Seminar Details
Title:
Markowitz Strategies Revised
[Joint Seminar Between DSAP, Department of Mathematics and RMI]
Speaker: Prof Yan Jia-An, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
Date: 03 December 2009 (Thursday)
Time: 03:00pm - 05:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
In this talk I will show that parameterized continuous-time Markowitz's mean--variance efficient strategies could reach any given target with arbitrarily high probabilities. This result indicates that the very popular risk measure VaR (Value at Risk) may not be a proper measure in guiding investment practice. This, in turn, motivates the introduction of certain stopped strategies where stock holdings are liquidated whenever the parameterized Markowitz strategies reach the present value of the mean target. The risk aspect of the revised Markowitz strategies are examined via expected discounted loss from the initial budget. A new portfolio selection model is suggested. This talk is based on a joint work with Professor Xunyu Zhou of University of Oxford.
Title:
Optimization in Some High-Dimensional Statistical Problems
Speaker: Dr Zhou Hua, Department of Human Genetics, University of California, LA, CA, USA
Date: 25 November 2009 (Wednesday)
Time: 11:00am - 12:00noon
Venue:
S16-06-118, DSAP Seminar Room
Abstract
Modern high-throughput datasets from data mining, genomics, and imaging demand high-dimensional models with ten to hundreds of thousands of parameters. This poses challenges to the classical techniques of optimization such as Newton's method and Fisher's scoring algorithm, which involves storing, computing, and inverting large Hessian or information matrix. If parameter constraints and parameter bounds intrude, then the algorithms require further modification. Although numerical analysts have devised numerous remedies and safeguards, these all come at a cost of greater implementation complexity.
In this talk, I first describe the minorization-maximization (MM) principle which generalizes the celebrated expectation-maximization (EM) algorithm and offers a versatile weapon for attacking optimization problems of this sort. Then I present two devices for accelerating MM algorithms for high-dimensional problems: a quasi-Newton scheme and a parallel computing method based on inexpensive graphics processing units (GPUs). Both offer one to two orders of magnitude improvement over the naive algorithm. Applications include positron emission tomography, nonnegative matrix factorization, a movie rating algorithm and multidimensional scaling. Time permitting, I will also present several variations of deterministic annealing that tend to avoid inferior modes and find the dominant mode in some non-convex statistical problems.
Title:
Some Statistical Issues in Population Genetics (PhD Presentation)
Speaker: Mr Khang Tsung Fei, Department of Statistics and Applied Probability, National University of Singapore
Date: 04 November 2009 (Wednesday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
We wish to report some improvements to existing statistical methodology that uses dominant marker data to infer population genetic structure. We first show that our proposed zero-correction procedure reduces the root mean square error of candidate estimators of locus-specific null allele frequency and heterozygosity. Next, we demonstrate how a linear transformation of the sample average heterozygosity leads to a nearly unbiased Bayes estimator. Subsequently, we propose two ways of evaluating the maximum likelihood estimator of average heterozygosity in a single population: one using the truncated beta-binomial likelihood, and another using the EM algorithm. Finally, using a simulation approach, we argue that the categorical analysis of variance (CATANOVA) framework, instead of the commonly used analysis of molecular variance (AMOVA), is the appropriate one for analysing genetic structure in a collection of populations, where interest is intrinsically centered on the latter.
Title:
Risk Estimation in Retrospective Studies (MSc Presentation)
Speaker: Mr Wei Xing, Department of Statistics and Applied Probability, National University of Singapore
Date: 04 November 2009 (Wednesday)
Time: 2:00pm - 3:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
The analysis of data arising from case-control studies have traditionally been following methods involving estimation of relative risks and/or odds ratios. Little attention was given to estimation of risks, presumably due to constraint of such experimental designs, as well as ease of modelling of odds ratio by logistic regression. Here we present some results for estimation of risks in a general 2 by k contingency table setting, for a dichotomous outcome variable and under some reasonable assumption of prevalence. We also examine the properties of the proposed estimators, and apply them to a large-scale genome wide association (GWA) study data to demonstrate some relevance of the methods.
Title:
Constrained Factor Models: Estimation and Applications
Speaker: Professor Ruey S. Tsay, Booth School of Business, University of Chicago, USA
Date: 29 October 2009 (Thursday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
We consider estimation and applications of constrained and partially constrained approximate factor models when the dimension of explanatory variables is high. It derives likelihood ratio test for the constraints under normality. It also shows that the least squares estimation is based on constrained principal component analysis and provides consistent estimates for the model under certain conditions. The normality condition is not used for the least squares estimation. The constraints are useful tools to incorporate prior information or substantive theory in empirical applications of approximate factor models. In addition, the constraints also serve as a statistical tool to obtain parsimonious econometric models for forecasting, to simplify the interpretations of the common factors, and to reduce the dimension. We use simulation and real examples to investigate the performance of constrained estimation in finite samples and to highlight the importance of noise-to-signal ratio in factor analysis. We also compare the constrained model with its unconstrained counterpart both in estimation and in forecasting. Two real examples are shown.
