statsmodels.tsa.deterministic.CalendarFourier¶

class statsmodels.tsa.deterministic.CalendarFourier(freq, order)[source]¶

Fourier series deterministic terms based on calendar time

Parameters:¶

freqstr

A string convertible to a pandas frequency.

orderint

The number of Fourier components to include. Must be <= 2*period.

Attributes:¶

freq

The frequency of the deterministic terms

is_dummy

Flag indicating whether the values produced are dummy variables

order

The order of the Fourier terms included

See also

DeterministicProcess

CalendarTimeTrend

CalendarSeasonality

Fourier

Notes

Both a sine and a cosine term are included for each i=1, …, order

$$\begin{array}{rl}{f}_{i,s,t}& =\sin \left(2\pi i{\tau }_t\right)\\ f_{i,c,t}& =\cos \left(2\pi i{\tau }_t\right)\end{array}$$

where m is the length of the period and ${\tau }_t$ is the frequency normalized time. For example, when freq is “D” then an observation with a timestamp of 12:00:00 would have ${\tau }_t=0.5$.

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)

Methods

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

freq	The frequency of the deterministic terms
is_dummy	Flag indicating whether the values produced are dummy variables
order	The order of the Fourier terms included