statsmodels.tsa.deterministic.DeterministicProcess¶

class statsmodels.tsa.deterministic.DeterministicProcess(index, *, period=None, constant=False, order=0, seasonal=False, fourier=0, additional_terms=(), drop=False)[source]¶

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.

Notes

See the notebook Deterministic Terms in Time Series Models for an overview.

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

Methods

`apply`(index)	Create an identical determinstic process with a different index
`in_sample`()	Produce deterministic trends for in-sample fitting.
`out_of_sample`(steps[, forecast_index])	Produce deterministic trends for out-of-sample forecasts
`range`(start, stop)	Deterministic terms spanning a range of observations

Properties

`index`	The index of the process
`terms`	The deterministic terms included in the process