Coverage for local/lib/python2.7/site-packages/sage/finance/markov_multifractal.py : 67%

""" 

Markov Switching Multifractal model 

REFERENCE: 

*How to Forecast Long-Run Volatility: Regime Switching and 

the Estimation of Multifractal Processes*, Calvet and Fisher, 2004. 

AUTHOR: 

- William Stein, 2008 

TESTS:: 

sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3) 

sage: loads(dumps(msm)) == msm 

True 

""" 

from __future__ import absolute_import 

import math 

class MarkovSwitchingMultifractal: 

def __init__(self, kbar, m0, sigma, gamma_kbar, b): 

""" 

INPUT: 

- ``kbar`` -- positive integer 

- ``m0`` -- float with ``0 <= m0 <= 2`` 

- ``sigma`` -- positive float 

- ``gamma_kbar`` -- float with ``0 <= gamma_kbar < 1`` 

- ``b`` -- float > 1 

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) 

""" 

self.__m0 = float(m0) 

assert self.__m0 >= 0 and self.__m0 <= 2, "m0 must be between 0 and 2" 

self.__sigma = float(sigma) 

assert self.__sigma > 0, "sigma must be positive" 

self.__b = float(b) 

assert self.__b > 1, "b must be bigger than 1" 

self.__gamma_kbar = float(gamma_kbar) 

assert self.__gamma_kbar >= 0 and self.__gamma_kbar < 1, \ 

"gamma_kbar must be between 0 and 1" 

self.__kbar = int(kbar) 

assert self.__kbar > 0, "kbar must be positive" 

def __eq__(self, other): 

""" 

Test equality of ``self`` and ``other``. 

Comparison is done on the tuple ``(m0, sigma, b, gamma_kbar, kbar)``. 

EXAMPLES:: 

sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3) 

sage: msm == msm 

True 

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 

sage: msm == cad_usd 

False 

""" 

if not isinstance(other, MarkovSwitchingMultifractal): 

return False 

return (self.__m0 == other.__m0 and 

self.__sigma == other.__sigma and 

self.__b == other.__b and 

self.__gamma_kbar == other.__gamma_kbar and 

self.__kbar == other.__kbar) 

def __hash__(self): 

""" 

Return the hash of ``self``. 

EXAMPLES:: 

sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3) 

sage: H = hash(msm) 

""" 

return hash((self.__m0, self.__sigma, self.__b, self.__gamma_kbar, 

self.__kbar)) 

def __ne__(self, other): 

""" 

Test inequality of ``self`` and ``other``. 

EXAMPLES:: 

sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3) 

sage: msm != msm 

False 

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 

sage: msm != cad_usd 

True 

""" 

return not (self == other) 

def __repr__(self): 

""" 

Return string representation of Markov switching multifractal model. 

EXAMPLES:: 

sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1,0.95,3) 

sage: msm.__repr__() 

'Markov switching multifractal model with m0 = 1.4, sigma = 1.0, b = 3.0, and gamma_8 = 0.95' 

""" 

return "Markov switching multifractal model with m0 = %s, sigma = %s, b = %s, and gamma_%s = %s"%(self.m0(), self.sigma(), self.b(), self.kbar(), self.gamma_kbar()) 

def m0(self): 

""" 

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 self.__m0 

def sigma(self): 

""" 

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 

""" 

return self.__sigma 

def b(self): 

""" 

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 self.__b 

def gamma_kbar(self): 

""" 

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 self.__gamma_kbar 

def kbar(self): 

""" 

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 self.__kbar 

def gamma(self): 

""" 

Return the vector of the kbar transitional probabilities. 

OUTPUT: 

- gamma -- a tuple of ``self.kbar()`` floats. 

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...) 

""" 

try: 

return self.__gamma 

except AttributeError: 

pass 

b = self.__b 

gamma_kbar = self.__gamma_kbar 

kbar = self.__kbar 

# We compute gamma1 from gamma_kbar by inverting the relation 

# that defines the gamma_k given on page 54 of Calvet-Fisher: 

gamma1 = 1 - math.exp(math.log(1-gamma_kbar)/(b**(kbar-1))) 

gamma = tuple([1 - (1 - gamma1)**(b**k) for k in range(kbar)]) 

self.__gamma = gamma 

return gamma 

def simulation(self, n): 

""" 

Same as ``self.simulations``, but run only 1 time, and returns a time 

series instead of a list of time series. 

INPUT: 

- ``n`` -- a positive integer. 

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 self.simulations(n, 1)[0] 

def simulations(self, n, k=1): 

""" 

Return ``k`` simulations of length ``n`` using this Markov switching 

multifractal model for ``n`` time steps. 

INPUT: 

- ``n`` -- positive integer; number of steps. 

- ``k`` -- positive integer (default: 1); number of simulations. 

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 

""" 

from . import markov_multifractal_cython 

return markov_multifractal_cython.simulations(n, k, 

self.__m0, self.__sigma, 

self.__kbar, self.gamma()) 

## def ml_estimation(v, kbar, M): 

## """ 

## Compute parameters that model the time series v, 

## INPUT: 

## v -- series of returns; e.g., sequence of 

## differences of logs of price 

## kbar -- positive integer; model parameter 

## m -- finite list of the values that the multiplier 

## M takes on. 

## OUTPUT: 

## m0, sigma, gamma_kbar, b 

## """