I want to optimize a portfolio based on regime switching model. Before optimization i need to detect the hidden regimes in the data. Let us suppose i want to start my analysis with GDP. What i want is to know the steps that are involved in identifying the regimes in a variable. There are many packages which do it.
The first step is to download data for GDP. Then how should i proceed to detect the regimes. I will appreciate if some one just list the steps. For now i am not interested in the model or calculation. I just need to know what are the general steps in detecting the regimes in a variable.
Suppose that the GDP is observed at fixed intervals of time of length ∆. Let the total number of observation is N. Let S(i) be the observation at the end of i-th interval. Now calculate the return
- r(i) =(S(i)−S(i−1))/S(i−1).
Choose n much smaller than N. A standard choice is n=20 whereas N is of the order 10^3 or more. For every i>n, calculate the moving mean ̄r(i) and moving standard deviation sd(i) of {r(i-1), r(i-2), ..., r(i-n)}
using
- ̄r(i) =average of {r(i-1), r(i-2), ..., r(i-n)} and
- sd(i)= √ (1/(n − 1) Σ0
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