Formal representation of a dynamic linear regression model.

The dynamic linear regression model is a special case of a linear Gaussian SSM and a generalization of typical (static) linear regression. The model represents regression weights with a latent state which evolves via a Gaussian random walk:

sts_dynamic_linear_regression(
  observed_time_series = NULL,
  design_matrix,
  drift_scale_prior = NULL,
  initial_weights_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.
design_matrix	float tensor of shape tf$concat(list(batch_shape, list(num_timesteps, num_features))). This may also optionally be an instance of tf$linalg$LinearOperator.
drift_scale_prior	instance of Distribution 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_weights_prior	instance of tfd_multivariate_normal representing the prior distribution on the latent states (the regression weights). Must have event shape list(num_features). If NULL, a weakly-informative Normal(0, 10) prior is used. Default value: NULL.
name	the name of this component. Default value: 'DynamicLinearRegression'.

Value

an instance of StructuralTimeSeries.

Details

weights[t] ~ Normal(weights[t-1], drift_scale)

The latent state has dimension num_features, while the parameters drift_scale and observation_noise_scale are each (a batch of) scalars. The batch shape of this distribution is the broadcast batch shape of these parameters, the initial_state_prior, and the design_matrix. num_features is determined from the last dimension of design_matrix (equivalent to the number of columns in the design matrix in linear regression).

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_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_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()