statsmodels.tsa.deterministic.Fourier¶

class statsmodels.tsa.deterministic.Fourier(period, order)[source]¶

Fourier series deterministic terms

Parameters:¶

periodint

The length of a full cycle. Must be >= 2.

orderint

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

Attributes:¶

is_dummy

Flag indicating whether the values produced are dummy variables

order

The order of the Fourier terms included

period

The period of the Fourier terms

See also

DeterministicProcess

TimeTrend

Seasonality

CalendarFourier

Notes

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

$$\begin{array}{rl}{f}_{i,s,t}& =\sin (2\pi i\times \frac{t}{m})\\ f_{i,c,t}& =\cos (2\pi i\times \frac{t}{m})\end{array}$$

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)

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

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