A comparative study of several bootstrap-based tests for the volatility in continuous-time diffusion models

This article develops three bootstrap-based tests for a parametric form of volatil- ity function in continuous-time diffusion models. The three tests are the generalized likelihood ratio test by Fan et al. (Ann Stat 29(1):153–193, 2001), the nonparamet- ric kernel test (LWZ) by Li and Wang (J Econometrics 87(1):145–165, 1998) and Zheng (J Econ 75(2):263–289, 1996) and the nonparametric test (CHS) by Chen et al. (2017). Monte Carlo simulations are performed to evaluate the sizes and power properties of these bootstrap-based tests in finite samples over a range of bandwidth values. We find that the bootstrap-based tests are not influenced by prior restrictions on the functional form of the drift function and that the bootstrap-based CHS test has better power performance than the bootstrap-based GLR and LWZ tests in detect- ing a parametric form of volatility. An empirical study on weekly treasury bill rate is further conducted to demonstrate these bootstrap-based test procedures.info:eu-repo/semantics/publishedVersio

Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics

We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations

Local Polynomial Regression Solution for Differential Equations with Initial and Boundary Values

Numerical solutions of the linear differential boundary issues are obtained by using a local polynomial estimator method with kernel smoothing. To achieve this, a combination of a local polynomial-based method and its differential form has been used. The computed results with the use of this technique have been compared with the exact solution and other existing methods to show the required accuracy of it. The effectiveness of this method is verified by three illustrative examples. The presented method is seen to be a very reliable alternative method to some existing techniques for such realistic problems. Numerical results show that the solution of this method is more accurate than that of other methods

Introduction of modern diagnostic approach to detect Babesia in clinical and animal samples

Babezija je parazit, ki se s klopom prenese na ljudi in živali, kjer lahko povzroči okužbo. Zlati standard dokazovanja babezioze je neposredni mikroskopski pregled barvanega krvnega razmaza, s katerimi ne moremo določiti babezije do vrste natančno. Babeziozo lahko dokažemo tudi z metodo posredne imunofluorescence, ki pa ni primerna pri imunsko oslabljenih bolnikih. Z magistrsko nalogo smo razvili PCR v realnem času za dokaz DNA babezij, ki povzročajo okužbe pri ljudeh in živalih v Sloveniji in s tem olajšali ter skrajšali čas do laboratorijskega izvida. Dokazali smo, da je metoda PCR v realnem času bolj občutljiva in bolj specifična od neposrednega mikroskopskega pregleda preparata krvi ter klasičnega PCR. Kot selekcijski marker smo uporabili gen 18S rRNA, ki vsebuje hipervariabilne odseke, obdane z visoko ohranjenimi regijami. Razvili smo visoko specifičen in občutljiv PCR v realnem času, ki pomnožuje sev humane babezije Babesia sp. Irk, ki so ga dokazali leta 2014 pri imunsko oslabljeni bolnici iz Prekmurja. S kvantifikacijo z digitalnim PCR smo spremljali potek parazitemije in zdravljenja pri bolnici ter dokazali babezijsko DNA tudi po 89. dneh zdravljenja, ko so bili rezultati ostalih metod že negativni. Zaključimo lahko, da je PCR v realnem času hitra, visoko občutljiva in enostavna metoda, ki omogoča dokaz babezioze v zgodnjih fazah bolezni ter spremljanje poteka zdravljenja.Babesia is a parasite that can be transmitted to humans and animals, where it causes infection. With methods like microscopic staining of blood smears, that do not give us the information about the species, and indirect immunofluorescence, that we can not use on immunocompromised patients, real time PCR seems to be a much better choice for diagnostics. Within M. Sc. Thesis we developed real time PCR for detection of Babesia species DNA, found in humans and animals around Slovenia. We proved that real time PCR is a more sensitive and specific method than the microscopic staining of blood smears and conventional PCR. As a selection marker we used 18S rRNA gene with hipervariable sections that are surrounded with highly conservative regions. Our real time PCR amplifies strain of human Babesia sp. Irk, that was first found in 2014 in an immunocompromised patient from Prekmurje. By using absolute quantification of a digital PCR, we were able to follow parasitemia and treatment of the patient and detected DNA of the parasite even after 89 days from the beginning of the treatment, when all the other methods showed negative results. In conclusion, we can say that real time PCR is a quick, highly sensitive method that is easy to use and is useful for detection of babesial DNA at the beginning of the infection as well as for monitoring the course of treatment

Solution of an Integral-Differential Equation Arising in Oscillating Magnetic Fields Using Local Polynomial Regression

An integrodifferential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The local polynomial regression method (LPR) is used to solve this equation. The reliability of this method and the reduction in the size of computational domain give this method a wider applicability. Several representative examples are given to reconfirm the efficiency of these algorithms. The results of applying this theory to the integro-differential equation with time-periodic coefficients reveal that LPR method possesses very high accuracy, adaptability, and efficiency

Estimation for a Second-Order Jump Diffusion Model from Discrete Observations: Application to Stock Market Returns

This paper proposes a second-order jump diffusion model to study the jump dynamics of stock market returns via adding a jump term to traditional diffusion model. We develop an appropriate maximum likelihood approach to estimate model parameters. A simulation study is conducted to evaluate the performance of the estimation method in finite samples. Furthermore, we consider a likelihood ratio test to identify the statistically significant presence of jump factor. The empirical analysis of stock market data from North America, Asia, and Europe is provided for illustration

Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in economics.

Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations