This module contains functions to define the seasonal components in a DGLM. These are *harmonic* seasonal components, meaning they are defined by sine and cosine functions with a specific period. For example, when working with daily time series we often use a weekly seasonal effect of period 7 or an annual seasonal effect of period 365.
This function is called from dglm.__init__ to define the seasonal components.
This function transforms the seasonal component of a model from fourier form into more interpretable seasonal components. For example, if seasPeriods = [7], then this would return a vector of length $7$, with each of the seasonal effects.
A simple use case is given below. For a more detailed use of this function, see the following example.
import numpy as np
import pandas as pd
from pybats.analysis import analysis
from pybats.shared import load_sales_example2
data = load_sales_example2()
prior_length = 21 # Number of days of data used to set prior
mod = analysis(data.Sales.values, data[['Price', 'Promotion']].values, k=1,
family='poisson',
seasPeriods=[7], seasHarmComponents=[[1,2,3]],
prior_length=prior_length, dates=data.index,
ret = ['model'])
seas_mean, seas_cov = fourierToSeasonal(mod)
days = ['Monday', 'Tuesday', 'Wednesday', 'Thursday', 'Friday', 'Saturday', 'Sunday']
lastday = data.index[-1]
days = [*days[lastday.isoweekday()-1:], *days[:lastday.isoweekday()-1]]
seas_eff = pd.DataFrame({'Day':days,
'Effect Mean':np.exp(seas_mean.reshape(-1))})
seas_eff