R Notebook

# defining ARMA(1,1) parameters
phi = 0.5
theta = 0.5
sigma2 = 1
# generating white noise
z = rnorm(100, mean = 0, sd = sqrt(sigma2))
# Simulating ARMA(1,1) process
x = arima.sim(model = list(ar = phi, ma = theta), n = 100, innov = z)
# Computing psi coefficients
arima_model = arima(x, order = c(1, 0, 1), include.mean = FALSE)
psi = -arima_model$coef[2]
# Printing results
cat("Psi: ")

## Psi:

## Psi:
print(psi)

##        ma1 
## -0.6705205

pi = ARMAacf(ar = phi, ma = theta, lag.max = 5)
# Printing results
cat("Psi: ")

## Psi:

## Psi:
print(psi)

##        ma1 
## -0.6705205

cat("Pi coefficients: ")

## Pi coefficients:

## Pi coefficients:
print(pi)

##          0          1          2          3          4          5 
## 1.00000000 0.71428571 0.35714286 0.17857143 0.08928571 0.04464286