fitCIR {yuima}

Calculate preliminary estimator and one-step improvements of a Cox-Ingersoll-Ross diffusion

Description

This is a function to simulate the preliminary estimator and the corresponding one step estimators based on the Newton-Raphson and the scoring method of the Cox-Ingersoll-Ross process given via the SDE

\mathrm{d} X_t = (\alpha-\beta X_t)\mathrm{d} t + \sqrt{\gamma X_t}\mathrm{d} W_t

with parameters \beta>0, 2\alpha>5\gamma>0 and a Brownian motion (W_t)_{t\geq 0}. This function uses the Gaussian quasi-likelihood, hence requires that data is sampled at high-frequency.

Usage

fitCIR(data)

Arguments

data

a numeric matrix containing the realization of (t_0,X_{t_0}), \dots,(t_n,X_{t_n}) with t_j denoting the j-th sampling times. data[1,] contains the sampling times t_0,\dots, t_n and data[2,] the corresponding value of the process X_{t_0},\dots,X_{t_n}. In other words data[,j]=(t_j,X_{t_j}). The observations should be equidistant.

Details

The estimators calculated by this function can be found in the reference below.

Value

A list with three entries each contain a vector in the following order: The result of the preliminary estimator, Newton-Raphson method and the method of scoring.

If the sampling points are not equidistant the function will return 'Please use equidistant sampling points'.

Author(s)

Nicole Hufnagel

Contacts: [e-mail]

References

Y. Cheng, N. Hufnagel, H. Masuda. Estimation of ergodic square-root diffusion under high-frequency sampling. Econometrics and Statistics, Article Number: 346 (2022).

Examples

#You can make use of the function simCIR to generate the data 
data <- simCIR(alpha=3,beta=1,gamma=1, n=5000, h=0.05, equi.dist=TRUE)
results <- fitCIR(data)