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Continuous‐time diffusion models with jumps, especially the jump intensity coefficient, can depict the impact of sudden and large shocks to financial markets. It is possible to disentangle, from the discrete observations, the contributions given by the jumps and those by the diffusion part through threshold functions. Based on this threshold technique, we employ non‐parametric local linear threshold estimator for the unknown jump intensity function of a semimartingale with jumps. The asymptotic normality of our estimator is provided in the presence of finite activity jumps under certain regular conditions. The finite‐sample performance for the underlying estimator has been shown through a Monte Carlo experiment and an empirical analysis on high frequency returns of indexes in the USA and China. [ABSTRACT FROM AUTHOR]

The occurrence of economic policies and other sudden and large shocks often bring out jumps in financial data, which can be characterized through continuous-time jump-diffusion model. In this paper, we will adopt convoluted smoothed approach to estimate unknown drift function of the potentially nonstationary diffusion models with jumps under high frequency sampling data. With Gaussian approximation of locally square-integrable martingales, we will establish large sample properties for the underlying nonparametric estimators. Furthermore, we construct Monte Carlo simulation study through three examples for the better finite-sample properties such as reduction of mean-squared error compared with the existing estimators. Finally, our estimator is verified through the actual data of Shibor in China for better performance. [ABSTRACT FROM AUTHOR]

This paper proposes a semiparametric solution to estimate the intensity (hazard) function of modulated renewal processes: a nonparametric estimate for the baseline intensity function together with a parametric estimate of the model parameters of the covariate processes. Based on the martingale property associated with the conditional intensity, we construct a statistic from a residual analysis to estimate the baseline renewal intensity function, when the model parameters of the covariate processes are known. In addition, when the baseline intensity is obtained, the model parameters can be estimated using the usual maximum likelihood estimation. In practice, both the baseline intensity and model parameters are suggested to be estimated simultaneously via an expectation–maximization (E–M)-type iterative algorithm. A more important feature of the newly proposed algorithm is that, given n events in the observation dataset, its computation time is of order O (n 2) , while the Nelson–Aalen–Breslow estimator takes a computation time of order O (n 3) . For illustration, we apply the proposed estimation procedure to a set of data simulated from a modulated gamma renewal process and the aftershock sequence following the M s 8 Wenchuan earthquake, which occurred in Sichuan Province, China on 12 May 2008. [ABSTRACT FROM AUTHOR]

In this article, we propose a general downside risk measure based on high-frequency downward moves below minimum acceptable target in asset prices. We derive the central limit theorem of this measure, and Monte Carlo simulation experiments support our theoretical results. We also investigate the distributional properties of this measure in China’s stock market. The theoretical and empirical works on realized downside risk measure shed light on the potential of this measure in measuring and modeling financial risk. [ABSTRACT FROM AUTHOR]

The local polynomial methods and martingale estimating equations are used to develop closed form estimators of the intensity function and its derivatives for multiplicative counting process models. The consistency and asymptotic normality of the estimators are established. The estimator generalizes that proposed by Ramlau-Hansen (1983) with a smaller bias than the Ramlau-Hansen intensity estimator. The derivative estimators give smoother estimates than the Ramlau-Hansen derivative estimators. The proposed estimators are applied to analyze the infection rate and its derivatives of the 2003 Severe Acute Respiratory Syndrome (SARS) epidemic in Beijing, China. [ABSTRACT FROM AUTHOR]

This paper examines the martin gale hypothesis for five Asian stock markets using the spectral shape tests of Durlauf (1991). Unlike the variance ratio test employed in previous studies (eg, Pan et al, 1991), the spectral shape tests are consistent against all stationary alternatives to the martingale null. The spectral shape tests were applied to daily and weekly returns on the stock indices of Thailand, Hong Kong, Korea, Malaysia and Taiwan over a period of 17 years. The results show that the martingale null is rejected for most markets. There is some evidence that the rejections may be due to low frequency or long memory influences. [ABSTRACT FROM AUTHOR]