Estimation of Continuous-Time Processes via the Empirical Characteristic Function

Jiang, George J.; Knight, John L.

doi:10.1198/073500102317351958

Cited by 144 publications

(75 citation statements)

References 39 publications

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“…case and the extension to dependent observations. Other references that are relevant here are Madan and Seneta (1987), Feuerverger (1990), , Jiang and Knight (2002), Yu (2004) who discusses in more depth empirical ch.f. estimation in a non i.i.d.…”

Section: X(t)mentioning

confidence: 99%

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Characteristic function estimation of Ornstein–Uhlenbeck-based stochastic volatility models

Taufer

Leonenko

Bee

2011

Computational Statistics & Data Analysis

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Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression.In this paper we propose a characteristic function-based estimation method for non-Gaussian Ornstein-Uhlenbeck-based stochastic volatility models. After deriving explicit expressions of the characteristic functions for various cases of interest we analyze the asymptotic properties of the estimators and evaluate their performance by means of a simulation experiment. Finally, a realdata application shows that the superposition of two Ornstein-Uhlenbeck processes gives a good approximation to the dependence structure of the process.

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Section: X(t)mentioning

confidence: 99%

“…propose an exponentially decreasing function, Epps (2005) suggests using dW Jiang and Knight (2002) use the the multivariate normal density. However, for non-Markovian processes, no general solution is available.…”

Section: Ou Process X(t)mentioning

confidence: 99%

Characteristic function estimation of Ornstein–Uhlenbeck-based stochastic volatility models

Taufer

Leonenko

Bee

2011

Computational Statistics & Data Analysis

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“…Jiang and Knight (2002) derive the joint CF of a particular class of affine jump diffusion models, where some of the state variables are unobserved. It includes as a special case the following continuous time square-root SV model…”

Section: Affine Jump Diffusion Modelsmentioning

confidence: 99%

“…The approach via the joint CF is used in Feuerverger (1990), Knight and Satchell (1996), Yu (1998), , , and Jiang and Knight (2002 The joint ECF is defined as…”

Section: Joint Ecfmentioning

confidence: 99%

Empirical Characteristic Function Estimation and its Applications

2003

SSRN Journal

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This paper reviews the method of model-fitting via the empirical characteristic function. The advantage of using this procedure is that one can avoid difficulties inherent in calculating or maximizing the likelihood function. Thus it is a desirable estimation method when the maximum likelihood approach encounters difficulties but the characteristic function has a tractable expression. The basic idea of the empirical characteristic function method is to match the characteristic function derived from the model and the empirical characteristic function obtained from data. Ideas are illustrated by using the methodology to estimate a diffusion model that includes a self-exciting jump component. A Monte Carlo study shows that the finite sample performance of the proposed procedure offers an improvement over a GMM procedure. An application using over 72 years of DJIA daily returns reveals evidence of jump clustering.

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“…Jump diffusions are widely used in the financial econometrics literature when analyzing returns or exchange rates, for example, as discussed in Duffie, Pan and Singleton (2000), Singleton (2001), Anderson, Benzoni and Lund (2002), Jiang and Knight (2002), Chacko and Viceira (2003) and Eraker, Johannes and Polson (2003), among others. Various estimation techniques have been developed, and the common practice is to jointly estimate the parameters of both the continuous time and the jump components of these diffusion models.…”

Section: Introductionmentioning

confidence: 99%

Consistent Pretesting for Jumps

Corradi

Swanson

2014

SSRN Journal

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If the intensity parameter in a jump diffusion model is identically zero, then parameters characterizing the jump size density cannot be identified. In general, this lack of identification precludes consistent estimation of identified parameters. Hence, it should be standard practice to consistently pretest for jumps, prior to estimating jump diffusions. Many currently available tests have power against the presence of jumps over a finite time span (typically a day or a week); and, as already noted by various authors, jumps may not be observed over finite time spans, even if the intensity parameter is strictly positive. Such tests cannot be consistent against non-zero intensity. Moreover, sequential application of finite time span tests usually leads to sequential testing bias, which in turn leads to jump discovery with probability one, in the limit, even if the true intensity is identically zero. This paper introduces tests for jump intensity, based on both in-fill and long-span asymptotics, which solve both the test consistency and the sequential testing bias problems discussed above, in turn facilitating consistent estimation of jump diffusion models. A "self excitement" test is also introduced, which is designed to have power against path dependent intensity, thus providing a direct test for the Hawkes diffusion model of Ait-Sahalia, Cacho-Diaz and Laeven (2013). In a series of Monte Carlo experiments, the proposed tests are evaluated, and are found to perform adequately in finite samples.

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Estimation of Continuous-Time Processes via the Empirical Characteristic Function

Cited by 144 publications

References 39 publications

Characteristic function estimation of Ornstein–Uhlenbeck-based stochastic volatility models

Characteristic function estimation of Ornstein–Uhlenbeck-based stochastic volatility models

Empirical Characteristic Function Estimation and its Applications

Consistent Pretesting for Jumps

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