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Decomposition of time series data with Bayesian Adaptive Seasonality Trend decomposition Incorporating Outlier and Noise (BASTION)

fit_BASTION.Rd

decompose time series data using BASTION. The time series should be a vector.

Usage

fit_BASTION(
  y,
  Ks,
  X = NULL,
  Outlier = FALSE,
  cl = 0.95,
  sparse = FALSE,
  obsSV = "const",
  nchains = 2,
  nsave = 1000,
  nburn = 1000,
  nskip = 4,
  verbose = TRUE,
  save_samples = FALSE
)

Arguments

y

numeric vector of the T x 1 vector of time series observations

Ks

list of values containing the seasonal periods

X

matrix for additional covariate for regression (default is NULL)

Outlier

logical flag (default is FALSE) to model outlier

cl

scalar between (0,1) for confidence leve (default is 0.95)

sparse

logical flag (default is FALSE) to induce additional shrinkage to the trend estimate

obsSV

options for modeling the error variance. It must be one of the following:

  • const: Constant error variance for all time points.

  • SV: Stochastic Volatility model.

nchains

integer scalar for the number of chains for MCMC sampling (default is 2)

nsave

integer scalar (default = 1000); number of MCMC iterations to record

nburn

integer scalar (default = 1000); number of MCMC iterations to discard (burn-in)

nskip

integer scalar (default = 4); number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw

verbose

logical; report extra information on progress if true. Defaults to FALSE

save_samples

logical; save and return posterior samples of each components if true. Default is FALSE

Value

fit_BASTION returns an object class list.

summary

A list providing summarized posterior estimates:

  • p_means: A matrix containing the posterior means of the observed data (y) and each decomposed component: Trend, Seasonality, and Outlier, if applicable.

  • Trend_sum: A matrix containing the posterior mean and 95% credible interval of the trend estimate.

  • Seasonal"k"_sum: A matrix containing the posterior mean and 95% credible interval of the seasonal estimate, where "k" is determined by the input.

  • Outlier_sum: A matrix containing the posterior mean and 95% credible interval of the outlier component.

samples

(returned only when save_samples = TRUE) A list containing MCMC samples of the relevant parameters:

  • beta_combined: Posterior samples of Trend + Seasonality.

  • beta: Posterior samples of each component excluding the remainder.

  • obs_sigma_t2: Posterior samples of the variance of the observation equation.

  • evol_sigma_t2: Posterior samples of the evolution error term.

  • remainder: Posterior samples of the remainder term.

  • yhat: Posterior samples of the signal + error term.