fitCIR: 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

$d X_{t} = (α - β X_{t}) d t + \sqrt{γ X_{t}} d W_{t}$

with parameters $β > 0,$ $2 α > 5 γ > 0$ 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)

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'.

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.

Author

Nicole Hufnagel

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

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).

Examples

Run this code

#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)

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