\left(2 \pi i \tau_t \right) \\
f_{i,c,t} & = \cos\left(2 \pi i \tau_t \right)
where m is the length of the period and :math:`\tau_t` is the frequency
normalized time. For example, when freq is "D" then an observation with
a timestamp of 12:00:00 would have :math:`\tau_t=0.5`.
Examples
--------
Here we simulate irregularly spaced hourly data and construct the calendar
Fourier terms for the data.
>>> import numpy as np
>>> import pandas as pd
>>> base = pd.Timestamp("2020-1-1")
>>> gen = np.random.default_rng()
>>> gaps = np.cumsum(gen.integers(0, 1800, size=1000))
>>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps]
>>> index = pd.DatetimeIndex(pd.to_datetime(times))
>>> from statsmodels.tsa.deterministic import CalendarFourier
>>> cal_fourier_gen = CalendarFourier("D", 2)
>>> cal_fourier_gen.in_sample(index)
"""
def __init__(self, freq: str, order: int) -> None:
super().__init__(freq)
FourierDeterministicTerm.__init__(self, order)
self._order = required_int_like(order, "terms")
@property
def _columns(self) -> List[str]:
columns = []
for i in range(1, self._order + 1):
for typ in ("sin", "cos"):
columns.append(f"{typ}({i},freq={self._freq.freqstr})")
return columns
[docs] @Appender(DeterministicTerm.in_sample.__doc__)
def in_sample(
self, index: Union[Sequence[Hashable], pd.Index]
) -> pd.DataFrame:
index = self._index_like(index)
index = self._check_index_type(index)
ratio = self._compute_ratio(index)
terms = self._get_terms(ratio)
return pd.DataFrame(terms, index=index, columns=self._columns)
[docs] @Appender(DeterministicTerm.out_of_sample.__doc__)
def out_of_sample(
self,
steps: int,
index: Union[Sequence[Hashable], pd.Index],
forecast_index: Optional[Sequence[Hashable]] = None,
) -> pd.DataFrame:
index = self._index_like(index)
fcast_index = self._extend_index(index, steps, forecast_index)
self._check_index_type(fcast_index)
assert isinstance(fcast_index, (pd.DatetimeIndex, pd.PeriodIndex))
ratio = self._compute_ratio(fcast_index)
terms = self._get_terms(ratio)
return pd.DataFrame(terms, index=fcast_index, columns=self._columns)
@property
def _eq_attr(self) -> Tuple[Hashable, ...]:
return self._freq.freqstr, self._order
def __str__(self) -> str:
return f"Fourier(freq={self._freq.freqstr}, order={self._order})"
[docs]class CalendarSeasonality(CalendarDeterministicTerm):
"""
Seasonal dummy deterministic terms based on calendar time
Parameters
----------
freq : str
The frequency of the seasonal effect.
period : str
The pandas frequency string describing the full period.
See Also
--------
DeterministicProcess
CalendarTimeTrend
CalendarFourier
Seasonality
Examples
--------
Here we simulate irregularly spaced data (in time) and hourly seasonal
dummies for the data.
>>> import numpy as np
>>> import pandas as pd
>>> base = pd.Timestamp("2020-1-1")
>>> gen = np.random.default_rng()
>>> gaps = np.cumsum(gen.integers(0, 1800, size=1000))
>>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps]
>>> index = pd.DatetimeIndex(pd.to_datetime(times))
>>> from statsmodels.tsa.deterministic import CalendarSeasonality
>>> cal_seas_gen = CalendarSeasonality("H", "D")
>>> cal_seas_gen.in_sample(index)
"""
_is_dummy = True
# out_of: freq
_supported = {
"W": {"H": 24 * 7, "B": 5, "D": 7},
"D": {"H": 24},
"Q": {"M": 3},
"A": {"M": 12, "Q": 4},
}
def __init__(self, freq: str, period: str) -> None:
freq_options: Set[str] = set()
freq_options.update(
*[list(val.keys()) for val in self._supported.values()]
)
period_options = list(self._supported.keys())
freq = string_like(
freq, "freq", options=tuple(freq_options), lower=False
)
period = string_like(
period, "period", options=period_options, lower=False
)
if freq not in self._supported[period]:
raise ValueError(
f"The combination of freq={freq} and "
f"period={period} is not supported."
