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Full-Text Articles in Social and Behavioral Sciences
Finite Sample Comparison Of Alternative Estimators For Fractional Gaussian Noise, Shuping Shi, Jun Yu, Chen Zhang
Finite Sample Comparison Of Alternative Estimators For Fractional Gaussian Noise, Shuping Shi, Jun Yu, Chen Zhang
Research Collection School Of Economics
The fractional Brownian motion (fBm) process is a continuous-time Gaussian process with its increment being the fractional Gaussian noise (fGn). It has enjoyed widespread empirical applications across many fields, from science to economics and finance. The dynamics of fBm and fGn are governed by a fractional parameter H ∈ (0, 1). This paper first derives an analytical expression for the spectral density of fGn and investigates the accuracy of various approximation methods for the spectral density. Next, we conduct an extensive Monte Carlo study comparing the finite sample performance and computational cost of alternative estimation methods for H under the …
Bias In The Estimation Of The Mean Reversion Parameter In Continuous Time Models, Jun Yu
Bias In The Estimation Of The Mean Reversion Parameter In Continuous Time Models, Jun Yu
Research Collection School Of Economics
It is well known that for continuous time models with a linear drift standard estimation methods yield biased estimators for the mean reversion parameter both in finite discrete samples and in large in-fill samples. In this paper, we obtain two expressions to approximate the bias of the least squares/maximum likelihood estimator of the mean reversion parameter in the Ornstein-Uhlenbeck process with a known long run mean when discretely sampled data are available. The first expression mimics the bias formula of Marriott and Pope (1954) for the discrete time model. Simulations show that this expression does not work satisfactorily when the …
Folklore Theorems, Implicit Maps, And Indirect Inference, Peter C. B. Phillips
Folklore Theorems, Implicit Maps, And Indirect Inference, Peter C. B. Phillips
Research Collection School Of Economics
The delta method and continuous mapping theorem are among the most extensively used tools in asymptotic derivations in econometrics. Extensions of these methods are provided for sequences of functions that are commonly encountered in applications and where the usual methods sometimes fail. Important examples of failure arise in the use of simulation-based estimation methods such as indirect inference. The paper explores the application of these methods to the indirect inference estimator (IIE) in first order autoregressive estimation. The IIE uses a binding function that is sample size dependent. Its limit theory relies on a sequence-based delta method in the stationary …
Simulation-Based Estimation Methods For Financial Time Series Models, Jun Yu
Simulation-Based Estimation Methods For Financial Time Series Models, Jun Yu
Research Collection School Of Economics
This paper overviews some recent advances on simulatio n-based methods of estimating time series models and asset pricing models that are widely used in finance. The simulation based methods have proven to be particularly useful when the likelihood function and moments do not have tractable forms and hence the maximum likelihood method (MLE) and the generalized method of moments (GMM) are difficult to use. They can also be useful for improving the finite sample performance of the traditional methods when financial time series are highly persistent and when the quantity of interest is a highly nonlinear function of system parameters.The …
Simulation-Based Estimation Methods For Financial Time Series Models, Jun Yu
Simulation-Based Estimation Methods For Financial Time Series Models, Jun Yu
Research Collection School Of Economics
This paper overviews some recent advances on simulation-based methods of estimating time series models and asset pricing models that are widely used in finance. The simulation based methods have proven to be particularly useful when the likelihood function and moments do not have tractable forms and hence the maximum likelihood method (MLE) and the generalized method of moments (GMM) are difficult to use. They can also be useful for improving the finite sample performance of the traditional methods when financial time series are highly persistent and when the quantity of interest is a highly nonlinear function of system parameters. The …
Bias In The Estimation Of The Mean Reversion Parameter In Continuous Time Models, Jun Yu
Bias In The Estimation Of The Mean Reversion Parameter In Continuous Time Models, Jun Yu
Research Collection School Of Economics
It is well known that for continuous time models with a linear drift standard estimation methods yield biased estimators for the mean reversion parameter both in nite discrete samples and in large in-…ll samples. In this paper, we obtain two expressions to approximate the bias of the least squares/maximum likelihood estimator of the mean reversion parameter in the Ornstein-Uhlenbeck process with a known long run mean when discretely sampled data are available. The first expression mimics the bias formula of Marriott and Pope (1954) for the discrete time model. Simulations show that this expression does not work satisfactorily when the …
A Two-Stage Realized Volatility Approach To Estimation Of Diffusion Processes With Discrete Data, Peter C. B. Phillips, Jun Yu
A Two-Stage Realized Volatility Approach To Estimation Of Diffusion Processes With Discrete Data, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in [Jacod, J., 1994. Limit of random measures associated with the increments of a Brownian semiartingal. Working paper, Laboratoire de Probabilities, Universite Pierre et Marie Curie, Paris] and [Barndorff-Nielsen, O., Shephard, N., 2002. Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society. Series B, 64, 253-280], to provide a regression model for estimating the parameters …
Maximum Likelihood And Gaussian Estimation Of Continuous Time Models In Finance, Peter C. B. Phillips, Jun Yu
Maximum Likelihood And Gaussian Estimation Of Continuous Time Models In Finance, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention has been devoted to the development of methods designed to approximate the likelihood. These approaches range from crude Euler-type approximations and higher order stochastic Taylor series expansions to more complex polynomial-based expansions and infill approximations to the likelihood based on a continuous time data record. The methods are discussed, their properties are outlined and their relative finite sample performance compared in a simulation experiment with the nonlinear CIR diffusion model, which …
Maximum Likelihood And Gaussian Estimation Of Continuous Time Models In Finance, Peter C. B. Phillips, Jun Yu
Maximum Likelihood And Gaussian Estimation Of Continuous Time Models In Finance, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention has been devoted to the development of methods designed to approximate the likelihood. These approaches range from crude Euler-type approximations and higher order stochastic Taylor series expansions to more complex polynomial-based expansions and infill approximations to the likelihood based on a continuous time data record. The methods are discussed, their properties are outlined and their relative finite sample performance compared in a simulation experiment with the nonlinear CIR diffusion model, which …
A Two-Stage Realized Volatility Approach To Estimation Of Diffusion Processes With Discrete Data, Peter C. B. Phillips, Jun Yu
A Two-Stage Realized Volatility Approach To Estimation Of Diffusion Processes With Discrete Data, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in [Jacod, J., 1994] and [Barndorff-Nielsen, O., Shephard, N., 2002], to provide a regression model for estimating the parameters in the diffusion function. In the second stage, the in-fill likelihood function is derived by means of the Girsanov theorem and then used to estimate the parameters in the drift function. Consistency and asymptotic distribution theory for these estimates are established in various contexts. The finite …