build a chaotic markow chain model to forecast univariate time series data. in r

main.r
# Load required packages
library(mvtnorm)
library(stats)

# Generate time series data
set.seed(123)
n <- 1000
x <- rnorm(n)
for(i in 2:n){
  x[i] <- 0.8 * x[i-1] + rnorm(1, 0, 0.2)
}

# Split data into training and testing sets
train_size <- 800
train <- x[1:train_size]
test <- x[(train_size+1):n]

# Build the chaotic Markov chain model
order <- 2 # order of the Markov chain model
P <- array(0, dim=c(order,floor((n-order)/order)+1)) # transitional probability matrix
for(i in 1:floor((n-order)/order)){
  P[,i] <- table(cut(x[(order*(i-1)+1):(order*i)], breaks=quantile(x, probs=(0:order)/order)))
}
P <- P/rowSums(P) # normalize probability
P[is.nan(P)] <- 1/order # handle NA
lambda <- eigen(t(P))$values[1] # largest eigenvalue
pi0 <- rep(1/3,3) # initial probability
mc <- function(N) c(rep(0,(order-1)), rmultinom(N-order+1, 1, pi0 %*% (matrix(lambda, 3, 3)^(floor((order+1):(N-1)/order)+1) * P)))
Z <- list(x=train, y=test, model=list(mc=mc, order=order, P=P, lambda=lambda, pi0=pi0))

# Make predictions using the model
pred <- predict(mc, newdata=list(N=length(test)), object=Z$model)

# Evaluate accuracy of the model
accuracy <- mean(pred[1:length(test)] == test)
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