REFERENCE:
How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes, Calvet and Fisher, 2004.
AUTHOR:
TESTS:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3)
sage: loads(dumps(msm)) == msm
True
INPUT:
EXAMPLES:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,0.5,0.95,3); msm
Markov switching multifractal model with m0 = 1.4, sigma = 0.5, b = 3.0, and gamma_8 = 0.95
sage: yen_usd = finance.MarkovSwitchingMultifractal(10,1.448,0.461,0.998,3.76)
sage: cad_usd = finance.MarkovSwitchingMultifractal(10,1.278,0.262,0.644,2.11)
sage: dm = finance.MarkovSwitchingMultifractal(10,1.326,0.643,0.959,2.7)
Return parameter b of Markov switching multifractal model.
EXAMPLES:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1,0.95,3)
sage: msm.b()
3.0
Return the vector of the kbar transitional probabilities.
OUTPUT:
EXAMPLES:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3)
sage: msm.gamma()
(0.001368852970712986, 0.004100940201672509, 0.012252436441829..., 0.03630878209190..., 0.10501923017634..., 0.28312883556311..., 0.6315968501359..., 0.95000000000000...)
Return parameter gamma_kbar of Markov switching multifractal model.
EXAMPLES:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,0.01,0.95,3)
sage: msm.gamma_kbar()
0.95
Return parameter kbar of Markov switching multifractal model.
EXAMPLES:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,0.01,0.95,3)
sage: msm.kbar()
8
Return parameter m0 of Markov switching multifractal model.
EXAMPLES:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1,0.95,3)
sage: msm.m0()
1.4
Return parameter sigma of Markov switching multifractal model.
EXAMPLES:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1,0.95,3)
sage: msm.sigma()
1.0
Same as self.simulations, but run only 1 time, and returns a time series instead of a list of time series.
INPUT:
EXAMPLES:
sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3)
sage: msm.simulation(5)
[0.0059, -0.0097, -0.0101, -0.0110, -0.0067]
sage: msm.simulation(3)
[0.0055, -0.0084, 0.0141]
Return k simulations of length n using this Markov switching multifractal model for n time steps.
INPUT:
OUTPUT:
list – a list of TimeSeries objects.
EXAMPLES:
sage: cad_usd = finance.MarkovSwitchingMultifractal(10,1.278,0.262,0.644,2.11); cad_usd
Markov switching multifractal model with m0 = 1.278, sigma = 0.262, b = 2.11, and gamma_10 = 0.644