scholarly journals Weighted least-squares estimation for the subcritical Heston process

2018 ◽  
Vol 55 (2) ◽  
pp. 543-558 ◽  
Author(s):  
M. du Roy de Chaumaray
Keyword(s):  
Least Squares ◽  
Stochastic Volatility ◽  
Strong Consistency ◽  
Weighted Least Squares ◽  
Estimation Procedure ◽  
Stopping Times ◽  
Weighted Least Squares Estimation ◽  
Weighted Least Squares Estimator ◽  
Consistency And Asymptotic Normality ◽  
Stochastic Volatility Process

Abstract We simultaneously estimate the four parameters of a subcritical Heston process. We do not restrict ourselves to the case where the stochastic volatility process never reaches zero. In order to avoid the use of unmanageable stopping times and a natural but intractable estimator, we use a weighted least-squares estimator. We establish strong consistency and asymptotic normality for this estimator. Numerical simulations are also provided, illustrating the favorable performance of our estimation procedure.

scholarly journals Strong Consistency of Estimators for Heteroscedastic Partly Linear Regression Model under Dependent Samples

2002 ◽  
Vol 15 (3) ◽  
pp. 207-219 ◽  
Author(s):  
Han-Ying Liang ◽  
Bing-Yi Jing
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Strong Consistency ◽  
Weighted Least Squares ◽  
Least Squares Estimator ◽  
Slope Parameter ◽  
Correlated Errors ◽  
Weighted Least Squares Estimator ◽  
Heteroscedastic Regression ◽  
Dependent Samples

In this paper we are concerned with the heteroscedastic regression model yi=xiβ+g(ti)+σiei, 1≤i≤n under correlated errors ei, where it is assumed that σi2=f(ui), the design points (xi,ti,ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance ei are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator.

scholarly journals Two Explicit Characterizations of the General Nonnegative-Definite Covariance Matrix Structure for Equality of BLUEs, WLSEs, and LSEs

2020 ◽  
Vol 9 (6) ◽  
pp. 108
Author(s):  
Phil D. Young ◽  
Joshua D. Patrick ◽  
Dean M. Young
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Sufficient Conditions ◽  
Covariance Structure ◽  
Least Squares Estimator ◽  
Weighted Least Squares Estimator ◽  
Best Linear Unbiased ◽  
Necessary And Sufficient ◽  
Nonnegative Definite

We provide a new, concise derivation of necessary and sufficient conditions for the explicit characterization of the general nonnegative-definite covariance structure V of a general Gauss-Markov model with E(y) and Var(y) such that the best linear unbiased estimator, the weighted least squares estimator, and the least squares estimator of Xβ are identical. In addition, we derive a representation of the general nonnegative-definite covariance structure V defined above in terms of its Moore-Penrose pseudo-inverse.

Effects of errors-in-variables on weighted least squares estimation

2014 ◽  
Vol 88 (7) ◽  
pp. 705-716 ◽  
Author(s):  
Peiliang Xu ◽  
Jingnan Liu ◽  
Wenxian Zeng ◽  
Yunzhong Shen
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Least Squares Estimation ◽  
Errors In Variables ◽  
Weighted Least Squares Estimation

Wavelet-based Estimation of Generalized Fractional Process

2007 ◽  
Vol 46 (02) ◽  
pp. 117-120 ◽  
Author(s):  
A. Kawanaka ◽  
A. Gonzaga
Keyword(s):  
Long Memory ◽  
General Model ◽  
Weighted Least Squares ◽  
Estimation Procedure ◽  
Heart Rate Data ◽  
Biomedical Signals ◽  
Weighted Least Squares Estimator ◽  
Short Memory ◽  
Wavelet Variance ◽  
Memory Parameter

Summary Objectives : This paper aims to propose an estimation procedure for the parameters of a generalized fractional process, a fairly general model of long-memory applicable in modeling biomedical signals whose autocorrelations exhibit hyperbolic decay. Methods : We derive a wavelet-based weighted least squares estimator of the long-memory parameter based on the maximal-overlap estimator of the wavelet variance. Short-memory parameters can then be estimated using standard methods. We illustrate our approach by an example applying ECG heart rate data. Results and Conclusion : The proposed method is relatively computationally and statistically efficient. It allows for estimation of the long-memory parameter without knowledge of the short-memory parameters. Moreover it provides a more general model of biomedical signals that exhibit periodic long-range dependence, such as ECG data, whose relatively unobtrusive recording may be advantageous in assessing or predicting some physiological or pathological conditions from the estimated values of the parameters.

Sign in / Sign up

Export Citation Format

Share Document