)
super().__init__(freq)
self._period = period
self._freq_str = self._freq.freqstr.split("-")[0]
@property
def freq(self) -> str:
"""The frequency of the deterministic terms"""
return self._freq.freqstr
@property
def period(self) -> str:
"""The full period"""
return self._period
def _weekly_to_loc(
self, index: Union[pd.DatetimeIndex, pd.PeriodIndex]
) -> np.ndarray:
if self._freq.freqstr == "H":
return index.hour + 24 * index.dayofweek
elif self._freq.freqstr == "D":
return index.dayofweek
else: # "B"
bdays = pd.bdate_range("2000-1-1", periods=10).dayofweek.unique()
loc = index.dayofweek
if not loc.isin(bdays).all():
raise ValueError(
"freq is B but index contains days that are not business "
"days."
)
return loc
def _daily_to_loc(
self, index: Union[pd.DatetimeIndex, pd.PeriodIndex]
) -> np.ndarray:
return index.hour
def _quarterly_to_loc(
self, index: Union[pd.DatetimeIndex, pd.PeriodIndex]
) -> np.ndarray:
return (index.month - 1) % 3
def _annual_to_loc(
self, index: Union[pd.DatetimeIndex, pd.PeriodIndex]
) -> np.ndarray:
if self._freq.freqstr == "M":
return index.month - 1
else: # "Q"
return index.quarter - 1
def _get_terms(
self, index: Union[pd.DatetimeIndex, pd.PeriodIndex]
) -> np.ndarray:
if self._period == "D":
locs = self._daily_to_loc(index)
elif self._period == "W":
locs = self._weekly_to_loc(index)
elif self._period == "Q":
locs = self._quarterly_to_loc(index)
else: # "A":
locs = self._annual_to_loc(index)
full_cycle = self._supported[self._period][self._freq_str]
terms = np.zeros((locs.shape[0], full_cycle))
terms[np.arange(locs.shape[0]), locs] = 1
return terms
@property
def _columns(self) -> List[str]:
columns = []
count = self._supported[self._period][self._freq_str]
for i in range(count):
columns.append(
f"s({self._freq_str}={i + 1}, period={self._period})"
)
return columns
[docs] @Appender(DeterministicTerm.in_sample.__doc__)
def in_sample(
self, index: Union[Sequence[Hashable], pd.Index]
) -> pd.DataFrame:
index = self._index_like(index)
index = self._check_index_type(index)
terms = self._get_terms(index)
return pd.DataFrame(terms, index=index, columns=self._columns)
[docs] @Appender(DeterministicTerm.out_of_sample.__doc__)
def out_of_sample(
self,
steps: int,
index: Union[Sequence[Hashable], pd.Index],
forecast_index: Optional[Sequence[Hashable]] = None,
) -> pd.DataFrame:
index = self._index_like(index)
fcast_index = self._extend_index(index, steps, forecast_index)
self._check_index_type(fcast_index)
assert isinstance(fcast_index, (pd.DatetimeIndex, pd.PeriodIndex))
terms = self._get_terms(fcast_index)
return pd.DataFrame(terms, index=fcast_index, columns=self._columns)
@property
def _eq_attr(self) -> Tuple[Hashable, ...]:
return self._period, self._freq_str
def __str__(self) -> str:
return f"Seasonal(freq={self._freq_str})"
[docs]class CalendarTimeTrend(CalendarDeterministicTerm, TimeTrendDeterministicTerm):
r"""
Constant and time trend determinstic terms based on calendar time
Parameters
----------
freq : str
A string convertible to a pandas frequency.
constant : bool
Flag indicating whether a constant should be included.
order : int
A non-negative int containing the powers to include (1, 2, ..., order).
base_period : {str, pd.Timestamp}, default None
The base period to use when computing the time stamps. This value is
treated as 1 and so all other time indices are defined as the number
of periods since or before this time stamp. If not provided, defaults
to pandas base period for a PeriodIndex.
