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Full-Text Articles in Econometrics
Volatility Puzzle: Long Memory Or Anti-Persistency, Shuping Shi, Jun Yu
Volatility Puzzle: Long Memory Or Anti-Persistency, Shuping Shi, Jun Yu
Research Collection School Of Economics
The log realized volatility (RV) is often modeled as an autoregressive fractionally integrated moving average model ARFIMA(1,d,01,d,0). Two conflicting empirical results have been found in the literature. One stream shows that log RV has a long memory (i.e., the fractional parameter d > 0). The other stream suggests that the autoregressive coefficient α is near unity with antipersistent errors (i.e., d α close to 0 and d close to 0.5) from Model 2Model 2 (ARFIMA(1,d,01,d,0) with α close to unity and d close to –0.5). An intuitive explanation is given. For the 10 financial assets considered, despite that no definitive conclusions …
Volatility Puzzle: Long Memory Or Antipersistency, Shuping Shi, Jun Yu
Volatility Puzzle: Long Memory Or Antipersistency, Shuping Shi, Jun Yu
Research Collection School Of Economics
The log realized volatility (RV) is often modeled as an autoregressive fractionally integrated moving average model ARFIMA(1, d, 0). Two conflicting empirical results have been found in the literature. One stream shows that log RV has a long memory (i.e., the fractional parameter d > 0). The other stream suggests that the autoregressive coefficient α is near unity with antipersistent errors (i.e., d
Weak Identification Of Long Memory With Implications For Inference, Jia Li, Peter C. B. Phillips, Shuping Shi, Jun Yu
Weak Identification Of Long Memory With Implications For Inference, Jia Li, Peter C. B. Phillips, Shuping Shi, Jun Yu
Research Collection School Of Economics
This paper explores weak identification issues arising in commonly used models of economic and financial time series. Two highly popular configurations are shown to be asymptotically observationally equivalent: one with long memory and weak autoregressive dynamics, the other with antipersistent shocks and a near-unit autoregressive root. We develop a data-driven semiparametric and identification-robust approach to inference that reveals such ambiguities and documents the prevalence of weak identification in many realized volatility and trading volume series. The identification-robust empirical evidence generally favors long memory dynamics in volatility and volume, a conclusion that is corroborated using social-media news flow data.
Different Strokes For Different Folks: Long Memory And Roughness, Shuping Shi, Jun Yu
Different Strokes For Different Folks: Long Memory And Roughness, Shuping Shi, Jun Yu
SMU Economics and Statistics Working Paper Series
The log realized volatility of financial assets is often modeled as an autoregressive fractionally integrated moving average model (ARFIMA) process, denoted by ARFIMA(p, d, q), with p = 1 and q = 0. Two conflicting results have been found in the literature regarding the dynamics. One stream shows that the data series has a long memory (i.e., the fractional parameter d > 0) with strong mean reversion (i.e., the autoregressive coefficient |α1| ≈ 0). The other stream suggests that the volatil-ity is rough (i.e., d < 0) with highly persistent dynamic (i.e., α1 → 1). To consolidate the findings, this paper first examines the finite sample properties of alternative estimation methods employed in the literature for the ARFIMA(1, d, 0) model and then applies the outperforming techniques to a wide range of financial assets. The candidate methods include two parametric maximum likeli-hood (ML) methods (the maximum time-domain modified profile likelihood (MPL) and maximum frequency-domain likelihood) and two semiparametric methods (the local Whittle method and log periodogram estimation method). The two parametric methods work well across all parameter set-tings, with the MPL method outperforming. In contrast, the two semiparametric methods have a very large upward bias for d and an equally large downward bias for α1 when α1 is close to unity. The poor performance of the semiparametric methods in the presence of a highly persistent dynamic might lead to a false conclusion of long memory. In the empirical applications, we find that the log realized volatilities of exchange rate futures over the past decade have a long memory, where the point estimate of d is between 0.4 and 0.5 and the estimate of α1 is near zero. For other finan-cial assets considered (including stock indices and industry indices), we find that they have rough volatility, with the point estimate of d being negative and the point estimates of α1 close to unity.
