mbsts (version 1.0)

tsc.setting: Specification of time series components

Description

Specify three time series components for MBSTS model (generalized linear trend, seasonality and cycle). A generalization of the local linear trend model where the slope exhibits stationarity instead of obeying a random walk, is expressed in the form as: $$\mu_{t+1}=\mu_t+\delta_t+rnorm(0,\Sigma_\mu)$$ $$\delta_{t+1}=D+\rho(\delta_t-D)+rnorm(0,\Sigma_\delta)$$ The seasonal model in the time domain is: $$\tau_{t+1}^{(i)}=-\sum_{k=0}^{S_i-2}\tau ^{(i)}_{t-k}+rnorm(0,\Sigma_\tau)$$ The cycle component is postulated as: $$\omega_{t+1}=varrho*cos(\lambda)\omega_{t}+varrho*sin(\lambda)\omega*_{t}+rnorm(0,\Sigma_\omega)$$ $$\omega*_{t+1}=-varrho*sin(\lambda)\omega_{t}+varrho*cos(\lambda)\omega*_{t}+rnorm(0,\Sigma_\omega)$$

Usage

tsc.setting(Y, mu = NULL, rho = NULL, S = NULL, vrho = NULL, lambda = NULL)

Arguments

Y

The multivariate time series to be modeled, as a numeric matrix convertible to xts. This state model assumes Y contain daily data.

mu

A vector of logic values, indicating whether to include a local trend for each target series.

rho

A vector of numerical values, all of which are between 0 and 1, describing the learning rates at which the local trend is updated for each target series. The value 0 in jth entry indicates that jth target series does not include slope of trend.

S

A vector of integer values, representing the number of seasons to be modeled for each target series. The value 0 in jth entry indicates that jth target series does not include seasonal component.

vrho

A vector of numerical values between 0 and 1, describing a damping factor for each target series. The value 0 in jth entry indicates that jth target series does not include cycle component.

lambda

A vector of numerical values, each of them is equal to \(2\pi/q\), describing the frequency with q being a period such that \(0<\lambda<\pi\).

Value

Returns a customerized State Space model, which is an object of class SSModel.

Details

The function allows users to include different combination of time series components for each target series.

References

Harvey (1990), "Forecasting, structural time series, and the Kalman filter", Cambridge University Press.

Durbin and Koopman (2001), "Time series analysis by state space methods", Oxford University Press.

See Also

SSModel

Examples

# NOT RUN {
data(exdata)
Y<-as.matrix(exdata[,1:2])
STmodel<-tsc.setting(Y,mu=c(1,1),rho=c(0.6,1),S=c(4,0),
                     vrho=c(0,0.5),lambda=c(0,pi/10))
# }