See Also
--------
DeterministicProcess
CalendarFourier
CalendarSeasonality
TimeTrend
Notes
-----
The time stamp, :math:`\tau_t`, is the number of periods that have elapsed
since the base_period. :math:`\tau_t` may be fractional.
Examples
--------
Here we simulate irregularly spaced hourly data and construct the calendar
time trend terms for the data.
>>> import numpy as np
>>> import pandas as pd
>>> base = pd.Timestamp("2020-1-1")
>>> gen = np.random.default_rng()
>>> gaps = np.cumsum(gen.integers(0, 1800, size=1000))
>>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps]
>>> index = pd.DatetimeIndex(pd.to_datetime(times))
>>> from statsmodels.tsa.deterministic import CalendarTimeTrend
>>> cal_trend_gen = CalendarTimeTrend("D", True, order=1)
>>> cal_trend_gen.in_sample(index)
Next, we normalize using the first time stamp
>>> cal_trend_gen = CalendarTimeTrend("D", True, order=1,
... base_period=index[0])
>>> cal_trend_gen.in_sample(index)
"""
def __init__(
self,
freq: str,
constant: bool = True,
order: int = 0,
*,
base_period: Optional[Union[str, DateLike]] = None,
) -> None:
super().__init__(freq)
TimeTrendDeterministicTerm.__init__(
self, constant=constant, order=order
)
self._ref_i8 = 0
if base_period is not None:
pr = pd.period_range(base_period, periods=1, freq=self._freq)
self._ref_i8 = pr.asi8[0]
self._base_period = None if base_period is None else str(base_period)
@property
def base_period(self) -> Optional[str]:
"""The base period"""
return self._base_period
[docs] @classmethod
def from_string(
cls,
freq: str,
trend: str,
base_period: Optional[Union[str, DateLike]] = None,
) -> "CalendarTimeTrend":
"""
Create a TimeTrend from a string description.
Provided for compatibility with common string names.
Parameters
----------
freq : str
A string convertible to a pandas frequency.
trend : {"n", "c", "t", "ct", "ctt"}
The string representation of the time trend. The terms are:
* "n": No trend terms
* "c": A constant only
* "t": Linear time trend only
* "ct": A constant and a time trend
* "ctt": A constant, a time trend and a quadratic time trend
base_period : {str, pd.Timestamp}, default None
The base period to use when computing the time stamps. This value
is treated as 1 and so all other time indices are defined as the
number of periods since or before this time stamp. If not
provided, defaults to pandas base period for a PeriodIndex.
Returns
-------
TimeTrend
The TimeTrend instance.
