19,664 research outputs found
Asymmetric Power Distribution: Theory and Applications to Risk Measurement
Theoretical literature in finance has shown that quantifying the risk of financial time series amounts to measuring their expected shortfall, also known as tail Value at Risk. Unfortunately, little empirical work has been devoted to the problem of modeling and inference of such risk measures and, in particular, to their estimation. In this paper, we construct a parametric estimator for the expected shortfall based on a new family of densities, which we call the Asymmetric Power Distribution (APD). The APD family extends the Generalized Power Distribution to cases where the data exhibits asymmetry. We provide a detailed description of the properties of an APD random variable, such as its quantiles, moments and moment related parameters. Moreover, we discuss the problem of simulation of such random variables and provide maximum likelihood estimates of the APD density parameters. The study of asymptotic properties of the latter falls outside the standard framework due to the non-differentiability of the APD log-likelihood. An empirical application to six daily financial market series reveals that returns tend to be asymmetric, with innovations which cannot be modeled by either Laplace (double-exponential) or Gaussian distribution, even if we allow the latter to be asymmetric. Under a more general assumption that the return innovations are APD, we are able to compute expected shortfalls and corresponding confidence intervals and thus compare the riskiness of the series examinedexpected shortfall, value-at-risk, generalized power distribution
Robust estimation and inference for heavy tailed GARCH
We develop two new estimators for a general class of stationary GARCH models
with possibly heavy tailed asymmetrically distributed errors, covering
processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH,
VGARCH and Quadratic GARCH. The first estimator arises from negligibly trimming
QML criterion equations according to error extremes. The second imbeds
negligibly transformed errors into QML score equations for a Method of Moments
estimator. In this case, we exploit a sub-class of redescending transforms that
includes tail-trimming and functions popular in the robust estimation
literature, and we re-center the transformed errors to minimize small sample
bias. The negligible transforms allow both identification of the true parameter
and asymptotic normality. We present a consistent estimator of the covariance
matrix that permits classic inference without knowledge of the rate of
convergence. A simulation study shows both of our estimators trump existing
ones for sharpness and approximate normality including QML, Log-LAD, and two
types of non-Gaussian QML (Laplace and Power-Law). Finally, we apply the
tail-trimmed QML estimator to financial data.Comment: Published at http://dx.doi.org/10.3150/14-BEJ616 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
On the Probability Distribution of Economic Growth
Normality is often mechanically and without sufficient reason assumed in econometric models. In this paper three important and significantly heteroscedastic GDP series are studied. Heteroscedasticity is removed and the distributions of the filtered series are then compared to a Normal, a Normal-Mixture and Normal-Asymmetric Laplace (NAL) distributions. NAL represents a reduced and empirical form of the Aghion and Howitt (1992) model for economic growth, based on Schumpeter's idea of creative destruction. Statistical properties of the NAL distributions are provided and it is shown that NAL competes well with the alternatives.The Aghion-Howitt model, asymmetric innovations, mixed normal- asymmetric Laplace distribution, Kernel density estimation, Method of Moments estimation.
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On a class of distributions with simple exponential tails
A simple general construction is put forward which covers many unimodal univariate distributions with simple exponentially decaying tails (e.g. asymmetric Laplace, log F and hyperbolic distributions as well as many new models). The proposed family is a special subset of a regular exponential family, and many properties flow therefrom. Two main practical points are made in the context of maximum likelihood fitting of these distributions to data. The first of these is that three, rather than an apparent four, parameters of the distributions suffice. The second is that maximum likelihood estimation of location in the new distributions is precisely equivalent to a standard form of kernel quantile estimation, choice of kernel being equivalent to specific choice of model within the class. This leads to a maximum likelihood method for bandwidth selection in kernel quantile estimation, but its practical performance is shown to be somewhat mixed. Further distribution theoretical aspects are also pursued, particularly distributions related to the main construction as special cases, limiting cases or by simple transformation
Comparison between mirror Langmuir probe and gas puff imaging measurements of intermittent fluctuations in the Alcator C-Mod scrape-off layer
Statistical properties of the scrape-off layer (SOL) plasma fluctuations are
studied in ohmically heated plasmas in the Alcator C-Mod tokamak. For the first
time, plasma fluctuations as well as parameters that describe the fluctuations
are compared across measurements from a mirror Langmuir probe (MLP) and from
gas-puff imaging (GPI) that sample the same plasma discharge. This comparison
is complemented by an analysis of line emission time-series data, synthesized
from the MLP electron density and temperature measurements. The fluctuations
observed by the MLP and GPI typically display relative fluctuation amplitudes
of order unity together with positively skewed and flattened probability
density functions. Such data time series are well described by an established
stochastic framework which model the data as a superposition of uncorrelated,
two-sided exponential pulses. The most important parameter of the process is
the intermittency parameter, {\gamma} = {\tau}d / {\tau}w where {\tau}d denotes
the duration time of a single pulse and {\tau}w gives the average waiting time
between consecutive pulses. Here we show, using a new deconvolution method,
that these parameters can be consistently estimated from different statistics
of the data. We also show that the statistical properties of the data sampled
by the MLP and GPI diagnostic are very similar. Finally, a comparison of the
GPI signal to the synthetic line-emission time series suggests that the
measured emission intensity can not be explained solely by a simplified model
which neglects neutral particle dynamics
Volatility forecasting
Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1
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