FourierForecast

A time-series forecaster that fits by decomposing a daily time-series into seasonality, trend and optional regressors.

• Fits seasonality & Fourier terms specified
• Fits specified trend type (e.g. linear, flat, logistic, logarithmic)
• Fits exogenous regressors
• Fits specified number of lag terms
• Option to include terms for regularizing fit for different types of component
• Optional log transform of time-series to model interaction amongst components (not just interaction with trend)
• Components can be visualised with plot_components method

Blog posts:

• Part I
• Part II

Seasonality:

• For best performance, aim to include at least two cycles of the largest seasonal component to be fitted
• Multiple waves per seasonality are fit according to the specified Fourier order
  • more terms results in better fit but can result in over-fitting
• Seasonal periods are set by pre-determined values:
  • weekly seasonality: 7 days
  • monthly seasonality: 30.43 days
  • quarterly seasonality: 91.31 days
  • yearly seasonality: 365.25 days

Future updates:

• prediction intervals

FourierForecast

Parameters

• growth: str, default='linear'. Possible values 'linear', 'flat', 'logistic', 'logarithmic'.
• weekly_seasonality_terms: int, default=3
  • number of Fourier terms to generate for fitting seasonality of 7 days
• monthly_seasonality_terms: int, default=0
  • number of Fourier terms to generate for fitting seasonality of 30.43 days
• quarterly_seasonality_terms: int, default=0
  • number of Fourier terms to generate for fitting seasonality of 91.31 days
• yearly_seasonality_terms: int, default=10
  • number of Fourier terms to generate for fitting seasonality of 365.25 days
• trend_reg: float, default=0
  • parameter regulating strength of trend fit
  • smaller values (~0-1) allow the model to fit larger seasonal fluctuations,
  • larger values (~1-100) dampen the seasonality.
• seasonality_reg: float, default=0
  • parameter regulating strength of seasonality fit
  • smaller values (~0-1) allow the model to fit larger seasonal fluctuations,
  • larger values (~1-100) dampen the seasonality.
• regressor_reg: float, default=0
  • parameter regulating strength of regressors fit
  • smaller values (~0-1) allow the model to fit larger seasonal fluctuations,
  • larger values (~1-100) dampen the seasonality.
• ar_reg: float, default=0
  • parameter regulating strength of fit against lags
  • smaller values (~0-1) allow the model to fit larger seasonal fluctuations,
  • larger values (~1-100) dampen the seasonality.
• log_y: bool, default=True
  • takes the natural logarithm of the timeseries before fitting (and the exponent after predicting)
  • all values must be positive or reverts back to False
  • useful for fitting interactive effects between seasonality, trend and regressors

Methods

• fit

  • y: NDArray[float]
    • daily time-series ordered by date
  • regressors: NDArray[float], default=None
    • optional regressors for fitting non-seasonal components ordered by date
  • sample_weight: NDArray[float], default=None
    • individual weights for each sample

• predict

  • h: int, default=1
    • number of horizons to predict
  • regressors: NDArray[float], default=None
    • regressors corresponding to days to predict
    • if regressors are present during fitting, these must have the same number of features
    • if None is passed, then all values will assume to be 0.

• fitted

  • returns fitted values

• plot_components

  • plots bias, trends, individual seasonality terms, regressors and lags

• plot_seasonality_components

  • plots individual seasonalities terms

• plot_lag_components

  • plots individual lags in their own subplot

• plot_regression_components

  • regressor_names: list[str], default=None
  • plots individual regressors as their own subplot

Examples

fit and predict example

from fourier_forecast.fourier_forecast import FourierForecast
import plotly.graph_objs as go


dates = ...
actuals = ...

train_test_split = .8
n_train = int(len(dates) * train_test_split)
n_predict = len(dates) - n_train

train_dates = dates[: n_train]
train_actuals = actuals[: n_train]

ff = FourierForecast()
                     
ff.fit(train_actuals)
preds = ff.predict(h=n_predict)

fig = go.Figure()
fig.add_trace(go.Scatter(x=dates, y=actuals, mode='lines', name='actuals'))
fig.add_trace(go.Scatter(x=dates[: n_train], y=ff.fitted(), mode='lines', name='fitted'))
fig.add_trace(go.Scatter(x=dates[n_train:], y=preds, mode='lines', name='preds'))
fig.update_layout(showlegend=True)
fig.show()

regressor example with plot_components()

from fourier_forecast.fourier_forecast import FourierForecast


actuals = ...
regressors = ...

ff = FourierForecast(weekly_seasonality_terms=3,
                     monthly_seasonality_terms=5,
                     quarterly_seasonality_terms=5,
                     yearly_seasonality_terms=7,
                     growth='logistic',
                     log_y=True,
                     n_lags=7
                     )
                     
ff.fit(actuals, regressors)
ff.plot_components()