Generate_Data {RobKF}

Simulate data from a Kalman model

Description

This function simulates data obeying a Kalman model whilst allowing the user to add innovative and additive anomalies.

Usage

Generate_Data(
  n,
  A,
  C,
  Sigma_Add,
  Sigma_Inn,
  mu_0 = NULL,
  anomaly_loc = integer(0),
  anomaly_type = character(0),
  anomaly_comp = integer(0),
  anomaly_strength = NULL
)

Arguments

n

A positive integer giving the number of observations desired

A

A matrix giving the updates for the hidden states.

C

A matrix mapping the hidden states to the observed states.

Sigma_Add

A positive definite diagonal matrix giving the additive noise covariance.

Sigma_Inn

A positive definite diagonal matrix giving the innovative noise covariance.

mu_0

A matrix indicating the mean of the prior for the hidden states. It defaults to a zero-vector.

anomaly_loc

A vector of integers giving the locations of anomalies.

anomaly_type

A vector of strings, either "Add" or "Inn" indicating whether the anomaly is additive or innovative.

anomaly_comp

A vector of integers giving the component affected by the anomalies.

anomaly_strength

A vector of numerics giving the strength of the anomalies (in sigmas).

Value

A list of matrices, each corresponding to an observation.

Examples

library(RobKF)
library(ggplot2)

set.seed(2018)

A = diag(2)*0.99
A[1,2] = -0.05
C = matrix(c(10,0.1),nrow=1)
mu = matrix(c(0,0),nrow=2)
Sigma_Inn = diag(c(1,0.01)*0.00001,nrow=2)
Sigma_Add = diag(c(1)*0.1,nrow=1)

Y_list = Generate_Data(100,A,C,Sigma_Add,Sigma_Inn, mu_0 = mu,  anomaly_loc = c(10,30,50), 
                      anomaly_type = c("Inn","Add","Inn"), 
                      anomaly_comp = c(1,1,2),  anomaly_strength = c(400,-10,3000))
                      
qplot(1:100,unlist(Y_list),xlab="time",ylab="observation")+theme_minimal()