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on Econometric Time Series |
| By: | Visser, Marcel P. |
| Abstract: | Daily volatility proxies based on intraday data, such as the high-low range and the realized volatility, are important to the specification of discrete time volatility models, and to the quality of their parameter estimation. The main result of this paper is a simple procedure for combining such proxies into a single, highly efficient volatility proxy. The approach is novel in optimizing proxies in relation to the scale factor (the volatility) in discrete time models, rather than optimizing proxies as estimators of the quadratic variation. For the S&P 500 index tick data over the years 1988-2006 the procedure yields a proxy which puts, among other things, more weight on the sum of the highs than on the sum of the lows over ten-minute intervals. The empirical analysis indicates that this finite-grid optimized proxy outperforms the standard five-minute realized volatility by at least 40%, and the limiting case of the square root of the quadratic variation by 25%. |
| Keywords: | volatility proxy; realized volatility; quadratic variation; scale factor; arch/garch/stochastic volatility; variance of logarithm |
| JEL: | G1 C65 C52 C22 |
| Date: | 2008–10–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:11001&r=ets |
| By: | Alessandro De Gregorio (Università di Milano, Italy); Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT) |
| Abstract: | In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete observations $\{X_{t_i}, i=0, \ldots, n\}$ with $t_i = i\Delta_n$, $i=0, 1, \ldots, n$, under the asymptotic scheme $\Delta_n\to0$, $n\Delta_n\to\infty$ and $n\Delta_n^2\to 0$. The class of $\phi$-divergences is wide and includes several special members like Kullback-Leibler, R\'enyi, power and $\alpha$-divergences. We derive the asymptotic distribution of the test statistics based on $\phi$-divergences. The limiting law takes different forms depending on the regularity of $\phi$. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test. |
| Keywords: | diffusion processes, empirical level, divergences, |
| Date: | 2008–08–06 |
| URL: | http://d.repec.org/n?u=RePEc:bep:unimip:1076&r=ets |
| By: | Alessandro De Gregorio (Università di Milano, Italy); Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT) |
| Abstract: | In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time. The mesh of observations is not required to shrink to zero. As distance between two observed paths, the quadratic distance of the corresponding estimated Markov operators is considered. Analysis of both synthetic data and real financial data from NYSE/NASDAQ stocks, give evidence that this distance seems capable to catch differences in both the drift and diffusion coefficients contrary to other commonly used metrics. |
| Keywords: | Clustering of time series; discretely observed diffusion processes, financial assets, markov processes, |
| Date: | 2008–09–18 |
| URL: | http://d.repec.org/n?u=RePEc:bep:unimip:1077&r=ets |
| By: | Xiaohong Chen (Cowles Foundation, Yale University); Roger Koenker (Dept. of Economics, University of Illinois at Urbana-Champaign; Dept. of Economics, Boston College) |
| Abstract: | Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data. |
| Keywords: | Quantile autoregression, Copula, Ergodic nonlinear Markov models |
| JEL: | C22 C63 |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1679&r=ets |
| By: | de Silva, Ashton |
| Abstract: | This paper has a twofold purpose; the first is to present a small macroeconomic model in state space form, the second is to demonstrate that it produces accurate forecasts. The first of these objectives is achieved by fitting two forms of a structural state space macroeconomic model to Australian data. Both forms model short and long run relationships. Forecasts from these models are subsequently compared to a structural vector autoregressive specification. This comparison fulfills the second objective demonstrating that the state space formulation produces more accurate forecasts for a selection of macroeconomic variables. |
| Keywords: | State space; multivariate time series; macroeconomic model; forecast; SVAR |
| JEL: | C32 C51 C53 |
| Date: | 2008–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:11060&r=ets |
| By: | Griffin, Jim; Steel, Mark F.J. |
| Abstract: | This paper discusses Bayesian inference for stochastic volatility models based on continuous superpositions of Ornstein-Uhlenbeck processes. These processes represent an alternative to the previously considered discrete superpositions. An interesting class of continuous superpositions is defined by a Gamma mixing distribution which can define long memory processes. We develop efficient Markov chain Monte Carlo methods which allow the estimation of such models with leverage effects. This model is compared with a two-component superposition on the daily Standard and Poor's 500 index from 1980 to 2000. |
| Keywords: | Leverage effect; Levy process; Long memory; Markov chain Monte Carlo; Stock price |
| JEL: | C32 G10 C11 |
| Date: | 2008–10–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:11071&r=ets |
| By: | Visser, Marcel P. |
| Abstract: | This paper decomposes volatility proxies according to upward and downward price movements in high-frequency financial data, and uses this decomposition for forecasting volatility. The paper introduces a simple Garch-type discrete time model that incorporates such high-frequency based statistics into a forecast equation for daily volatility. Analysis of S&P 500 index tick data over the years 1988-2006 shows that taking into account the downward movements improves forecast accuracy significantly. The R2 statistic for evaluating daily volatility forecasts attains a value of 0.80, both for in-sample and out-of-sample prediction. |
| Keywords: | volatility proxy; downward absolute power variation; log-Garch; volatility asymmetry; leverage effect; SP500; volatility forecasting; high-frequency data |
| JEL: | C53 C22 G10 |
| Date: | 2008–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:11100&r=ets |
| By: | Pepa Ramirez; Rosa E. Lillo; Michael P. Wiper |
| Abstract: | Two types of transitions can be found in the Markovian Arrival process or MAP: with and without arrivals. In transient transitions the chain jumps from one state to another with no arrival; in effective transitions, a single arrival occurs. We assume that in practice, only arrival times are observed in a MAP. This leads us to define and study the Effective Markovian Arrival process or E-MAP. In this work we define identifiability of MAPs in terms of equivalence between the corresponding E-MAPs and study conditions under which two sets of parameters induce identical laws for the observable process, in the case of 2 and 3-states MAP. We illustrate and discuss our results with examples. |
| Keywords: | Batch Markovian Arrival process, Hidden Markov models, Identifiability problems |
| Date: | 2008–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws084613&r=ets |
| By: | Roxana Chiriac (Universität Konstanz); Valeri Voev |
| Abstract: | This paper proposes a methodology for modelling time series of realized covariance matrices in order to forecast multivariate risks. The approach allows for flexible dynamic dependence patterns and guarantees positive definiteness of the resulting forecasts without imposing parameter restrictions. We provide an empirical application of the model, in which we show by means of stochastic dominance tests that the returns from an optimal portfolio based on the model’s forecasts second-order dominate returns of portfolios optimized on the basis of traditional MGARCH models. This result implies that any risk-averse investor, regardless of the type of utility function, would be better-off using our model. |
| Date: | 2008–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:knz:cofedp:0806&r=ets |
| By: | Seymen, Atilim |
| Abstract: | The paper questions the reasonability of using forecast error variance decompositions for assessing the role of different structural shocks in business cycle fluctuations. It is shown that the forecast error variance decomposition is related to a dubious definition of the business cycle. A historical variance decomposition approach is proposed to overcome the problems related to the forecast error variance decomposition. |
| Keywords: | Business Cycles, Structural Vector Autoregression Models, Forecast Error Variance Decomposition, Historical Variance Decomposition |
| JEL: | C32 E32 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:zewdip:7388&r=ets |