An investigation of long memory in various measures of stock market volatility, using wavelets and aggregate series

Using methods based on wavelets and aggregate series, long memory in the absolute daily returns, squared daily returns, and log squared daily returns of the S&P 500 Index are investigated. First, we estimate the long memory parameter in each series using a method based on the discrete wavelet transform. For each series, the variance method and the absolute value method based on aggregate series are then employed to investigate long memory. Our findings suggest that these methods provide evidence of long memory in the volatility of the S&P 500 Index. Our esteemed colleague, Robert DiSario, passed away on December 31, 2005.     

Description, modelling and forecasting of data with optimal wavelets

Cascade processes have been used to model many different self-similar systems, as they are able to accurately describe most of their global statistical properties. The so-called optimal wavelet basis allows to achieve a geometrical representation of the cascade process-named microcanonical cascade- that describes the behavior of local quantities and thus it helps to reveal the underlying dynamics of the system. In this context, we study the benefits of using the optimal wavelet in contrast to other wavelets when used to define cascade variables, and we provide an optimality degree estimator that is appropriate to determine the closest-to-optimal wavelet in real data. Particularizing the analysis to stock market series, we show that they can be represented by microcanonical cascades in both the logarithm of the price and the volatility. Also, as a promising application in forecasting, we derive the distribution of the value of next point of the series conditioned to the knowledge of past points and the cascade structure, i.e., the stochastic kernel of the cascade process.     

A heuristic method for parameter selection in LS-SVM: Application to time series prediction

Least Squares Support Vector Machines (LS-SVM) are the state of the art in kernel methods for regression. These models have been successfully applied for time series modelling and prediction. A critical issue for the performance of these models is the choice of the kernel parameters and the hyperparameters which define the function to be minimized. In this paper a heuristic method for setting both the σ parameter of the Gaussian kernel and the regularization hyperparameter based on information extracted from the time series to be modelled is presented and evaluated.     

Implied risk aversion and pricing kernel in the FTSE 100 index

This paper studies the estimation of the pricing kernel and explains the pricing kernel puzzle found in the FTSE 100 index. We use prices of options and futures on the FTSE 100 index to derive the risk neutral density (RND). The option-implied RND is inverted by using two nonparametric methods: the implied-volatility surface interpolation method and the positive convolution approximation (PCA) method. The actual density distribution is estimated from the historical data of the FTSE 100 index by using the threshold GARCH (TGARCH) model. The results show that the RNDs derived from the two methods above are relatively negatively skewed and fat-tailed, compared to the actual probability density, that is consistent with the phenomenon of “volatility smile.” The derived risk aversion is found to be locally increasing at the center, but decreasing at both tails asymmetrically. This is the so-called pricing kernel puzzle. The simulation results based on a representative agent model with two state variables show that the pricing kernel is locally increasing with the wealth at the level of 1 and is consistent with the empirical pricing kernel in shape and magnitude.     

THE CONTINUOUS WAVELET TRANSFORM: MOVING BEYOND UNI‐ AND BIVARIATE ANALYSIS

A body of work using the continuous wavelet transform has been growing. We provide a self‐contained summary on its most relevant theoretical results, describe how such transforms can be implemented in practice, and generalize the concept of simple coherency to partial wavelet coherency and multiple wavelet coherency, moving beyond bivariate analysis. We also describe a family of wavelets, which emerges as an alternative to the popular Morlet wavelet, the generalized Morse wavelets. A user‐friendly toolbox, with examples, is attached to this paper.     

Estimators of long-memory: Fourier versus wavelets

Semi-parametric estimation methods of the long-memory exponent of a time series have been studied in several papers, some applied, others theoretical, some using Fourier methods, others using a wavelet-based technique. In this paper, we compare the Fourier and wavelet approaches to the local regression method and to the local Whittle method. We provide an overview of these methods, describe what has been done and indicate the available results and the conditions under which they hold. We discuss their relative strengths and weaknesses both from a practical and a theoretical perspective. We also include a simulation-based comparison. The software written to support this work is available on demand and we illustrate its use at the end of the paper.     