"""
constant = trend.startswith("c")
order = 0
if "tt" in trend:
order = 2
elif "t" in trend:
order = 1
return cls(freq, constant, order, base_period=base_period)
def _terms(
self, index: Union[pd.DatetimeIndex, pd.PeriodIndex], ratio: np.ndarray
) -> pd.DataFrame:
if isinstance(index, pd.DatetimeIndex):
index = index.to_period(self._freq)
index_i8 = index.asi8
index_i8 = index_i8 - self._ref_i8 + 1
time = index_i8.astype(np.double) + ratio
time = time[:, None]
terms = self._get_terms(time)
return pd.DataFrame(terms, columns=self._columns, index=index)
[docs] @Appender(DeterministicTerm.in_sample.__doc__)
def in_sample(
self, index: Union[Sequence[Hashable], pd.Index]
) -> pd.DataFrame:
index = self._index_like(index)
index = self._check_index_type(index)
ratio = self._compute_ratio(index)
return self._terms(index, ratio)
[docs] @Appender(DeterministicTerm.out_of_sample.__doc__)
def out_of_sample(
self,
steps: int,
index: Union[Sequence[Hashable], pd.Index],
forecast_index: Optional[Sequence[Hashable]] = None,
) -> pd.DataFrame:
index = self._index_like(index)
fcast_index = self._extend_index(index, steps, forecast_index)
self._check_index_type(fcast_index)
assert isinstance(fcast_index, (pd.PeriodIndex, pd.DatetimeIndex))
ratio = self._compute_ratio(fcast_index)
return self._terms(fcast_index, ratio)
@property
def _eq_attr(self) -> Tuple[Hashable, ...]:
attr: Tuple[Hashable, ...] = (
self._constant,
self._order,
self._freq.freqstr,
)
if self._base_period is not None:
attr += (self._base_period,)
return attr
def __str__(self) -> str:
value = TimeTrendDeterministicTerm.__str__(self)
value = "Calendar" + value[:-1] + f", freq={self._freq.freqstr})"
if self._base_period is not None:
value = value[:-1] + f"base_period={self._base_period})"
return value
[docs]class DeterministicProcess:
"""
Container class for deterministic terms.
Directly supports constants, time trends, and either seasonal dummies or
fourier terms for a single cycle. Additional deterministic terms beyond
the set that can be directly initialized through the constructor can be
added.
Parameters
----------
index : {Sequence[Hashable], pd.Index}
The index of the process. Should usually be the "in-sample" index when
used in forecasting applications.
period : {float, int}, default None
The period of the seasonal or fourier components. Must be an int for
seasonal dummies. If not provided, freq is read from index if
available.
constant : bool, default False
Whether to include a constant.
order : int, default 0
The order of the tim trend to include. For example, 2 will include
both linear and quadratic terms. 0 exclude time trend terms.
seasonal : bool = False
Whether to include seasonal dummies
fourier : int = 0
The order of the fourier terms to included.
additional_terms : Sequence[DeterministicTerm]
A sequence of additional deterministic terms to include in the process.
drop : bool, default False
A flag indicating to check for perfect collinearity and to drop any
linearly dependent terms.
See Also
--------
TimeTrend
Seasonality
Fourier
CalendarTimeTrend
CalendarSeasonality
CalendarFourier
Examples
--------
>>> from statsmodels.tsa.deterministic import DeterministicProcess
>>> from pandas import date_range
>>> index = date_range("2000-1-1", freq="M", periods=240)
First a determinstic process with a constant and quadratic time trend.
>>> dp = DeterministicProcess(index, constant=True, order=2)
>>> dp.in_sample().head(3)
const trend trend_squared
2000-01-31 1.0 1.0 1.0
2000-02-29 1.0 2.0 4.0
2000-03-31 1.0 3.0 9.0
Seasonal dummies are included by setting seasonal to True.
>>> dp = DeterministicProcess(index, constant=True, seasonal=True)
>>> dp.in_sample().iloc[:3,:5]
const s(2,12) s(3,12) s(4,12) s(5,12)
2000-01-31 1.0 0.0 0.0 0.0 0.0
2000-02-29 1.0 1.0 0.0 0.0 0.0
2000-03-31 1.0 0.0 1.0 0.0 0.0
Fourier components can be used to alternatively capture seasonal patterns,
>>> dp = DeterministicProcess(index, constant=True, fourier=2)
>>> dp.in_sample().head(3)
const sin(1,12) cos(1,12) sin(2,12) cos(2,12)
2000-01-31 1.0 0.000000 1.000000 0.000000 1.0
2000-02-29 1.0 0.500000 0.866025 0.866025 0.5
2000-03-31 1.0 0.866025 0.500000 0.866025 -0.5
Multiple Seasonalities can be captured using additional terms.
