# Simulate data Generate simulated data in the form of structural time series methods ```r 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 signature '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). ## Examples ```r ###############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)) ``` ## 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. ## Author(s) Jinwen Qiu qjwsnow_ctw@hotmail.com Ning Ning patricianing@gmail.com

sim_data function