scholarly journals Estimation for the Discretely Observed Cox–Ingersoll–Ross Model Driven by Small Symmetrical Stable Noises

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 327 ◽  
Author(s):  
Chao Wei
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Explicit Formula ◽  
Asymptotic Distribution ◽  
Least Squares Estimation ◽  
Discrete Observations ◽  
Cir Model ◽  
Contrast Function ◽  
Model Driven ◽  
Numerical Calculus

This paper is concerned with the least squares estimation of drift parameters for the Cox–Ingersoll–Ross (CIR) model driven by small symmetrical α-stable noises from discrete observations. The contrast function is introduced to obtain the explicit formula of the estimators and the error of estimation is given. The consistency and the rate of convergence of the estimators are proved. The asymptotic distribution of the estimators is studied as well. Finally, some numerical calculus examples and simulations are given.

scholarly journals Least Squares Estimator for Vasicek Model Driven by Fractional Levy Processes

2018 ◽  
Vol 14 (2) ◽  
pp. 8013-8024
Author(s):  
Qingbo Wang ◽  
Xiuwei Yin
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Lévy Processes ◽  
Levy Processes ◽  
Estimation Problem ◽  
Least Squares Estimator ◽  
Parameter Estimation Problem ◽  
Vasicek Model ◽  
Model Driven

In this paper, we consider parameter estimation problem for Vasicek model driven by fractional lévy processes defined We construct least squares estimator for drift parameters based on time?continuous observations, the consistency and asymptotic distribution of these estimators are studied in the non?ergodic case. In contrast to the fractional Vasicek model, it can be regarded as a Lévy generalization of fractional Vasicek model.

scholarly journals Least Squares Estimation forα-Fractional Bridge with Discrete Observations

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guangjun Shen ◽  
Xiuwei Yin
Keyword(s):  
Brownian Motion ◽  
Least Squares ◽  
Fractional Brownian Motion ◽  
Discrete Time ◽  
Unknown Parameter ◽  
Least Squares Estimation ◽  
Least Squares Estimator ◽  
Hurst Parameter ◽  
Discrete Observations ◽  
Observation Window

We consider a fractional bridge defined asdXt=-α(Xt/(T-t))dt+dBtH,  0≤t<T, whereBHis a fractional Brownian motion of Hurst parameterH>1/2and parameterα>0is unknown. We are interested in the problem of estimating the unknown parameterα>0. Assume that the process is observed at discrete timeti=iΔn,  i=0,…,n, andTn=nΔndenotes the length of the “observation window.” We construct a least squares estimatorα^nofαwhich is consistent; namely,α^nconverges toαin probability asn→∞.

scholarly journals LIMIT LAWS IN TRANSACTION-LEVEL ASSET PRICE MODELS

2013 ◽  
Vol 30 (3) ◽  
pp. 536-579 ◽  
Author(s):  
Alexander Aue ◽  
Lajos Horváth ◽  
Clifford Hurvich ◽  
Philippe Soulier
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Asymptotic Distribution ◽  
Point Processes ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Fractional Cointegration ◽  
Limit Laws ◽  
Ordinary Least Squares Estimator ◽  
Transaction Level

We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such effects as intraday seasonal patterns in volatility and nontrading periods that may be different for the two assets. We also allow for asymmetries (leverage effects). We obtain the asymptotic distribution of the log-price process. For the weak fractional cointegration case, we obtain the asymptotic distribution of the ordinary least squares estimator of the cointegrating parameter based on data sampled from an equally spaced discretization of calendar time, and we justify a feasible method of hypothesis testing for the cointegrating parameter based on the correspondingt-statistic. In the strong fractional cointegration case, we obtain the limiting distribution of a continuously averaged tapered estimator as well as other estimators of the cointegrating parameter, and we find that the rate of convergence can be affected by properties of intertrade durations. In particular, the persistence of durations (hence of volatility) can affect the degree of cointegration. We also obtain the rate of convergence of several estimators of the cointegrating parameter in the standard cointegration case. Finally, we consider the properties of the ordinary least squares estimator of the regression parameter in a spurious regression, i.e., in the absence of cointegration.

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

Least Squares Estimation in Uncertain Differential Equations

2020 ◽  
Vol 28 (10) ◽  
pp. 2651-2655 ◽  
Author(s):  
Yuhong Sheng ◽  
Kai Yao ◽  
Xiaowei Chen
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Least Squares Estimation

A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems

2020 ◽  
Vol 20 (4) ◽  
pp. 783-798
Author(s):  
Shukai Du ◽  
Nailin Du
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Convergence Conditions ◽  
Principal Angles ◽  
Factorization Formula ◽  
Ill Posed

AbstractWe give a factorization formula to least-squares projection schemes, from which new convergence conditions together with formulas estimating the rate of convergence can be derived. We prove that the convergence of the method (including the rate of convergence) can be completely determined by the principal angles between {T^{\dagger}T(X_{n})} and {T^{*}T(X_{n})}, and the principal angles between {X_{n}\cap(\mathcal{N}(T)\cap X_{n})^{\perp}} and {(\mathcal{N}(T)+X_{n})\cap\mathcal{N}(T)^{\perp}}. At the end, we consider several specific cases and examples to further illustrate our theorems.

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