Generate scenarios of multiple related parameters

Question

Assume I have three industry datasets: interest rates, inflation and unemployment. Data contains information of last ten years and it's monthly.

Now, I would like to create N possible scenarios of the next year, also monthly.

The idea is to run a Monte Carlo simulation that calculates a function that has interest rates, inflation and unemployment as input parameters. So I would like to create possible scenarios, but since there's a relationship between the parameters I cannot randomly select values. Is there a method to generate random data of multiple parameters taking into account that they are related?

Answer 1

This is a common occurrence in monte carlo models. I suggest you look into Cholesky decomposition. The basic idea is that if you have a covariance matrix M that describes the relationship between your data, the cholesky decomposition will produce a lower triangular matrix L such that M = L * L'

Now if you generate a vector X of random normals you can take L * X to get a matrix of simulated variables that preserves the covariance structure. I recommend reading https://www.r-bloggers.com/simulating-data-following-a-given-covariance-structure/ which it explains why this is true.