>>> from statsmodels.tsa.deterministic import Fourier
>>> index = date_range("2000-1-1", freq="D", periods=5000)
>>> fourier = Fourier(period=365.25, order=1)
>>> dp = DeterministicProcess(index, period=3, constant=True,
... seasonal=True, additional_terms=[fourier])
>>> dp.in_sample().head(3)
const s(2,3) s(3,3) sin(1,365.25) cos(1,365.25)
2000-01-01 1.0 0.0 0.0 0.000000 1.000000
2000-01-02 1.0 1.0 0.0 0.017202 0.999852
2000-01-03 1.0 0.0 1.0 0.034398 0.999408
"""
def __init__(
self,
index: Union[Sequence[Hashable], pd.Index],
*,
period: Optional[Union[float, int]] = None,
constant: bool = False,
order: int = 0,
seasonal: bool = False,
fourier: int = 0,
additional_terms: Sequence[DeterministicTerm] = (),
drop: bool = False,
):
if not isinstance(index, pd.Index):
index = pd.Index(index)
self._index = index
self._deterministic_terms: List[DeterministicTerm] = []
self._extendable = False
self._index_freq = None
self._validate_index()
period = float_like(period, "period", optional=True)
self._constant = constant = bool_like(constant, "constant")
self._order = required_int_like(order, "order")
self._seasonal = seasonal = bool_like(seasonal, "seasonal")
self._fourier = required_int_like(fourier, "fourier")
additional_terms = tuple(additional_terms)
self._cached_in_sample = None
self._drop = bool_like(drop, "drop")
self._additional_terms = additional_terms
if constant or order:
self._deterministic_terms.append(TimeTrend(constant, order))
if seasonal and fourier:
raise ValueError(
"""seasonal and fourier can be initialized through the constructor since\
these will be necessarily perfectly collinear. Instead, you can pass \
additional components using the additional_terms input."""
)
if (seasonal or fourier) and period is None:
if period is None:
self._period = period = freq_to_period(self._index_freq)
if seasonal:
period = required_int_like(period, "period")
self._deterministic_terms.append(Seasonality(period))
elif fourier:
period = float_like(period, "period")
assert period is not None
self._deterministic_terms.append(Fourier(period, order=fourier))
for term in additional_terms:
if not isinstance(term, DeterministicTerm):
raise TypeError(
"All additional terms must be instances of subsclasses "
"of DeterministicTerm"
)
if term not in self._deterministic_terms:
self._deterministic_terms.append(term)
else:
raise ValueError(
"One or more terms in additional_terms has been added "
"through the parameters of the constructor. Terms must "
"be unique."
)
self._period = period
self._retain_cols: Optional[List[Hashable]] = None
@property
def index(self) -> pd.Index:
"""The index of the process"""
return self._index
@property
def terms(self) -> List[DeterministicTerm]:
"""The deterministic terms included in the process"""
return self._deterministic_terms
def _adjust_dummies(self, terms: List[pd.DataFrame]) -> List[pd.DataFrame]:
has_const: Optional[bool] = None
for dterm in self._deterministic_terms:
if isinstance(dterm, (TimeTrend, CalendarTimeTrend)):
has_const = has_const or dterm.constant
if has_const is None:
has_const = False
for term in terms:
const_col = (term == term.iloc[0]).all() & (term.iloc[0] != 0)
has_const = has_const or const_col.any()
drop_first = has_const
for i, dterm in enumerate(self._deterministic_terms):
is_dummy = dterm.is_dummy
