# 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.

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