CHARACTERISTIC FUNCTION–BASED TESTING FOR MULTIFACTOR CONTINUOUS-TIME MARKOV MODELS VIA NONPARAMETRIC REGRESSION

2009 ◽  
Vol 26 (4) ◽  
pp. 1115-1179 ◽  
Author(s):  
Bin Chen ◽  
Yongmiao Hong
Keyword(s):  
Characteristic Function ◽  
Nonparametric Regression ◽  
Continuous Time ◽  
Goodness Of Fit ◽  
Markov Models ◽  
Computational Cost ◽  
Model Specification ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Goodness Of Fit Test

We develop a nonparametric regression-based goodness-of-fit test for multifactor continuous-time Markov models using the conditional characteristic function, which often has a convenient closed form or can be approximated accurately for many popular continuous-time Markov models in economics and finance. An omnibus test fully utilizes the information in the joint conditional distribution of the underlying processes and hence has power against a vast class of continuous-time alternatives in the multifactor framework. A class of easy-to-interpret diagnostic procedures is also proposed to gauge possible sources of model misspecification. All the proposed test statistics have a convenient asymptotic N(0, 1) distribution under correct model specification, and all asymptotic results allow for some data-dependent bandwidth. Simulations show that in finite samples, our tests have reasonable size, thanks to the dimension reduction in nonparametric regression, and good power against a variety of alternatives, including misspecifications in the joint dynamics, but the dynamics of each individual component is correctly specified. This feature is not attainable by some existing tests. A parametric bootstrap improves the finite-sample performance of proposed tests but with a higher computational cost.

scholarly journals On the Infinitely Divisible of Meixner Distribution

2018 ◽  
Vol 3 (4) ◽  
pp. 147
Author(s):  
Dodi Devianto ◽  
Jayanti Herli ◽  
Maiyastri Maiyastri ◽  
Rahma Diana Safitri
Keyword(s):  
Characteristic Function ◽  
Lévy Process ◽  
Goodness Of Fit ◽  
Divisible Distribution ◽  
Levy Process ◽  
Financial Data ◽  
Infinitely Divisible Distribution ◽  
Goodness Of Fit Test ◽  
Infinitely Divisible

The log-returns of most financial data show a significant leptokurtosis. For the better fit we showed a special levy process which is called the Meixner process. The Meixner distribution belongs to the class of infinitely divisible distribution chracterized by using characteristic function and it was proposed as a model for represented efficiently of the log-returns of financial data. The perfect fit of underlying Meixner distribution performing by using goodness of fit test.

A guided nonparametric goodness-of-fit test with application to income distributions

2019 ◽  
Vol 22 (3) ◽  
pp. 207-222
Author(s):  
Kuangyu Wen ◽  
Ximing Wu
Keyword(s):  
Goodness Of Fit ◽  
Bias Reduction ◽  
Density Estimator ◽  
Consistent Estimate ◽  
Finite Sample ◽  
Goodness Of Fit Test ◽  
Normal Mixtures ◽  
Parametric Density ◽  
Income Distributions ◽  
Goodness Of Fit Tests

Summary We have developed a customizable goodness-of-fit test of a parametric density based on its distance to a consistently estimated density. This consistent estimate is obtained via a nonparametric density estimator with a parametric start, wherein the start is set to be the hypothesized parametric density. To cope with the influence of nonparametric estimation bias, nonparametric goodness-of-fit tests have resorted to remedies such as undersmoothing or convolution of the hypothesized density. Our test requires no such devices and possesses enhanced powers against alternative densities because the guided density estimator is free of the typical nonparametric bias under the null hypothesis and attains bias reduction when the underlying density is in a broad nonparametric neighborhood of the hypothesized density. Here, we establish the statistical properties of our test and use Monte Carlo simulations to demonstrate its finite sample performance. We use this test to examine the goodness-of-fit of normal mixtures to the distributions of log income of U.S. states. Although normality is rejected decisively, our results suggest that normal mixtures with two or three components suffice for all but one state.

