Markov-Switching Multifractal Model

This Julia module implements the Markov-Switching Multifractal model of Calvet, L. E. and Fisher, A. J. (2004). How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes. Journal of Financial Econometrics, 2(1):49-83.

The code can be used to run the module on a time-series of returns, as well as on the residuals of an ARMA(1,1) process.

Example

Load the module

using MSM

Simulate a return series by setting the parameters of the process. The number of states is given by $\bar{k}$

kbar = 5 

The parameter controling the binomial distribution from which the states are drawn is $m_0 \in (0,2]$

m0 = 1.6

The state transition probabilities are given by $\gamma_k = 1 - (1 - \gamma_0)^b$, where $\gamma_0 \in (0,1)$ and $b \in (1,\infty)$

b = 1.1 
γ₀ = 0.5

Finally, $\sigma>0$ is a positive constant in the volatility process

σ = 2.0/sqrt(252)

The number of time periods is given by

T = 2000

To simulate the process, we can use the function

data = MSM.simulate(b,m0,γ₀,σ,kbar,T)

and to estimate the parameters

ψ = MSM.estimate(data,kbar,scale)