Title:
Two New Ideas For Volatility Using Old Tool
Speaker: Prof Howell Tong, Holders of Saw Swee Hock Professorship of Statistics,Department of Statistics & Applied Probability, National University of Singapore, Singapore
Date: 28 October 2009 (Wednesday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
This talk revisits two old tools to show how they can be used to study the heteroscedasticity in time series, typically found in financial time series.
Title:
Central Limit Theorem Of Linear Spectral Statistics For Lanrge Dimensional Random Matrices
Speaker: Ms Wang Xiaoying, Department of Statistics and Applied Probability, National University of Singapore
Date: 07 October 2009 (Wednesday)
Time: 2:00pm - 3:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
With the development of computer science, large dimensional data have become increasingly common in various disciplines. These data resist conventional multivariate analysis that rely on large sample theory, since the number of variables for each observation can be very large and even comparable to the sample size.
The limiting distributions of the linear spectral statistics of large dimensional random matrices play an important role in large dimensional data analysis. In this thesis, using the Bernstein polynomial approximation and Stieltjes transform method, we prove the central limit theorem of linear spectral statistics with a generalized regular class C4 of the kernel functions for large dimensional Wigner matrices and sample covariance matrices.
Title:
Proportional Odds Model With Varying Coefficients For Censored Data
Speaker: Professor Tong Xingwei, School of Mathematical Sciences, Beijing Normal University, China
Date: 09 September 2009 (Wednesday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
In this article, we consider a proportional odds model, which allows one to examine the extent to which to which covariates interact nonlinearly with an exposure variable for analysis of right-censored data. A local maximum likelihood approach is presented to estimate nonlinear interaction and the baseline function.
The proposed estimators are shown to be consistent and asymptotically normal. The variance of the local likelihood estimator can be consistently estimated. Simulation studies are conducted to evaluate the performance of the proposed estimators. The method is illustrated with Stanford heart transplant data.
Title:
A Journey to the Center of the Earth
Speaker: Dr Ma Ping, University of Illinois, Urbana Champaign (UIUC)
Date:13 August 2009 (Thursday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
At a depth of ~2890 km, the core-mantle boundary (CMB) separates turbulent flow of liquid metals in the outer core from slowly convecting, highly viscous mantle silicates. The CMB marks the most dramatic change in dynamic processes and material properties in our planet, and accurate images of the structure at or near the CMB -- over large areas -- are crucially important for our understanding of present day geodynamical processes and the thermo-chemical structure and history of the mantle and mantle-core system. In addition to mapping the CMB we need to know if other structures exist directly above or below it, what they look like, and what they mean (in terms of physical and chemical material properties and geodynamical processes). Detection, imaging, (multi-scale) characterization, and understanding of structure (e.g., interfaces) in this remote region have been -- and are likely to remain -- a frontier in cross-disciplinary geophysics research. I will discuss the statistical problems and challenges in imaging the CMB through generalized Radon transform.
Title:
Similar States in Markov Chains
Speaker: Dr Yap Von Bing, Department of Statistics and Applied Probability, National University of Singapore
Date:12 August 2009 (Wednesday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
The Jukes-Cantor DNA substitution model is a continuous-time Markov chain on 4 states where the transition rates are all equal, say u. Hence the transitions constitute a Poisson process of rate 3u. The transition matrix P(t) contains only two distinct terms, on and off the diagonal. The diagonal term can be calculated in at least two ways: (1) solving an ordinary differential equation from the Kolmogorov forward equation, (2) summing the conditional probability that the initial state is revisited at time t, weighted by Poisson probabilities. I will describe a simpler way that relies on the fact that all the states are similar in some well-defined sense. Moreover, the new way generalises very nicely to other DNA substitution models. It has connections with the uniformisation technique and lumped Markov chains. All the above will be described in some detail, assuming a rudimentary understanding of continuous-time Markov chains.
Title:
Some Statistical Issues in Population Genetics
Speaker: Mr Khang Tsung Fei, Department of Statistics and Applied Probability, National University of Singapore
Date: 24 June 2009 (Wednesday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
The present work contains three parts. First, I shall present results of a comparative study of the bias, standard error and root mean square error of several estimators of population genetic parameters using dominant marker data. In the second part, we shall look at some results that establish conditions whereby inferences of population genetic structure using Wright’s F-statistics under the assumption of equal subpopulation weights are valid. In the third part, I shall argue that a special case of the analysis of molecular variance (AMOVA) method for studying the apportionment of total genetic variation to between and within group variation is a form of multivariate categorical analysis of variance (CATANOVA). Using a mitochondrial haplotype dataset, I show that the AMOVA exaggerates the relative contribution of between group variation to total variation whenever an inequality is satisfied. The present study also shows that an alternative method based on the distribution of site-specific is more resistant to unbalanced subpopulation weights. Finally, I shall discuss some possible ways of dealing with practical difficulties in adhering to the implicit sampling schemes that underpin the theoretical results.
