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