if is_dummy and drop_first:
# drop first
terms[i] = terms[i].iloc[:, 1:]
drop_first = drop_first or is_dummy
return terms
def _remove_zeros_ones(self, terms: pd.DataFrame) -> pd.DataFrame:
all_zero = np.all(terms == 0, axis=0)
if np.any(all_zero):
terms = terms.loc[:, ~all_zero]
is_constant = terms.max(axis=0) == terms.min(axis=0)
if np.sum(is_constant) > 1:
# Retain first
const_locs = np.where(is_constant)[0]
is_constant[const_locs[:1]] = False
terms = terms.loc[:, ~is_constant]
return terms
[docs] @Appender(DeterministicTerm.in_sample.__doc__)
def in_sample(self) -> pd.DataFrame:
if self._cached_in_sample is not None:
return self._cached_in_sample
index = self._index
if not self._deterministic_terms:
return pd.DataFrame(np.empty((index.shape[0], 0)), index=index)
raw_terms = []
for term in self._deterministic_terms:
raw_terms.append(term.in_sample(index))
raw_terms = self._adjust_dummies(raw_terms)
terms: pd.DataFrame = pd.concat(raw_terms, axis=1)
terms = self._remove_zeros_ones(terms)
if self._drop:
terms_arr = to_numpy(terms)
res = qr(terms_arr, mode="r", pivoting=True)
r = res[0]
p = res[-1]
abs_diag = np.abs(np.diag(r))
tol = abs_diag[0] * terms_arr.shape[1] * np.finfo(float).eps
rank = int(np.sum(abs_diag > tol))
rpx = r.T @ terms_arr
keep = [0]
last_rank = 1
# Find the left-most columns that produce full rank
for i in range(1, terms_arr.shape[1]):
curr_rank = np.linalg.matrix_rank(rpx[: i + 1, : i + 1])
if curr_rank > last_rank:
keep.append(i)
last_rank = curr_rank
if curr_rank == rank:
break
if len(keep) == rank:
terms = terms.iloc[:, keep]
else:
terms = terms.iloc[:, np.sort(p[:rank])]
self._retain_cols = terms.columns
self._cached_in_sample = terms
return terms
[docs] @Appender(DeterministicTerm.out_of_sample.__doc__)
def out_of_sample(
self,
steps: int,
forecast_index: Optional[Union[Sequence[Hashable], pd.Index]] = None,
) -> pd.DataFrame:
steps = required_int_like(steps, "steps")
if self._drop and self._retain_cols is None:
self.in_sample()
index = self._index
if not self._deterministic_terms:
return pd.DataFrame(np.empty((index.shape[0], 0)), index=index)
raw_terms = []
for term in self._deterministic_terms:
raw_terms.append(term.out_of_sample(steps, index, forecast_index))
terms: pd.DataFrame = pd.concat(raw_terms, axis=1)
assert self._retain_cols is not None
if terms.shape[1] != len(self._retain_cols):
terms = terms[self._retain_cols]
return terms
def _extend_time_index(
self,
stop: pd.Timestamp,
) -> Union[pd.DatetimeIndex, pd.PeriodIndex]:
index = self._index
if isinstance(index, pd.PeriodIndex):
return pd.period_range(index[0], end=stop, freq=index.freq)
return pd.date_range(start=index[0], end=stop, freq=self._index_freq)
def _range_from_range_index(self, start: int, stop: int) -> pd.DataFrame:
index = self._index
is_int64_index = is_int_index(index)
assert isinstance(index, pd.RangeIndex) or is_int64_index
if start < index[0]:
raise ValueError(START_BEFORE_INDEX_ERR)
if isinstance(index, pd.RangeIndex):
idx_step = index.step
else:
idx_step = np.diff(index).max() if len(index) > 1 else 1
if idx_step != 1 and ((start - index[0]) % idx_step) != 0:
raise ValueError(
f"The step of the index is not 1 (actual step={idx_step})."
" start must be in the sequence that would have been "
"generated by the index."
