			Home About us Contact

Integrated Variance (integrate + variance)

Distribution by Scientific Domains

Business, Economics, Finance and Accounting	80%

Selected Abstracts

Bias in the estimation of non-linear transformations of the integrated variance of returns

JOURNAL OF FORECASTING, Issue 7 2006
Richard D. F. Harris
Abstract Volatility models such as GARCH, although misspecified with respect to the data-generating process, may well generate volatility forecasts that are unconditionally unbiased. In other words, they generate variance forecasts that, on average, are equal to the integrated variance. However, many applications in finance require a measure of return volatility that is a non-linear function of the variance of returns, rather than of the variance itself. Even if a volatility model generates forecasts of the integrated variance that are unbiased, non-linear transformations of these forecasts will be biased estimators of the same non-linear transformations of the integrated variance because of Jensen's inequality. In this paper, we derive an analytical approximation for the unconditional bias of estimators of non-linear transformations of the integrated variance. This bias is a function of the volatility of the forecast variance and the volatility of the integrated variance, and depends on the concavity of the non-linear transformation. In order to estimate the volatility of the unobserved integrated variance, we employ recent results from the realized volatility literature. As an illustration, we estimate the unconditional bias for both in-sample and out-of-sample forecasts of three non-linear transformations of the integrated standard deviation of returns for three exchange rate return series, where a GARCH(1, 1) model is used to forecast the integrated variance. Our estimation results suggest that, in practice, the bias can be substantial.,,Copyright © 2006 John Wiley & Sons, Ltd. [source]

Testing range estimators of historical volatility

THE JOURNAL OF FUTURES MARKETS, Issue 3 2006
Jinghong Shu
This study investigates the relative performance of various historical volatility estimators that incorporate daily trading range: M. Parkinson (1980), M. Garman and M. Klass (1980), L. C. G. Rogers and S. E. Satchell (1991), and D. Yang and Q. Zhang (2000). It is found that the range estimators all perform very well when an asset price follows a continuous geometric Brownian motion. However, significant differences among various range estimators are detected if the asset return distribution involves an opening jump or a large drift. By adding microstructure noise to the Monte Carlo simulation, the finding of S. Alizadeh, M. W. Brandt, and F. X. Diebold (2002),that range estimators are fairly robust toward microstructure effects,is confirmed. An empirical test with S&P 500 index return data shows that the variances estimated with range estimators are quite close to the daily integrated variance. The empirical results support the use of range estimators for actual market data. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:297,313, 2006 [source]

Prediction variance and G-criterion location for split-plot designs

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 4 2009
Wayne R. Wesley
Abstract Prediction variance properties for completely randomized designs (CRD) are fairly well covered in the response surface literature for both spherical and cuboidal designs. This paper evaluates the impact of changes in the variance ratio on the prediction properties of second-order split-plot designs (SPD). It is shown that the variance ratio not only influences the value of the G-criterion but also its location, in contrast with the G-criterion tendencies in CRD. An analytical method, rather than a heuristic optimization algorithm, is used to compute the prediction variance properties, which include the maximum, minimum and integrated variances for second-order SPD. The analytical equations are functions of the design parameters, radius and variance ratio. As a result, the exact values for these quantities are reported along with the location of the maximum prediction variance used in the G-criterion. The two design spaces of the whole plot and the subplot are studied and as a result, relative efficiency values for these distinct spaces are suggested. Copyright © 2008 John Wiley & Sons, Ltd. [source]