Formal representation of a seasonal effect model.

A seasonal effect model posits a fixed set of recurring, discrete 'seasons', each of which is active for a fixed number of timesteps and, while active, contributes a different effect to the time series. These are generally not meteorological seasons, but represent regular recurring patterns such as hour-of-day or day-of-week effects. Each season lasts for a fixed number of timesteps. The effect of each season drifts from one occurrence to the next following a Gaussian random walk:

sts_seasonal(
  observed_time_series = NULL,
  num_seasons,
  num_steps_per_season = 1,
  drift_scale_prior = NULL,
  initial_effect_prior = NULL,
  constrain_mean_effect_to_zero = TRUE,
  name = NULL
)

Arguments

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 sts_masked_time_series, which includes a mask tensor to specify timesteps with missing observations. Default value: NULL.
num_seasons	Scalar integer number of seasons.
num_steps_per_season	integer number of steps in each season. This may be either a scalar (shape []), in which case all seasons have the same length, or an array of shape [num_seasons], in which seasons have different length, but remain constant around different cycles, or an array of shape [num_cycles, num_seasons], in which num_steps_per_season for each season also varies in different cycle (e.g., a 4 years cycle with leap day). Default value: 1.
drift_scale_prior	optional tfd$Distribution instance specifying a prior on the drift_scale parameter. If NULL, a heuristic default prior is constructed based on the provided observed_time_series. Default value: NULL.
initial_effect_prior	optional tfd$Distribution instance specifying a normal prior on the initial effect of each season. This may be either a scalar tfd_normal prior, in which case it applies independently to every season, or it may be multivariate normal (e.g., tfd_multivariate_normal_diag) with event shape [num_seasons], in which case it specifies a joint prior across all seasons. If NULL, a heuristic default prior is constructed based on the provided observed_time_series. Default value: NULL.
constrain_mean_effect_to_zero	if TRUE, use a model parameterization that constrains the mean effect across all seasons to be zero. This constraint is generally helpful in identifying the contributions of different model components and can lead to more interpretable posterior decompositions. It may be undesirable if you plan to directly examine the latent space of the underlying state space model. Default value: TRUE.
name	the name of this model component. Default value: 'Seasonal'.

Value

an instance of StructuralTimeSeries.

Details

effects[season, occurrence[i]] = (
  effects[season, occurrence[i-1]] + Normal(loc=0., scale=drift_scale))

The drift_scale parameter governs the standard deviation of the random walk; for example, in a day-of-week model it governs the change in effect from this Monday to next Monday.

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_state_space_model(), sts_autoregressive(), sts_constrained_seasonal_state_space_model(), sts_dynamic_linear_regression_state_space_model(), sts_dynamic_linear_regression(), sts_linear_regression(), sts_local_level_state_space_model(), sts_local_level(), sts_local_linear_trend_state_space_model(), sts_local_linear_trend(), sts_seasonal_state_space_model(), sts_semi_local_linear_trend_state_space_model(), sts_semi_local_linear_trend(), sts_smooth_seasonal_state_space_model(), sts_smooth_seasonal(), sts_sparse_linear_regression(), sts_sum()