R: Formal representation of a semi-local linear trend model.

sts_semi_local_linear_trend {tfprobability}

R Documentation

Formal representation of a semi-local linear trend model.

Description

Like the sts_local_linear_trend model, a semi-local linear trend posits a latent level and slope, with the level component updated according to the current slope plus a random walk:

Usage

sts_semi_local_linear_trend(
  observed_time_series = NULL,
  level_scale_prior = NULL,
  slope_mean_prior = NULL,
  slope_scale_prior = NULL,
  autoregressive_coef_prior = NULL,
  initial_level_prior = NULL,
  initial_slope_prior = NULL,
  constrain_ar_coef_stationary = TRUE,
  constrain_ar_coef_positive = FALSE,
  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$distribution` instance specifying a prior on the `level_scale` parameter. If `NULL`, a heuristic default prior is constructed based on the provided `observed_time_series`. Default value: `NULL`.
`slope_mean_prior`	optional `tfd$Distribution` instance specifying a prior on the `slope_mean` parameter. If `NULL`, a heuristic default prior is constructed based on the provided `observed_time_series`. Default value: `NULL`.
`slope_scale_prior`	optional `tfd$Distribution` instance specifying a prior on the `slope_scale` parameter. If `NULL`, a heuristic default prior is constructed based on the provided `observed_time_series`. Default value: `NULL`.
`autoregressive_coef_prior`	optional `tfd$Distribution` instance specifying a prior on the `autoregressive_coef` parameter. If `NULL`, the default prior is a standard `Normal(0, 1)`. Note that the prior may be implicitly truncated by `constrain_ar_coef_stationary` and/or `constrain_ar_coef_positive`. Default value: `NULL`.
`initial_level_prior`	optional `tfp$distribution` instance specifying a prior on the initial level. If `NULL`, a heuristic default prior is constructed based on the provided `observed_time_series`. Default value: `NULL`.
`initial_slope_prior`	optional `tfd$Distribution` instance specifying a prior on the initial slope. If `NULL`, a heuristic default prior is constructed based on the provided `observed_time_series`. Default value: `NULL`.
`constrain_ar_coef_stationary`	if `TRUE`, perform inference using a parameterization that restricts `autoregressive_coef` to the interval `⁠(-1, 1)⁠`, or `⁠(0, 1)⁠` if `force_positive_ar_coef` is also `TRUE`, corresponding to stationary processes. This will implicitly truncate the support of `autoregressive_coef_prior`. Default value: `TRUE`.
`constrain_ar_coef_positive`	if `TRUE`, perform inference using a parameterization that restricts `autoregressive_coef` to be positive, or in `⁠(0, 1)⁠` if `constrain_ar_coef_stationary` is also `TRUE`. This will implicitly truncate the support of `autoregressive_coef_prior`. Default value: `FALSE`.
`name`	the name of this model component. Default value: 'SemiLocalLinearTrend'.

Details

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

The slope component in a sts_semi_local_linear_trend model evolves according to a first-order autoregressive (AR1) process with potentially nonzero mean:

slope[t] = (slope_mean + autoregressive_coef * (slope[t-1] - slope_mean) + Normal(0., slope_scale))

Unlike the random walk used in LocalLinearTrend, a stationary AR1 process (coefficient in ⁠(-1, 1)⁠) maintains bounded variance over time, so a SemiLocalLinearTrend model will often produce more reasonable uncertainties when forecasting over long timescales.

Value