Time Series estimation of Cyclical data process

Procedure for estimation cyclical data

The datafile represents 19 years of a cyclical data process with monthly output for month(i) of year y: output(i,y)

The empirical means and standard deviations for month(i) are m(i) and s(i) respectively

The correlation between month(i) and month(i+1) is c(i+1). (Note: due to cyclical nature, c(i) is computed using correlation of month(12) and month(1))

The goal is to simulate this process 'x' amount of years into the future so that the data generated keeps the same means, standard deviations for each month as well as the correlations between months.

This code constructs an ar(1) process that can be use to replicate data of this type. It then plots the historical and simulates estimates of the parameters for comparison.

This code can be used to replicate the means, standard deviations, correlation dynamics of any cyclical process