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time-seriessimulationalphaarimabeta

Simulating Time Series Model in R

I want to answer the following question, I know that I can use the arima.sim function but I am not sure how to simulate model asked:

I want to simulate the following:

yt =α+βt+φyt−1 +εt, εt ∼IIDN(0,1)

when: alpha=1, beta=0 and theta=0.8

Before each simulation we should set the seed to 100,000. Assume a starting value of y0=0 and obtain 500 observations. I have tried the following but it doesn't seem to work:

set.seed(seed = 100000)
e <- rnorm(500)
m1 <- arima.sim(model = list(c(ma=0.8,alpha=1,beta=0)),n=500)

I have to simulate 4 different models for 4 different values of beta, theta and alpha. Any suggestions?

Thanks in advance.

Solution

  • 1. (α,β,φ) = (1,0,0.8)

    set.seed(seed = 1232020)
e <- rnorm(500,mean=0,sd=1)

alpha <- 1
beta <- 0
theta <- 0.8
m_1 <- 0
for(i in 2:length(e)){
  m_1[i] <- alpha+beta*i+theta*m_1[i-1]+e[i]
}

    Think this should do the trick :)