A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation

This paper presents a Bayesian approach to bandwidth selection for multivariate kernel regression. A Monte Carlo study shows that under the average squared error criterion, the Bayesian bandwidth selector is comparable to the cross-validation method and clearly outperforms the bootstrapping and rule-of-thumb bandwidth selectors. The Bayesian bandwidth selector is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow–Debreu securities with the S&P 500 index options data and the DAX index options data. The proposed Bayesian bandwidth selector represents a data-driven solution to the problem of choosing bandwidths for the multivariate kernel regression involved in the nonparametric estimation of the state-price density pioneered by Aït-Sahalia and Lo [Aït-Sahalia, Y., Lo, A.W., 1998. Nonparametric estimation of state-price densities implicit in financial asset prices. The Journal of Finance, 53, 499, 547.]     

Measure preserving derivatives and the pricing kernel puzzle

Recent empirical studies have found evidence of nonmonotonicity in the pricing kernels for a variety of market indices. This phenomenon is known as the pricing kernel puzzle. The payoff distribution pricing model of Dybvig predicts that the payoff distribution of a direct investment of $1 in a market index may be replicated by investing less than $1 in some derivative written on that market index whenever the associated pricing kernel is nondecreasing. Using the Hardy–Littlewood rearrangement inequality, we obtain an explicit solution for the cheapest replicating derivative, which we refer to as the optimal measure preserving derivative. The optimal measure preserving derivative is the permutation appearing in Ryff’s decomposition of the pricing kernel with respect to the market payoff measure. We compute optimal measure preserving derivatives corresponding to the estimated physical and risk neutral distributions in the paper by Jackwerth (2000) that first brought attention to the pricing kernel puzzle.     

基于小波分析与数学形态学融合的降噪算法研究

本文建立了实际工程应用中信号的仿真模型和干扰模型,运用小波变换和数学形态学相融合的方法进行降噪,并将该方法与小波阈值方法、小波模极大值法、数学形态学方法的仿真结果进行对比分析,仿真分析结果发现小波-形态融合方法能够有效的消除噪声且能较好地保留原信号的形态特征。     

Bayesian inference in a time varying cointegration model

There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper, we develop a new time varying parameter model which permits cointegration. We use a specification which allows for the cointegrating space to evolve over time in a manner comparable to the random walk variation used with TVP–VARs. The properties of our approach are investigated before developing a method of posterior simulation. We use our methods in an empirical investigation involving the Fisher effect.     

Nonparametric estimation and inference about the overlap of two distributions

This paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years using household survey data from two provinces taken in 1987 and 2001. We find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space.     

An alternative quasi likelihood approach,Bayesian analysis and data-based inference for model specification

This paper studies an alternative quasi likelihood approach under possible model misspecification. We derive a filtered likelihood from a given quasi likelihood (QL), called a limited information quasi likelihood (LI-QL), that contains relevant but limited information on the data generation process. Our LI-QL approach, in one hand, extends robustness of the QL approach to inference problems for which the existing approach does not apply. Our study in this paper, on the other hand, builds a bridge between the classical and Bayesian approaches for statistical inference under possible model misspecification. We can establish a large sample correspondence between the classical QL approach and our LI-QL based Bayesian approach. An interesting finding is that the asymptotic distribution of an LI-QL based posterior and that of the corresponding quasi maximum likelihood estimator share the same “sandwich”-type second moment. Based on the LI-QL we can develop inference methods that are useful for practical applications under possible model misspecification. In particular, we can develop the Bayesian counterparts of classical QL methods that carry all the nice features of the latter studied in  White (1982). In addition, we can develop a Bayesian method for analyzing model specification based on an LI-QL.     

Projecting supply and use tables: new variants and fair comparisons

ABSTRACT

We have introduced in this paper new variants of two methods for projecting Supply and Use Tables that are based on a distance minimisation approach (SUT-RAS) and the Leontief model (SUT-EURO). We have also compared them under similar and comparable exogenous information, i.e.: with and without exogenous industry output, and with explicit consideration of taxes less subsidies on products. We have conducted an empirical assessment of all of these methods against a set of annual tables between 2000 and 2005 for Austria, Belgium, Spain and Italy. From the empirical assessment, we obtained three main conclusions: (a) the use of extra information (i.e. industry output) generally improves projected estimates in both methods; (b) whenever industry output is available, the SUT-RAS method should be used and otherwise the SUT-EURO should be used instead; and (c) the total industry output is best estimated by the SUT-EURO method when this is not available.     

