statsmodels.tsa.deterministic.CalendarTimeTrend¶

class statsmodels.tsa.deterministic.CalendarTimeTrend(freq: str, constant: bool = True, order: int = 0, *, base_period: Optional[Union[str, datetime.datetime, pandas._libs.tslibs.timestamps.Timestamp, numpy.datetime64]] = None)[source]¶

Constant and time trend determinstic terms based on calendar time

Parameters

freqstr: A string convertible to a pandas frequency.
constantbool: Flag indicating whether a constant should be included.
orderint: 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, \(\tau_t\), is the number of periods that have elapsed since the base_period. \(\tau_t\) 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)

Attributes

base_period: The base period
constant: Flag indicating that a constant is included
freq: The frequency of the deterministic terms
is_dummy: Flag indicating whether the values produced are dummy variables
order: Order of the time trend

Methods

`from_string`(freq, trend[, base_period])	Create a TimeTrend from a string description.
`in_sample`(index)	Produce deterministic trends for in-sample fitting.
`out_of_sample`(steps, index[, forecast_index])	Produce deterministic trends for out-of-sample forecasts

Methods

`from_string`(freq, trend[, base_period])	Create a TimeTrend from a string description.
`in_sample`(index)	Produce deterministic trends for in-sample fitting.
`out_of_sample`(steps, index[, forecast_index])	Produce deterministic trends for out-of-sample forecasts

Properties

`base_period`	The base period
`constant`	Flag indicating that a constant is included
`freq`	The frequency of the deterministic terms
`is_dummy`	Flag indicating whether the values produced are dummy variables
`order`	Order of the time trend