Forecasting Realized Volatility Using A Nonnegative Semiparametric Model, Anders Eriksson, Daniel P. A. Preve, Jun Yu
Forecasting Realized Volatility Using A Nonnegative Semiparametric Model, Anders Eriksson, Daniel P. A. Preve, Jun Yu
Research Collection School Of Economics
This paper introduces a parsimonious and yet flexible semiparametric model to forecastfinancial volatility. The new model extends a related linear nonnegative autoregressive modelpreviously used in the volatility literature by way of a power transformation. It is semiparametric inthe sense that the distributional and functional form of its error component is partially unspecified.The statistical properties of the model are discussed and a novel estimation method is proposed.Simulation studies validate the new method and suggest that it works reasonably well in finitesamples. The out-of-sample forecasting performance of the proposed model is evaluated against anumber of standard models, using data on S&P 500 …
Estimation Of Monthly Volatility: An Empirical Comparison Of Realized Volatility, Garch And Acd-Icv Methods, Shouwei Liu, Yiu Kuen Tse
Estimation Of Monthly Volatility: An Empirical Comparison Of Realized Volatility, Garch And Acd-Icv Methods, Shouwei Liu, Yiu Kuen Tse
Research Collection School Of Economics
We apply the ACD-ICV method proposed by Tse and Yang (2011) for the estimation of intraday volatility to estimate monthly volatility, and empirically compare this method against the realized volatility (RV) and generalized autoregressive conditional heteroskedasticity (GARCH) methods. Our Monte Carlo results show that the ACD-ICV method performs well against the other two methods. Evidence on the Chicago Board Options Exchange volatility index (VIX) shows that it predicts the ACD-ICV volatility estimates better than it predicts the RV estimates. While the RV method is popular for the estimation of monthly volatility, its performance is inferior to the GARCH method.
Estimation Of High-Frequency Volatility: An Autoregressive Conditional Duration Approach, Yiu Kuen Tse, Thomas Tao Yang
Estimation Of High-Frequency Volatility: An Autoregressive Conditional Duration Approach, Yiu Kuen Tse, Thomas Tao Yang
Research Collection School Of Economics
We propose a method to estimate the intraday volatility of a stock by integrating the instantaneous conditional return variance per unit time obtained from the autoregressive conditional duration (ACD) model, called the ACD-ICV method. We compare the daily volatility estimated using the ACD-ICV method against several versions of the realized volatility (RV) method, including the bipower variation RV with subsampling, the realized kernel estimate, and the duration-based RV. Our Monte Carlo results show that the ACD-ICV method has lower root mean-squared error than the RV methods in almost all cases considered. This article has online supplementary material.
Forecasting Realized Volatility Using A Nonnegative Semiparametric Time Series Model, A. Eriksson, D. Preve, Jun Yu
Forecasting Realized Volatility Using A Nonnegative Semiparametric Time Series Model, A. Eriksson, D. Preve, Jun Yu
Research Collection School Of Economics
This paper introduces a parsimonious and yet flexible nonnegative semiparametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the distributional form of its error component is left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Asymptotic properties are established for the new estimation method. Simulation studies validate the new estimation method. The out-of-sample performance of the proposed model is evaluated against a number …
Forecasting Realized Volatility Using A Nonnegative Semiparametric Model, D. Preve, A. Eriksson, Jun Yu
Forecasting Realized Volatility Using A Nonnegative Semiparametric Model, D. Preve, A. Eriksson, Jun Yu
Research Collection School Of Economics
This paper introduces a parsimonious and yet flexible nonnegative semiparametric model to forecast volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen and Shephard (2001) and Nielsen and Shephard (2003) by way of a Box-Cox transformation. It is semiparametric in the sense that the dependency structure and the distributional form of its error component are left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Its out-of-sample performance is evaluated against a number of standard methods, using data on S&P 500 monthly realized volatilities. The competing models include the exponential …
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 …
A Semiparametric Stochastic Volatility Model, Jun Yu
A Semiparametric Stochastic Volatility Model, Jun Yu
Research Collection School Of Economics
This paper examines how volatility responds to return news in the context of stochastic volatility (SV) using a nonparametric method. The correlation structure in the classical leverage SV model is generalized based on a linear spline. In the new model the correlation between the return innovation and volatility innovation is dependent on the type of news arrived to the market. Theoretical properties of the proposed model are examined. A simulation-based maximum likelihood method is developed to estimate the new model. Simulations show that the estimation method provides reliable parameter estimates. The new model is fitted to daily and weekly data …
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 …
Asymmetric Response Of Volatility: Evidence From Stochastic Volatility Models And Realized Volatility, Jun Yu
Research Collection School Of Economics
This paper examines the asymmetric response of equity volatility to return shocks. We generalize the news impact function (NIF), originally introduced by Engle and Ng (1993) to study asymmetric volatility under the ARCH-type models, to be applicable to both stochastic volatility (SV) and ARCH-type models. Based on the generalized concept, we provide a unified framework to examine asymmetric properties of volatility. A new asymmetric volatility model, which nests both ARCH and SV models and at the same time allows for a more flexible NIF, is proposed. Empirical results based on daily index return data support the classical asymmetric SV model …