Jie Cheng
Deparment: School of Science

Items: 5

Views: 200

1. Spectral density of Markov switching models: Derivation, simulation studies and application


Source:Model Assisted Statistics and Applications,2016,Vol.11

Abstract:© 2016 - IOS Press and the authors. This paper is concerned with frequency domain analysis of Markov mean-switching autoregressive (MMSAR) models, linear Markov switching autoregressive (LMSAR) model and transitional Markov switching autoregressive (TMSAR) model. We derive the general expressions of autocovariance functions and spectra for these three models. Simulation studies of theoretical spectral density functions of these three models are presented. The results show that Markov chain seems to be the most important determinants of the frequency distribution of the volatility. A time series is analysed and both smoothed periodogram and theoretical spectra (of LMSAR and TMSAR models) show similar pattern and give clear ideas of business cycle.
2. How do risk attitudes of clearing firms matter for managing default exposure in futures markets?

Author:Cheng, J;Hong, Y;Tao, J


Abstract:This article proposes a theoretical framework that is built upon extreme value theory to study three instruments (i.e. margin, capital requirement and price limits) for managing default risk in futures markets. Specifically, the exceedances over a price threshold are modeled using a generalized Pareto distribution, and the models are static (one-period). We incorporate the risk attitudes of clearing firms into the framework to investigate the efficacy of these instruments under several risk measures, including value-at-risk measures, expected-shortfall measures and spectral risk measures. An empirical study on the VIX futures (or VX) data shows that the effectiveness of these market instruments rests not only on clearing firms' risk attitudes, but also on the tail fatness of the futures price distribution. Moreover, the shift in the risk attitudes of clearing firms may cause interactions among these instruments, which casts new light on the economic rationale of price limits.
3. Reducible diffusions with time-varying transformations with application to short-term interest rates

Author:Bu, RJ;Cheng, J;Hadri, K


Abstract:Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical points of view. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintaining sufficient tractability of the resulting models. In the meantime, our modeling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to the UK and the US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly. (C) 2014 Elsevier B.V. All rights reserved.
4. Specification analysis in regime-switching continuous-time diffusion models for market volatility

Author:Bu, R;Cheng, J;Hadri, K


Abstract:We examine model specification in regime-switching continuous-time diffusions for modeling S&P 500 Volatility Index (VIX). Our investigation is carried out under two nonlinear diffusion frameworks, the NLDCEV and the CIRCEV frameworks, and our focus is on the nonlinearity in regime-dependent drift and diffusion terms, the switching components, and the endogeneity in regime changes. While we find strong evidence of regime-switching effects, models with a switching diffusion term capture the VIX dynamics considerably better than models with only a switching drift, confirming the presence and importance of volatility regimes. Strong evidence of nonlinear endogeneity in regime changes is also detected. Meanwhile, we find significant nonlinearity in the regime-dependent diffusion specification, suggesting that the nonlinearity in the VIX dynamics cannot be accounted for by regime-switching effects alone. Finally, we find that models based on the CIRCEV specification are significantly closer to the true data generating process of VIX than models based on the NLDCEV specification uniformly across all regime-switching specifications.
5. A transitional Markov switching autoregressive model

Author:Cheng, J


Abstract:This paper is concerned with properties of a transitional Markov switching autoregressive (TMSAR) model, together with its maximum-likelihood estimation and inference. We extend existing MSAR models by allowing dependence of AR parameters on hidden states at time points prior to the current time t. A stationary solution is given and expressions for the theoretical autocovariance function are derived. Two time series are analyzed and the new model outperforms two existing MSAR models in terms of maximized log-likelihood, residual correlations, and one-step-ahead forecasting performance. The new model also gives more regime changes in agreement with real events.
Total 5 results found
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