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15
An adaptive empirical likelihood test for parametric time series regression models
- J. R. STATIST. SOC. - SERIES B
, 2006
"... A test for a parametric regression model against a sequence of local alternative is constructed based on an empirical likelihood test statistic that measures the goodness-of-fit between the parametric model and its nonparametric counterpart. To reduce the dependence of the test on a single smoothing ..."
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Cited by 13 (7 self)
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A test for a parametric regression model against a sequence of local alternative is constructed based on an empirical likelihood test statistic that measures the goodness-of-fit between the parametric model and its nonparametric counterpart. To reduce the dependence of the test on a single smoothing bandwidth, the test is formulated by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. It is demonstrated that the proposed test is able to distinguish local alternatives from the null hypothesis at an optimal rate.
A TEST FOR MODEL SPECIFICATION OF DIFFUSION PROCESSES
, 2008
"... We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized L2-distance between ..."
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Cited by 9 (2 self)
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We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized L2-distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process. To reduce the sensitivity of the test on smoothing bandwidth choice, the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths. To better capture the finite sample distribution of the test statistic and data dependence, the critical value of the test is obtained by a parametric bootstrap procedure. Properties of the test are evaluated asymptotically and numerically by simulation and by a real data example. 1. Introduction. Let X1,...,Xn+1 be n+1 equally spaced (with spacing
NONPARAMETRIC TESTS OF THE MARKOV HYPOTHESIS IN CONTINUOUS-TIME MODELS 1
"... We propose several statistics to test the Markov hypothesis for β-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman–Kolmogorov equation. We establish the asymptotic null distributions of the proposed test statistics, showing that Wilks’s phenomenon ho ..."
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Cited by 6 (2 self)
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We propose several statistics to test the Markov hypothesis for β-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman–Kolmogorov equation. We establish the asymptotic null distributions of the proposed test statistics, showing that Wilks’s phenomenon holds. We compute the power of the test and provide simulations to investigate the finite sample performance of the test statistics when the null model is a diffusion process, with alternatives consisting of models with a stochastic mean reversion level, stochastic volatility and jumps.
Testing Conditional Uncorrelatedness
- Journal of Business and Economic Statistics
, 2009
"... We propose a nonparametric test for conditional uncorrelatedness in multiple-equation models such as seemingly unrelated regressions (SURs), multivariate volatility models, and vector autoregressions (VARs). Under the null hypothesis of conditional uncorrelatedness, the test statistic converges to t ..."
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Cited by 5 (2 self)
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We propose a nonparametric test for conditional uncorrelatedness in multiple-equation models such as seemingly unrelated regressions (SURs), multivariate volatility models, and vector autoregressions (VARs). Under the null hypothesis of conditional uncorrelatedness, the test statistic converges to the standard normal distribution asymptotically. We also study the local power property of the test. Simulation shows that the test behaves quite well in finite samples. KEY WORDS: Conditional heteroscedasticity; Local polynomial estimator; Nonparametric multivariate regression; Seemingly unrelated regressions; Vector autoregressions.
Testing the Markov property with high frequency data
- Journal of Econometrics
, 2007
"... Abstract: This paper develops a framework to nonparametrically test whether discrete-valued irregularly-spaced financial transactions data follow a Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses so ..."
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Cited by 3 (0 self)
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Abstract: This paper develops a framework to nonparametrically test whether discrete-valued irregularly-spaced financial transactions data follow a Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates the irregular spacing that characterizes transactions data. Under such an observation rule, the current price duration is independent of a previous price duration given the previous price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Monte Carlo simulations suggest that the asymptotic test has huge size distortions, though a bootstrap-based variant entails reasonable size and power properties in finite samples. As for an empirical illustration, we investigate whether bid-ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid-ask spread. We robustly reject the Markov assumption for three out of the five stocks under scrutiny. Finally, it is reassuring that our results are consistent with two alternative measures of asymmetric information.
MPRA Munich Personal RePEc Archive
, 2005
"... A test for model specification of diffusion processes ..."
Model Specification Testing in Nonparametric Time Series Regression with Nonstationarity
"... This paper considers a class of nonparametric autoregression models with nonstationarity in the mean and then a class of nonparametric time series regression models with nonstationarity in both the conditional mean and conditional variance. For the nonparametric autoregression case, we propose a non ..."
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This paper considers a class of nonparametric autoregression models with nonstationarity in the mean and then a class of nonparametric time series regression models with nonstationarity in both the conditional mean and conditional variance. For the nonparametric autoregression case, we propose a nonparametric unit–root test for the conditional mean. For the nonparametric time series regression case, we construct a nonparametric test for testing whether the conditional mean of the nonparametric regression is of a known parametric form indexed by a vector of unknown parameters. We then establish asymptotic distributions of the proposed test statistics. Both the setting and the results differ from earlier work on nonparametric time series regression with stationarity. In addition, we develop a novel bootstrap simulation scheme for the selection of suitable bandwidth parameters involved in the kernel tests as well as the choice of simulated critical values. An example of implementation is given to show how to implement the proposed tests in practice. Key words: Co–integration, kernel test, nonparametric regression, nonstationary time series, time series econometrics.
International market links and realized volatility transmission
"... Abstract: The analysis of volatility transmission is not only essential to understand the information flow process, but also helps identifying the appropriate multivariate model for estimating and predicting volatility. In this paper, we develop formal statistical tools for testing conditional indep ..."
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Abstract: The analysis of volatility transmission is not only essential to understand the information flow process, but also helps identifying the appropriate multivariate model for estimating and predicting volatility. In this paper, we develop formal statistical tools for testing conditional independence and noncausality that are suitable for checking for volatility spillovers in asset prices. We take a different route from the previous papers in the literature in that we make no parametric assumption on the stochastic volatility processes and on the form that they interrelate. In particular, our testing procedure is in two steps. In the first stage, we estimate the daily volatilities of the assets under consideration by means of realized measures under the mild assumption that asset prices follow continuous-time jump-diffusion processes with stochastic volatility. In the second step, we then test for conditional independence by checking whether the corresponding density restrictions hold for the nonparametric estimates of the volatility distributions. The asymptotic results that we derive entail some interesting contributions to the nonparametric literature by clarifying the impact of the realized volatility estimation error. We also contribute to the volatility transmission literature by empirically investigating volatility spillovers between the stock markets
