est.CKLS.LL: ML estimation for the CKLS model (local linearization)

In alejandralopezperez/estsde: Parametric Estimation of SDE

ML estimation for the CKLS model (local linearization)

Description

Parametric estimation for the CKLS model using maximum likelihood and the discretized version of the model, obtained with the local linearization method. The parametric form of the CKLS model used here is given by

dX_t = (α - κ X_t)dt + σ X_t^γ dW_t.

Usage

est.CKLS.LL(X, Delta = deltat(X), par = NULL)

Arguments

X	a numeric vector, the sample path of the SDE.
Delta	a single numeric, the time step between two consecutive observations.
par	a numeric vector with dimension four indicating initial values of the parameters. Defaults to NULL, fits a linear model using generalized least squares with AR1 correlation and a power variance heteroscedasticity structure.

Value

A list containing a matrix with the estimated coefficients and the associated standard errors.

References

Ozaki, T. (1992). A bridge between nonlinear time series models and nonlinear stochastic dynamical systems: a local linearization approach. Statistica Sinica, pages 113–135.

Shoji, I. and Ozaki, T. (1998). Estimation for nonlinear stochastic differential equations by a local linearization method. Stochastic Analysis and Applications, 16(4):733–752.

Examples

x <- rCKLS(360, 1/12, 0.09, 0.08, 0.9, 1.2, 1.5)
est.CKLS.LL(x)

alejandralopezperez/estsde documentation built on Sept. 4, 2022, 4:48 a.m.