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Empirical properties of asset returns: stylized facts and statistical issues
 Quantitative Finance
, 2001
"... We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then des ..."
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Cited by 149 (2 self)
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We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
The Long Range Dependence Paradigm for Macroeconomics and Finance
, 2002
"... The long range dependence paradigm appears to be a suitable description of the data generating process for many observed economic time series. This is mainly due to the fact that it naturally characterizes time series displaying a high degree of persistence, in the form of a long lasting effect of u ..."
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Cited by 12 (1 self)
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The long range dependence paradigm appears to be a suitable description of the data generating process for many observed economic time series. This is mainly due to the fact that it naturally characterizes time series displaying a high degree of persistence, in the form of a long lasting effect of unanticipated shocks, yet exhibiting mean reversion. Whereas linear long range dependent time series models have been extensively used in macroeconomics, empirical evidence from financial time series prompted the development of nonlinear long range dependent time series models, in particular models of changing volatility. We discuss empirical evidence of long range dependence as well as the theoretical issues, both for economics and econometrics, such evidence has stimulated
Aggregation and memory of models of changing volatility
, 2001
"... In this paper we study the effect of contemporaneous aggregation of an arbitrarily large number of processes featuring dynamic conditional heteroskedasticity with short memory when heterogeneity across units is allowed for. We look at the memory properties of the limit aggregate. General, necessary, ..."
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Cited by 5 (0 self)
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In this paper we study the effect of contemporaneous aggregation of an arbitrarily large number of processes featuring dynamic conditional heteroskedasticity with short memory when heterogeneity across units is allowed for. We look at the memory properties of the limit aggregate. General, necessary, conditions for long memory are derived. More specific results relative to certain stochastic volatility models are also developed, providing some examples of how long memory volatility can be obtained by aggregation. JEL classification: C43
PSEUDOMAXIMUM LIKELIHOOD Estimation Of ARCH(∞) models
"... The strong consistency and asymptotic normality of the Gaussian pseudomaximum likelihood estimate of the parameters in a class of ARCH(∞) processes are established. The conditions imply that the process need not have finite variance, and allow for a wide range of rates of decay of the influence of ..."
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Cited by 3 (1 self)
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The strong consistency and asymptotic normality of the Gaussian pseudomaximum likelihood estimate of the parameters in a class of ARCH(∞) processes are established. The conditions imply that the process need not have finite variance, and allow for a wide range of rates of decay of the influence of observations in the remote past on the conditional variance, thereby covering a variety of parametric specifications of interest.
Modeling and Forecasting Stock Return Volatility Using a Random Level Shift Model
, 2008
"... We consider the estimation of a random level shift model for which the series of interest is the sum of a short memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process w ..."
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Cited by 3 (2 self)
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We consider the estimation of a random level shift model for which the series of interest is the sum of a short memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1−α) and is a random variable with probability α. Our estimation method transforms such a model into a linear state space with mixture of normal innovations, so that an extension of Kalman filter algorithm can be applied. We apply this random level shift model to the logarithm of absolute returns for the S&P 500, AMEX, Dow Jones and NASDAQ stock market return indices. Our point estimates imply few level shifts for all series. But once these are taken into account, there is little evidence of serial correlation in the remaining noise and, hence, no evidence of longmemory. Once the estimated shifts are introduced to a standard GARCH model applied to the returns series, any evidence of GARCH effects disappears. We also produce rolling outofsample forecasts of squared returns. In most cases, our simple random level shifts model clearly outperforms a standard GARCH(1,1) model and, in many cases, it also provides better forecasts than a fractionally integrated GARCH model.
ON THE MACROECONOMIC CAUSES OF EXCHANGE RATES VOLATILITY
, 2007
"... Working Paper No. 8/2007On the macroeconomic causes of exchange rates volatility ..."
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Working Paper No. 8/2007On the macroeconomic causes of exchange rates volatility
WHITTLE ESTIMATION OF EXPONENTIAL VOLATILITY MODELS
, 2007
"... The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Among many models of interest, this class includes oneshock models, such as the EGARCH model of Nelson (1991), and twoshock models, such as the ..."
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The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Among many models of interest, this class includes oneshock models, such as the EGARCH model of Nelson (1991), and twoshock models, such as the SV model of Taylor (1986). The variable of interest might not have finite fractional moment of any order and so, in particular, finite variance is not imposed. We allow for a wide range of degrees of persistence of shocks to conditional variance, allowing for both short and long memory. A detailed MonteCarlo exercise shows the smallsample properties of the estimator. We present an empirical application using the Standard & Poor’s 500 composite stock index.
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quant.iop.org Empirical properties of asset returns: stylized facts and statistical issues