fitCIR function

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

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.

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.

Returns

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'.

Details

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

References

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

Author(s)

Nicole Hufnagel

Contacts: nicole.hufnagel@math.tu-dortmund.de

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)