mbsts (version 3.0)

sim_data: Simulate data

Description

Generate simulated data in the form of structural time series

Usage

sim_data(
  X,
  beta,
  cov,
  k,
  mu,
  rho,
  mean_trend = 1,
  sd_trend = 0.5,
  mean_season = 20,
  sd_season = 0.5,
  mean_cycle = 20,
  sd_cycle = 0.5,
  Dtilde,
  Season,
  vrho,
  lambda
)
# S4 method for array
sim_data(
  X,
  beta,
  cov,
  k,
  mu,
  rho,
  mean_trend = 1,
  sd_trend = 0.5,
  mean_season = 20,
  sd_season = 0.5,
  mean_cycle = 20,
  sd_cycle = 0.5,
  Dtilde,
  Season,
  vrho,
  lambda
)

Arguments

X

A (\(n*K\))-dimensional matrix containing predictors, where \(n\) is the number of observations. \(K=\sum k_i\) is the number of all candidate predictors for all target series. The first \(k_1\) variables are the set of candidate predictors for the first target series, and the next \(k_2\) variables are the set of candidate predictors for the second target series, etc.

beta

A (\(K*m\))-dimensional matrix containing all candidate predictor series for each target series.

cov

A (\(m*m\))-dimensional matrix containing covariances

k

A \(m\)-dimensional array containing the number of candidate predictors for each of the \(m\) target series.

mu

A \(m\)-dimensional array with \(1\) representing modeling with trend for this target time series.

rho

A \(m\)-dimensional array representing the learning rates at which the local trend is updated.

mean_trend

A numerical value standing for the mean of the error term of the trend component. The default value is \(1\).

sd_trend

A numerical value standing for the standard deviation of the error term of the trend component. The default value is \(0.5\).

mean_season

A numerical value standing for the mean of the error term of the seasonal component. The default value is \(20\).

sd_season

A numerical value standing for the standard deviation of the error term of the seasonal component. The default value is \(0.5\).

mean_cycle

A numerical value standing for the mean of the error term of the cycle component. The default value is \(20\).

sd_cycle

A numerical value standing for the standard deviation of the error term of the cycle component. The default value is \(0.5\).

Dtilde

A \(m\)-dimensional array with \(1\) representing level in the trend component.

Season

A \(m\)-dimensional array indicating the seasonality for each target series, such as c(12,0).

vrho

A \(m\)-dimensional array of the decay value parameter of the cycle component for each target series, such as c(0,0.99).

lambda

A \(m\)-dimensional array of the frequence parameter of the cycle component for each target series, such as c(0,pi/100).

Author

Jinwen Qiu Ning Ning

References

Qiu, Jammalamadaka and Ning (2018), Multivariate Bayesian Structural Time Series Model, Journal of Machine Learning Research 19.68: 1-33.

Ning and Qiu (2021), The mbsts package: Multivariate Bayesian Structural Time Series Models in R.

Jammalamadaka, Qiu and Ning (2019), Predicting a Stock Portfolio with the Multivariate Bayesian Structural Time Series Model: Do News or Emotions Matter?, International Journal of Artificial Intelligence, Vol. 17, Number 2.

Examples

###############Setup###########
n<-505 #n: sample size
m<-2 #m: dimension of target series

cov<-matrix(c(1.1,0.7,0.7,0.9), nrow=2, ncol=2) #covariance matrix of target series 

###############Regression component###########
#coefficients for predictors
beta<-t(matrix(c(2,-1.5,0,4,2.5,0,0,2.5,1.5,-1,-2,0,0,-3,3.5,0.5),nrow=2,ncol=8)) 

set.seed(100)
X1<-rnorm(n,5,5^2)
X4<-rnorm(n,-2,5)
X5<-rnorm(n,-5,5^2)
X8<-rnorm(n,0,100)
X2<-rpois(n, 10)
X6<-rpois(n, 15)
X7<-rpois(n, 20)
X3<-rpois(n, 5)
X<-cbind(X1,X2,X3,X4,X5,X6,X7,X8) 

###############Simulated data################
set.seed(100)
data=sim_data(X=X, beta=beta, cov, k=c(8,8), mu=c(1,1), rho=c(0.6,0.8), 
              Dtilde=c(-1,3), Season=c(100,0), vrho=c(0,0.99), lambda=c(0,pi/100))