A general goodness-of-fit test for Markov and hidden Markov models

2007 ◽  
Vol 27 (12) ◽  
pp. 2177-2195 ◽  
Author(s):  
Andrew C. Titman ◽  
Linda D. Sharples
Keyword(s):  
Hidden Markov Models ◽  
Goodness Of Fit ◽  
Markov Models ◽  
Hidden Markov ◽  
Goodness Of Fit Test

scholarly journals Goodness-of-fit test for nonparametric regression models: Smoothing spline ANOVA models as example

2018 ◽  
Vol 122 ◽  
pp. 135-155 ◽  
Author(s):  
Sebastian J. Teran Hidalgo ◽  
Michael C. Wu ◽  
Stephanie M. Engel ◽  
Michael R. Kosorok
Keyword(s):  
Nonparametric Regression ◽  
Regression Models ◽  
Goodness Of Fit ◽  
Smoothing Spline ◽  
Goodness Of Fit Test ◽  
Smoothing Spline Anova

scholarly journals Goodness-of-fit Test for the Bivariate Hermite Distribution

2020 ◽  
Author(s):  
Francisco Novoa-Muñoz ◽  
Pablo González-Albornoz
Keyword(s):  
Goodness Of Fit ◽  
Null Distribution ◽  
Test Statistics ◽  
Finite Sample ◽  
Goodness Of Fit Test ◽  
Bootstrap Approach ◽  
Type Test ◽  
Empirical Probability ◽  
Hermite Distribution ◽  
Von Mises

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

scholarly journals Problems of nonparametric goodness-of-fit test application in tasks of measurement results processing

2021 ◽  
pp. 47-66
Author(s):  
Boris Lemeshko ◽  
◽  
Stanislav Lemeshko ◽  
Keyword(s):  
Measurement Errors ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Asymptotic Distributions ◽  
Test Statistics ◽  
Sample Sizes ◽  
Asymptotic Results ◽  
Goodness Of Fit Test ◽  
Composite Hypotheses ◽  
Simple And Composite Hypotheses

It is argued that in most cases two reasons underlie the incorrect application of nonparametric goodness-of-fit tests in various applications. The first reason is that when testing composite hypotheses and evaluating the parameters of the law for the analyzed sample, classical results associated with testing simple hypotheses are used. When testing composite hypotheses, the distributions of goodness-of-fit statistics are influenced by the form of the observed law F(x, q) corresponding to the hypothesis being tested, by the type and number of estimated parameters, by the estimation method, and in some cases by the value of the shape parameter. The paper shows the influence of all mentiomed factors on the distribution of test statistics. It is emphasized that, when testing composite hypotheses, the neglect, of the fact that the test has lost the property of “freedom from distribution” leads to an increase in the probability of the 2nd kind errors. It is shown that the distribution of the statistics of the test necessary for the formation of a conclusion about the results of testing a composite hypothesis can be found using simulation in an interactive mode directly in the process of testing. The second reason is associated with the presence of round-off errors which can significantly change the distributions of test statistics. The paper shows that asymptotic results when testing simple and composite hypotheses can be used with round -off errors D much less than the standard deviation s of the distribution law of measurement errors and sample sizes n not exceeding some maximum values. For sample sizes larger than these maximum values, the real distributions of the test statistics deviate from asymptotic ones towards larger statistics values. In such situations, the use of asymptotic distributions to arrive at a conclusion about the test results leads to an increase in the probabilities of errors of the 1st kind (to the rejection of a valid hypothesis being tested). It is shown that when the round-off errors and s are commensurable, the distributions of the test statistics deviate from the asymptotic distributions for small n. And as n grows, the situation only gets worse. In the paper, changes in the distributions of statistics under the influence of rounding are demonstrated both when testing both simple and composite hypotheses. It is shown that the only way out that ensures the correctness of conclusions according to the applied tests in such non-standard conditions is the use of real distributions of statistics. This task can be solved interactively (in the process of verification) and rely on computer research technologies and the apparatus of mathematical statistics.

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