Formal representation of a local level model

The local level model posits a level evolving via a Gaussian random walk:

level[t] = level[t-1] + Normal(0., level_scale)

sts_local_level(
  observed_time_series = NULL,
  level_scale_prior = NULL,
  initial_level_prior = NULL,
  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.
level_scale_prior	optional tfp$distribution instance specifying a prior on the level_scale parameter. If NULL, a heuristic default prior is constructed based on the provided observed_time_series. Default value: NULL.
initial_level_prior	optional tfp$distribution instance specifying a prior on the initial level. If NULL, a heuristic default prior is constructed based on the provided observed_time_series. Default value: NULL.
name	the name of this model component. Default value: 'LocalLevel'.

Value

an instance of StructuralTimeSeries.

Details

The latent state is [level]. We observe a noisy realization of the current level: f[t] = level[t] + Normal(0., observation_noise_scale) at each timestep.

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_linear_trend_state_space_model(), sts_local_linear_trend(), sts_seasonal_state_space_model(), sts_seasonal(), 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()