)
if is_int64_index:
new_idx = pd.Index(np.arange(start, stop))
else:
new_idx = pd.RangeIndex(start, stop, step=idx_step)
if new_idx[-1] <= self._index[-1]:
# In-sample only
in_sample = self.in_sample()
in_sample = in_sample.loc[new_idx]
return in_sample
elif new_idx[0] > self._index[-1]:
# Out of-sample only
next_value = index[-1] + idx_step
if new_idx[0] != next_value:
tmp = pd.RangeIndex(next_value, stop, step=idx_step)
oos = self.out_of_sample(tmp.shape[0], forecast_index=tmp)
return oos.loc[new_idx]
return self.out_of_sample(new_idx.shape[0], forecast_index=new_idx)
# Using some from each in and out of sample
in_sample_loc = new_idx <= self._index[-1]
in_sample_idx = new_idx[in_sample_loc]
out_of_sample_idx = new_idx[~in_sample_loc]
in_sample_exog = self.in_sample().loc[in_sample_idx]
oos_exog = self.out_of_sample(
steps=out_of_sample_idx.shape[0], forecast_index=out_of_sample_idx
)
return pd.concat([in_sample_exog, oos_exog], axis=0)
def _range_from_time_index(
self, start: pd.Timestamp, stop: pd.Timestamp
) -> pd.DataFrame:
index = self._index
if isinstance(self._index, pd.PeriodIndex):
if isinstance(start, pd.Timestamp):
start = start.to_period(freq=self._index_freq)
if isinstance(stop, pd.Timestamp):
stop = stop.to_period(freq=self._index_freq)
if start < index[0]:
raise ValueError(START_BEFORE_INDEX_ERR)
if stop <= self._index[-1]:
return self.in_sample().loc[start:stop]
new_idx = self._extend_time_index(stop)
oos_idx = new_idx[new_idx > index[-1]]
oos = self.out_of_sample(oos_idx.shape[0], oos_idx)
if start >= oos_idx[0]:
return oos.loc[start:stop]
both = pd.concat([self.in_sample(), oos], axis=0)
return both.loc[start:stop]
def _int_to_timestamp(self, value: int, name: str) -> pd.Timestamp:
if value < 0:
raise ValueError(f"{name} must be non-negative.")
if value < self._index.shape[0]:
return self._index[value]
add_periods = value - (self._index.shape[0] - 1) + 1
index = self._index
if isinstance(self._index, pd.PeriodIndex):
pr = pd.period_range(
index[-1], freq=self._index_freq, periods=add_periods
)
return pr[-1].to_timestamp()
dr = pd.date_range(
index[-1], freq=self._index_freq, periods=add_periods
)
return dr[-1]
[docs] def range(
self,
start: Union[IntLike, DateLike, str],
stop: Union[IntLike, DateLike, str],
) -> pd.DataFrame:
"""
Deterministic terms spanning a range of observations
Parameters
----------
start : {int, str, dt.datetime, pd.Timestamp, np.datetime64}
The first observation.
stop : {int, str, dt.datetime, pd.Timestamp, np.datetime64}
The final observation. Inclusive to match most prediction
function in statsmodels.
Returns
-------
DataFrame
A data frame of deterministic terms
"""
if not self._extendable:
raise TypeError(
"""The index in the deterministic process does not \
support extension. Only PeriodIndex, DatetimeIndex with a frequency, \
RangeIndex, and integral Indexes that start at 0 and have only unit \
differences can be extended when producing out-of-sample forecasts.
"""
)
if type(self._index) in (pd.RangeIndex,) or is_int_index(self._index):
start = required_int_like(start, "start")
stop = required_int_like(stop, "stop")
# Add 1 to ensure that the end point is inclusive
stop += 1
return self._range_from_range_index(start, stop)
if isinstance(start, (int, np.integer)):
start = self._int_to_timestamp(start, "start")
else:
start = pd.Timestamp(start)
if isinstance(stop, (int, np.integer)):
stop = self._int_to_timestamp(stop, "stop")
else:
stop = pd.Timestamp(stop)
return self._range_from_time_index(start, stop)
def _validate_index(self) -> None:
if isinstance(self._index, pd.PeriodIndex):
self._index_freq = self._index.freq
self._extendable = True
elif isinstance(self._index, pd.DatetimeIndex):
self._index_freq = self._index.freq or self._index.inferred_freq
self._extendable = self._index_freq is not None
elif isinstance(self._index, pd.RangeIndex):
self._extendable = True
elif is_int_index(self._index):
self._extendable = self._index[0] == 0 and np.all(
np.diff(self._index) == 1
)