bsm_lg {bssm}

Basic Structural (Time Series) Model

Description

Constructs a basic structural model with local level or local trend component and seasonal component.

Usage

bsm_lg(
  y,
  sd_y,
  sd_level,
  sd_slope,
  sd_seasonal,
  beta,
  xreg = NULL,
  period,
  a1 = NULL,
  P1 = NULL,
  D = NULL,
  C = NULL
)

Arguments

y

A vector or a ts object of observations.

sd_y

Standard deviation of the noise of observation equation. Should be an object of class bssm_prior or scalar value defining a known value such as 0.

sd_level

Standard deviation of the noise of level equation. Should be an object of class bssm_prior or scalar value defining a known value such as 0.

sd_slope

Standard deviation of the noise of slope equation. Should be an object of class bssm_prior, scalar value defining a known value such as 0, or missing, in which case the slope term is omitted from the model.

sd_seasonal

Standard deviation of the noise of seasonal equation. Should be an object of class bssm_prior, scalar value defining a known value such as 0, or missing, in which case the seasonal term is omitted from the model.

beta

A prior for the regression coefficients. Should be an object of class bssm_prior or bssm_prior_list (in case of multiple coefficients) or missing in case of no covariates.

xreg

A matrix containing covariates with number of rows matching the length of y. Can also be ts, mts or similar object convertible to matrix.

period

Length of the seasonal pattern. Must be a positive value greater than 2 and less than the length of the input time series. Default is frequency(y), which can also return non-integer value (in which case error is given).

a1

Prior means for the initial states (level, slope, seasonals). Defaults to vector of zeros.

P1

Prior covariance matrix for the initial states (level, slope, seasonals).Default is diagonal matrix with 100 on the diagonal.

D

Intercept terms for observation equation, given as a length n numeric vector or a scalar in case of time-invariant intercept.

C

Intercept terms for state equation, given as a m times n matrix or m times 1 matrix in case of time-invariant intercept.

Value

An object of class bsm_lg.

Examples

set.seed(1)
n <- 50
x <- rnorm(n)
level <- numeric(n)
level[1] <- rnorm(1)
for (i in 2:n) level[i] <- rnorm(1, -0.2 + level[i-1], sd = 0.1)
y <- rnorm(n, 2.1 + x + level)
model <- bsm_lg(y, sd_y = halfnormal(1, 5), sd_level = 0.1, a1 = level[1], 
  P1 = matrix(0, 1, 1), xreg = x, beta = normal(1, 0, 1),
  D = 2.1, C = matrix(-0.2, 1, 1))
  
ts.plot(cbind(fast_smoother(model), level), col = 1:2)

prior <- uniform(0.1 * sd(log10(UKgas)), 0, 1)
# period here is redundant as frequency(UKgas) = 4
model_UKgas <- bsm_lg(log10(UKgas), sd_y = prior, sd_level =  prior,
  sd_slope =  prior, sd_seasonal =  prior, period = 4)

# Note small number of iterations for CRAN checks
mcmc_out <- run_mcmc(model_UKgas, iter = 5000)
summary(mcmc_out, return_se = TRUE)
# Use the summary method from coda:
summary(expand_sample(mcmc_out, "theta"))$stat
mcmc_out$theta[which.max(mcmc_out$posterior), ]
sqrt((fit <- StructTS(log10(UKgas), type = "BSM"))$coef)[c(4, 1:3)]