一种改进的不完全指数复制方法

本文在考虑交易成本和投资组合动态调整的基础上,建立混合整数线性规划模型,引入内核搜索分析框架进行近似求解,并利用沪深300进行实证研究。研究发现,一是相比于基本内核搜索法,增强型内核搜索法仅在基准指数成分股数量很大时才会较大幅度提高求解质量;二是考虑投资组合动态调整的模型不仅更稳健,而且跟踪的继承性和保持性更好,尤其适用于单边市场;三是过度刻画现实交易特征一定程度上会降低不完全指数复制模型的复制和预测效果。     

EMI滤波器的设计

文章从建立EMI滤波器的共模、差模噪声源等效电路及电路模型入手,进而探讨了EMI滤波器的设计方法及其在实际应用的结构和结构参数的选择问题。     

An Empirical Test of Pricing Kernel Monotonicity

A large class of asset pricing models predicts that securities which have high payoffs when market returns are low tend to be more valuable than those with high payoffs when market returns are high. More generally, we expect the projection of the stochastic discount factor on the market portfolio—that is, the discounted pricing kernel evaluated at the market portfolio—to be a monotonically decreasing function of the market portfolio. Numerous recent empirical studies appear to contradict this prediction. The non‐monotonicity of empirical pricing kernel estimates has become known as the pricing kernel puzzle. In this paper we propose and apply a formal statistical test of pricing kernel monotonicity. We apply the test using 17 years of data from the market for European put and call options written on the S&P 500 index. Statistically significant violations of pricing kernel monotonicity occur in a substantial proportion of months, suggesting that observed non‐monotonicities are unlikely to be the product of statistical noise. Copyright © 2014 John Wiley & Sons, Ltd.     

Convergence and performance of the peeling wavelet denoising algorithm

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the useful signal are modeled by generalized Gaussian random variables and its noisy part by independent Gaussian variables, we compute a critical thresholding constant for the algorithm, which depends on the shape parameter of the generalized Gaussian distribution. We also quantify the optimal number of steps which have to be performed, and analyze the convergence of the algorithm. Several implementations are tested against classical wavelet denoising procedures on benchmark and simulated biological signals.     

Time-frequency co-movements between oil prices and interest rates: Evidence from a wavelet-based approach

This paper investigates time–frequency co-movements between crude oil prices and interest rates. To test this relationship, the study applied a continuous wavelet and cross wavelet approaches to data from West Texas Intermediate (WTI) crude oil prices and interest rates in the United States (U.S.). Results from the sample period revealed significant relationships, in the intermediate term, between WTI crude oil prices and U.S. interest rates. Moreover, co-movements between oil price and interest rate variables were especially sensitive during abnormal political events and periods of financial ‘meltdown’. We further use Partial Wavelet Coherence (PWC) and Multiple Wavelet Coherence (MWC) methods to investigate the impacts of five major control variables namely GDP growth, unemployment, three-month Treasury bill, CPI index and industrial production index. The results show a powerful impact of control variables on oil-interest rates co-movements under different frequencies. Finally, we show evidence of co-integrating long run relationship between oil markets and control variables. These results have important implications for energy investors and policy makers.     

Estimation of dynamic models with nonparametric simulated maximum likelihood

We propose an easy-to-implement simulated maximum likelihood estimator for dynamic models where no closed-form representation of the likelihood function is available. Our method can handle any simulable model without latent dynamics. Using simulated observations, we nonparametrically estimate the unknown density by kernel methods, and then construct a likelihood function that can be maximized. We prove that this nonparametric simulated maximum likelihood (NPSML) estimator is consistent and asymptotically efficient. The higher-order impact of simulations and kernel smoothing on the resulting estimator is also analyzed; in particular, it is shown that the NPSML does not suffer from the usual curse of dimensionality associated with kernel estimators. A simulation study shows good performance of the method when employed in the estimation of jump-diffusion models.     

A wavelet-based assessment of market risk: The emerging markets case

The measurement of market risk poses major challenges to researchers and different economic agents. On one hand, it is by now widely recognized that risk varies over time. On the other hand, the risk profile of an investor, in terms of investment horizon, makes it crucial to also assess risk at the frequency level. We propose a novel approach to measuring market risk based on the continuous wavelet transform. Risk is allowed to vary both through time and at the frequency level within a unified framework. In particular, we derive the wavelet counterparts of well-known measures of risk. One is thereby able to assess total risk, systematic risk and the importance of systematic risk to total risk in the time-frequency space. To illustrate the method we consider the emerging markets case over the last twenty years, finding noteworthy heterogeneity across frequencies and over time, which highlights the usefulness of the wavelet approach.