Outliers: Simulated time series data for detecting outliers.

In dynr: Dynamic Models with Regime-Switching

Simulated time series data for detecting outliers.

Description

This is a list object containing true outliers, the dataset, and the saved result from running dynr.taste.

Usage

data(Outliers)

Format

A data frame with 6000 rows and 6 variables

Details

The true outliers for observed variables are saved in ‘Outliers$generated$shockO’.

• id. Six outliers were added for each ID.

• time_O. Time points where the outliers were added.

• obs. Variable indices where the outliers were added.

• shock.O. The magnitude of outliers.

The true outliers for state variables are saved in ‘Outliers$generated$shockL’.

• id. Three outliers were added for each ID.

• time_L. Time points where the outliers were added.

• lat. Variable indices where the outliers were added.

• shock.L. The magnitude of outliers.

A dataset simulated based on state-space model including the outliers. The data is saved in ‘Outliers$generated$y’. The variables are as follows:

• id. ID of the systems (1 to 100)

• times. Time indices (100 time points for each participant)

• V1 - V6. observed variables

The detected innovative outliers from dynr.taste for this dataset, which is used for testing whether the dynr.taste replicate the same result. The data is saved in ‘Outliers$detect_O’. The variables are as follows:

• id. IDs

• time_L. Time points where the outliers were detected

• obs. Variable indices for observed variables where the outliers were detected

The detected additive outliers from dynr.taste for this dataset, which is used for testing whether the dynr.taste replicate the same result. The data is saved in ‘Outliers$detect_L’. The variables are as follows:

• id. IDs

• time_L. Time points where the outliers were detected

• obs. Variable indices for latent variables where the outliers were detected

Examples

## Not run: 
 #The following was used to generate the data
 #---------------------------------------
 lambda <- matrix(c(1.0, 0.0,
 0.9, 0.0,
 0.8, 0.0,
 0.0, 1.0,
 0.0, 0.9,
 0.0, 0.8), ncol=2, byrow=TRUE)
 psi <- matrix(c(0.3, -0.1,
                 -0.1, 0.3), ncol=2, byrow=TRUE)
 beta <- matrix(c(0.8, -0.2,
                  -0.2,  0.7), ncol=2, byrow=TRUE)
 theta <- diag(c(0.2, 0.2, 0.2, 0.2, 0.2, 0.2), ncol=6, nrow=6)
 nlat <- 2; nobs <- 6
 mean_0 <- rep(0, nlat)
 psi_inf <- diag(1, 2*2) - kronecker(beta, beta)
 psi_inf_inv <- try(solve(psi_inf), silent=TRUE)
 if("try-error" %in% class(psi_inf_inv)) {
   psi_inf_inv <- MASS::ginv(psi_inf)}
 psi_0 <- psi_inf_inv %*% as.vector(psi)
 dim(psi_0) <- c(2, 2)
 # measurement error covariance matrix
 mea_cov <- lambda %*% psi_0 %*% t(lambda) + theta
 resL <- lapply(1:100, function(subj) {
   # initial state
   eta_0 <- mvtnorm::rmvnorm(1, mean=mean_0, sigma=psi_0)#[1,nlat]
   zeta_0 <- mvtnorm::rmvnorm(1, mean=rep(0, nlat), sigma=psi)
   eta <- matrix(0, nrow=time, ncol=nlat)
   eta[1, ] <- beta %*% t(eta_0) + t(zeta_0) 
   zeta <- mvtnorm::rmvnorm(time, mean=rep(0, nlat), sigma=psi)
   # random shock generation
   # to avoid shock appearing too early or late (first and last 3)
   shkLat_time <- sample(4:(time-3), nshockLat)
   shk_lat <- sample(1:nlat, nshockLat, replace=TRUE)
   shockLatIdx <- matrix(c(shkLat_time, shk_lat), ncol=2)
   shockSignL <- sample(c(1,-1), nshockLat, replace=TRUE)
   colnames(shockLatIdx) <- c("time_L","lat")
   shockLatV <- shockSignL*( shockMag*sqrt(diag(shockPsi)))[shockLatIdx[,"lat"]]
   shockLatM <- matrix(0, time, nlat)
   shockLatM[shockLatIdx] <- shockLatV
   shkObs_time <- sample(4:(time-3), nshockObs)
   shk_obs <- sample(1:nobs, nshockObs, replace=TRUE)
   shockObsIdx <- matrix(c(shkObs_time, shk_obs), ncol=2)
   shockSignO <- sample(c(1,-1), nshockObs, replace=TRUE)
   colnames(shockObsIdx) <- c("time_O","obs")
   shockObsV <- shockSignO*( shockMag*sqrt(diag(mea_cov)) )[shockObsIdx[,"obs"]]
   shockObsM <- matrix(0, time, nobs)
   shockObsM[shockObsIdx] <- shockObsV
   # generate state process WITH shock
   for (t in 1:(time-1)) {
     eta[t+1, ] <- shockLatM[t, ] + beta %*% eta[t, ] + zeta[t, ]
   }
   # generate observed process
   y <- shockObsM + eta %*% t(lambda) +
     mvtnorm::rmvnorm(time, mean=rep(0, nobs), sigma=theta)# epsilon
 }
 
## End(Not run)

dynr documentation built on Oct. 17, 2022, 9:06 a.m.