tfprobability (version 0.15.2)

sts_smooth_seasonal: Formal representation of a smooth seasonal effect model

Description

The smooth seasonal model uses a set of trigonometric terms in order to capture a recurring pattern whereby adjacent (in time) effects are similar. The model uses frequencies calculated via:

Usage

sts_smooth_seasonal(
  period,
  frequency_multipliers,
  allow_drift = TRUE,
  drift_scale_prior = NULL,
  initial_state_prior = NULL,
  observed_time_series = NULL,
  name = NULL
)

Value

an instance of StructuralTimeSeries.

Arguments

period

positive scalar float Tensor giving the number of timesteps required for the longest cyclic effect to repeat.

frequency_multipliers

One-dimensional float Tensor listing the frequencies (cyclic components) included in the model, as multipliers of the base/fundamental frequency 2. * pi / period. Each component is specified by the number of times it repeats per period, and adds two latent dimensions to the model. A smooth seasonal model that can represent any periodic function is given by frequency_multipliers = [1,2, ..., floor(period / 2)]. However, it is often desirable to enforce a smoothness assumption (and reduce the computational burden) by dropping some of the higher frequencies.

allow_drift

optional logical specifying whether the seasonal effects can drift over time. Setting this to FALSE removes the drift_scale parameter from the model. This is mathematically equivalent to drift_scale_prior = tfd.Deterministic(0.), but removing drift directly is preferred because it avoids the use of a degenerate prior. Default value: TRUE.

drift_scale_prior

optional tfd$Distribution instance specifying a prior on the drift_scale parameter. If NULL, a heuristic default prior is constructed based on the provided observed_time_series. Default value: NULL.

initial_state_prior

instance of tfd$MultivariateNormal representing the prior distribution on the latent states. Must have event shape [2 * len(frequency_multipliers)]. If NULL, a heuristic default prior is constructed based on the provided observed_time_series.

observed_time_series

optional float Tensor of shape batch_shape + [T, 1] (omitting the trailing unit dimension is also supported when T > 1), specifying an observed time series. Any priors not explicitly set will be given default values according to the scale of the observed time series (or batch of time series). May optionally be an instance of tfp$sts$MaskedTimeSeries, which includes a mask Tensor to specify timesteps with missing observations. Default value: NULL.

name

the name of this model component. Default value: 'LocalLinearTrend'.

Details

frequencies[j] = 2. * pi * frequency_multipliers[j] / period

and then posits two latent states for each frequency. The two latent states associated with frequency j drift over time via:

effect[t] = (effect[t-1] * cos(frequencies[j]) +
             auxiliary[t-] * sin(frequencies[j]) +
             Normal(0., drift_scale))
auxiliary[t] = (-effect[t-1] * sin(frequencies[j]) +
                auxiliary[t-] * cos(frequencies[j]) +
                Normal(0., drift_scale))

where effect is the smooth seasonal effect and auxiliary only appears as a matter of construction. The interpretation of auxiliary is thus not particularly important.

See Also

For usage examples see sts_fit_with_hmc(), sts_forecast(), sts_decompose_by_component().

Other sts: sts_additive_state_space_model(), sts_autoregressive(), sts_autoregressive_state_space_model(), sts_constrained_seasonal_state_space_model(), sts_dynamic_linear_regression(), sts_dynamic_linear_regression_state_space_model(), sts_linear_regression(), sts_local_level(), sts_local_level_state_space_model(), sts_local_linear_trend(), sts_local_linear_trend_state_space_model(), sts_seasonal(), sts_seasonal_state_space_model(), sts_semi_local_linear_trend(), sts_semi_local_linear_trend_state_space_model(), sts_smooth_seasonal_state_space_model(), sts_sparse_linear_regression(), sts_sum()