Mean-reversion for random process

Question

I moedelled following ARIMA Process which I also smoothed.

abc1 <- (arima.sim(n = 1400, list(ar = c(0.3, 0.2, 0.15, 0.1, 0.1, 0.1)), sd = sqrt(0.5)))
plot(abc1)
abc2 <- SMA(abc1, n=360)
plot(abc2)

My aim is it to add a component for mean-reversion to describe a business cycle model. Ideas?

thanks, F!

Answer 1

If the ARIMA models doesn't fit because of a cyclic component with a known period you can use seasonal differencing to handle the periodic component. Another possibility is to incorporate a sine wave with the amplitude as a parameter for the model. If you are not sure of the exact length of the period you can make the frequency component in the sine function a model parameter. Periods can also be identified by looking at the periodogram of a smoothed version called the spetral density function.