8,467 research outputs found
Estimation of AR and ARMA models by stochastic complexity
In this paper the stochastic complexity criterion is applied to estimation of
the order in AR and ARMA models. The power of the criterion for short strings
is illustrated by simulations. It requires an integral of the square root of
Fisher information, which is done by Monte Carlo technique. The stochastic
complexity, which is the negative logarithm of the Normalized Maximum
Likelihood universal density function, is given. Also, exact asymptotic
formulas for the Fisher information matrix are derived.Comment: Published at http://dx.doi.org/10.1214/074921706000000941 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Cramer–Rao lower bounds for change points in additive and multiplicative noise
The paper addresses the problem of determining the Cramer–Rao lower bounds (CRLBs) for noise and change-point parameters, for steplike signals corrupted by multiplicative and/or additive white noise. Closed-form expressions for the signal and noise CRLBs are first derived for an ideal step with a known change point. For an unknown change-point, the noise-free signal is modeled by a sigmoidal function parametrized by location and step rise parameters. The noise and step change CRLBs corresponding to this model are shown to be well approximated by the more tractable expressions derived for a known change-point. The paper also shows that the step location parameter is asymptotically decoupled from the other parameters, which allows us to derive simple CRLBs for the step location. These bounds are then compared with the corresponding mean square errors of the maximum likelihood estimators in the pure multiplicative case. The comparison illustrates convergence and efficiency of the ML estimator. An extension to colored multiplicative noise is also discussed
A rigorous and efficient asymptotic test for power-law cross-correlation
Podobnik and Stanley recently proposed a novel framework, Detrended
Cross-Correlation Analysis, for the analysis of power-law cross-correlation
between two time-series, a phenomenon which occurs widely in physical,
geophysical, financial and numerous additional applications. While highly
promising in these important application domains, to date no rigorous or
efficient statistical test has been proposed which uses the information
provided by DCCA across time-scales for the presence of this power-law
cross-correlation. In this paper we fill this gap by proposing a method based
on DCCA for testing the hypothesis of power-law cross-correlation; the method
synthesizes the information generated by DCCA across time-scales and returns
conservative but practically relevant p-values for the null hypothesis of zero
correlation, which may be efficiently calculated in software. Thus our
proposals generate confidence estimates for a DCCA analysis in a fully
probabilistic fashion
Finite Sample Performance in CointegrationAnalysis of Nonlinear Time Series with LongMemory
Nonlinear functions of multivariate financial time series can exhibit longmemory and fractional cointegration. However, tools for analysingthese phenomena have principally been justified under assumptionsthat are invalid in this setting. Determination of asymptotic theoryunder more plausible assumptions can be complicated and lengthy.We discuss these issues and present a Monte Carlo study, showingthat asymptotic theory should not necessarily be expected to provide agood approximation to finite-sample behaviour.Fractional cointegration, memory estimation,stochastic volatility.
Asteroseismology of Solar-Type and Red-Giant Stars
We are entering a golden era for stellar physics driven by satellite and
telescope observations of unprecedented quality and scope. New insights on
stellar evolution and stellar interiors physics are being made possible by
asteroseismology, the study of stars by the observation of natural, resonant
oscillations. Asteroseismology is proving to be particularly significant for
the study of solar-type and red-giant stars. These stars show rich spectra of
solar-like oscillations, which are excited and intrinsically damped by
turbulence in the outermost layers of the convective envelopes. In this review
we discuss the current state of the field, with a particular emphasis on recent
advances provided by the Kepler and CoRoT space missions and the wider
significance to astronomy of the results from asteroseismology, such as stellar
populations studies and exoplanet studies.Comment: The following paper will appear in the 2013 volume of Annual Reviews
of Astronomy and Astrophysics (88 pages, 7 figures; references updated;
further corrections to typos during galley-proof review
When Should Time be Continuous? Volatility Modeling and Estimation of High-Frequency Data
The paper studies the problem of volatility modeling and estimation of high-frequency data undercontinuous record asymptotics. The approach decomposes the observed data into pricediffusion and stationary components. The diffusion component may be identified as the"true" value of the underlying asset. The stationary component, termed as thehigh-frequency "noise" (HFN), accommodates pertinent market microstructure features.A simple condition, characterizing the HFN component on which conventional volatilityestimators on the basis of noisy observations will be consistent for diffusion volatility, is derived, and is applied to Reuters FXFX data. It is shown that conventional volatility estimators lead to substantial spurious volatility in high-frequency returns. The failure of conventional estimators in providing consistent estimates is due to the higher irregularities of the HFN sample path, which is induced, at least in part, by trader heterogeneity. In addition, the optimal sampling frequency is acquired which justifies theappropriateness of the use of the 10- to 15-minute sampling intervals - the benchmark noisefilter used in many recent empirical studies dealing with high-frequency foreign exchangedata.
Combining long memory and level shifts in modeling and forecasting the volatility of asset returns
We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons
Modelling squared returns using a SETAR model with long-memory dynamics
This paper presents a 2-regime SETAR model for the volatility with a long-memory process in the first regime and a short-memory process in the second regime. Persistence properties are studied and estimation methods are proposed. Such a process is applied to stock indices and individual asset prices.SETAR - Long-memory - FARIMA models - Stock indices
Combining long memory and level shifts in modeling and forecasting the volatility of asset returns
We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons
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