Create a trend-periodic-local time-series kernel — time_series

Constructs a transparent additive example consisting of a nonstationary linear covariance component, a periodic covariance component, and a local Matérn-3/2 component. The components are explicit so stationarity is never implied for the full model.

Usage

time_series_kernel(
  period,
  trend_variance = 1,
  periodic_variance = 1,
  periodic_length_scale = 1,
  local_variance = 1,
  local_length_scale = 1,
  changepoint = NULL,
  changepoint_steepness = 1
)

Arguments

period: Positive period in the same units as the time index.
trend_variance: Positive variance of the linear trend component.
periodic_variance: Positive variance of the periodic component.
periodic_length_scale: Positive periodic length scale.
local_variance: Positive variance of the local Matérn component.
local_length_scale: Positive local Matérn length scale.
changepoint: Optional location of a structural break, on the time index scale of gp_time_index(): elapsed time since the first training time, in its unit.
changepoint_steepness: Positive steepness of the break.

Value

A composite gaussianprocesses_kernel.

Details

With a changepoint, the kernel is a changepoint_kernel() between two independent copies of the trend-periodic-local kernel, so every component can change at the break; the copies start from the same parameter values and are estimated separately. To place a break at a date, convert it with the training times: gp_time_index(c(time[1], date), unit)[2].

Stability

Stable: from version 1.0.0 this interface changes incompatibly only in a major release, after a deprecation period. Results and options that concern an experimental model class, kernel, or argument follow that interface's tier. See gaussianprocesses-package for the policy. The changepoint argument, which builds a changepoint_kernel(), is experimental.

Examples

kernel <- time_series_kernel(period = 12)
kernel
#> SumKernel(
#>   Linear(variance=1)
#>   Periodic(variance=1, length_scale=1, period=12)
#>   Matern-3/2(variance=1, length_scale=1)
#> )

# A structural break 30 time units after the first observation.
names(kernel_parameters(
  time_series_kernel(period = 12, changepoint = 30),
  flatten = TRUE
))
#>  [1] "location"                    "steepness"                  
#>  [3] "before.kernel1.variance"     "before.kernel2.variance"    
#>  [5] "before.kernel2.length_scale" "before.kernel2.period"      
#>  [7] "before.kernel3.variance"     "before.kernel3.length_scale"
#>  [9] "after.kernel1.variance"      "after.kernel2.variance"     
#> [11] "after.kernel2.length_scale"  "after.kernel2.period"       
#> [13] "after.kernel3.variance"      "after.kernel3.length_scale"