6.11.2. statsmodels.sandbox.tsa.diffusion¶
getting started with diffusions, continuous time stochastic processes
Author: josef-pktd License: BSD
6.11.2.1. References¶
An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations Author(s): Desmond J. Higham Source: SIAM Review, Vol. 43, No. 3 (Sep., 2001), pp. 525-546 Published by: Society for Industrial and Applied Mathematics Stable URL: http://www.jstor.org/stable/3649798
http://www.sitmo.com/ especially the formula collection
6.11.2.2. Notes¶
OU process: use same trick for ARMA with constant (non-zero mean) and drift some of the processes have easy multivariate extensions
Open Issues
include xzero in returned sample or not? currently not
TODOS
- Milstein from Higham paper, for which processes does it apply
- Maximum Likelihood estimation
- more statistical properties (useful for tests)
- helper functions for display and MonteCarlo summaries (also for testing/checking)
- more processes for the menagerie (e.g. from empirical papers)
- characteristic functions
- transformations, non-linear e.g. log
- special estimators, e.g. Ait Sahalia, empirical characteristic functions
- fft examples
- check naming of methods, “simulate”, “sample”, “simexact”, ... ?
stochastic volatility models: estimation unclear
finance applications ? option pricing, interest rate models
6.11.2.3. Classes¶
AffineDiffusion() |
differential equation: |
ArithmeticBrownian(xzero, mu, sigma) |
:math: |
BrownianBridge() |
|
CompoundPoisson(lambd[, randfn]) |
nobs iid compound poisson distributions, not a process in time |
Diffusion() |
Wiener Process, Brownian Motion with mu=0 and sigma=1 |
ExactDiffusion() |
Diffusion that has an exact integral representation |
GeometricBrownian(xzero, mu, sigma) |
Geometric Brownian Motion |
OUprocess(xzero, mu, lambd, sigma) |
Ornstein-Uhlenbeck |
SchwartzOne(xzero, mu, kappa, sigma) |
the Schwartz type 1 stochastic process |