Title:
Allan Variance of Time Series Models for Measurement Data
Speaker: Dr Zhang Nien-Fan,
Statistical Engineering Division, National Institute of Standards and Technology, U.S.A.
Date: 12 June 2009 (Friday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
The variance of the mean of autocorrelated measurements from a stationary process has been discussed in literature. However, when the measurements are from a nonstationary process, how to assess their uncertainty or variance remains unresolved. Allan variance or two-sample variance has been used in time and frequency metrology for more than three decades as a substitute for the classical variance to characterize the stability of clocks or frequency standards when the underlying process is a 1/f noise process. However, its applications are related only to the noise models characterized by the power law of the spectral density. In this talk, from the point view of the time domain, we provide a statistical underpinning of the Allan variance for discrete stationary processes, random walk, and long-memory processes such as the fractional difference processes including the noise models usually considered in time and frequency metrology. Results show that the Allan variance is a more meaningful measure of the process variation than the classical variance of the random walk and the nonstationary fractional difference processes including the 1/f noise.
Title:
The Asymptotic Distribution and Berry-Esseen Bound of a New
Test for Independence in High Dimension
Speaker: Professor Shao Qi-Man,
Department of Mathematics, University of Science and Technology
Hong Kong
Date: 8 May 2009 (Friday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
Let X1, X2, …, Xn be a random sample from a p-dimensional population distribution. Assume that both p and n are large. To test whether the
p-variates of the population are independent, Jiang (2004) uses the largest entry of the sample correlation matrix as a test statistic and the limiting
distribution is the extreme distribution of type I. It is known that the rate of convergence to this type of extreme distribution is typically slow, of order
of O(1/log n). In this talk we will introduce a new test statistic which also has an extreme limiting distribution of type I but with a rate of convergence
O((log n)3/n1/2). Other related problems will also be discussed.
This talk is based on a joint work with W.D. Liu and Z.Y. Lin of Zhejiang University.
Title:
Exponential Limits in Heavy Traffic for Single-Server Queues:
Stationary Input
Speaker: Professor Karl Sigman, Columbia University, Dept. IEOR, New York City, NY, USA
Date: 22 April 2009 (Wednesday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
We obtain the classical exponential limit law for steady-state FIFO customer delay in heavy traffic for single-server queues fed by stationary input; the G/G/1 case. By postulating a given fixed stationary input, and modifying it to reach heavy traffic, our method considerably weakens previously known sufficient conditions. We assume only that the stationary input satisfies a functional central limit theorem to Brownian motion, and a minor integrability condition. We also discuss results under an alternative condition that only requires the input to satisfy a strong approximation principle
(to Brownian motion).
(Joint work with Peter Glynn, Stanford University)
Title:
Simultaneous Confidence Band and Hypothesis Test in Generalised Varying-Coefficient Models
Speaker: Professor Zhang Wenyang, Department of Mathematical Sciences, University of Bath, UK
Date: 8 April 2009 (Wednesday)
Time: 4:00pm - 5:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
Generalised varying-coefficient models (GVC) are very important models. In this talk, we systematically investigate the statistical inference for GVC, which includes confidence band as well as hypothesis test. We establish the asymptotic distribution of the maximum discrepancy between the estimated functional coefficient and the true functional coefficient.
We compare different approaches for the construction of confidence band and hypothesis test.
Finally, the proposed statistical inference methods will be used to analyse the data from China about contraceptive use there, which leads to some interesting findings.
Title:
A Graphical Diagnostic for Identifying Influential
Model Choices in Bayesian Hierarchical Models
Speaker: Dr Ida Scheel, Department of Mathematics, University of Oslo, Norway
Date: 7 April 2009 (Tuesday)
Time: 4:00pm - 5:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
Real-world phenomena are frequently modelled by Bayesian hierarchical models. The building-blocks in such models are the distribution of each variable conditional on parent and/or neighbour variables in the graph.
The specifications of centre and spread of these conditional distributions may be well-motivated, while the tail specifications are often left to convenience. However, the posterior distribution of a parameter may depend strongly on such arbitrary tail specifications.
This is not easily detected in complex models. We propose a graphical diagnostic which detects such influential statistical modelling choices at the node level. Our diagnostic, the local critique plot, examines local conflict between the information coming from the parents and neighbours (local prior) and from the children and co-parents (lifted likelihood). It identifies properties of the local prior and the lifted likelihood that are influential on the posterior distribution. The local critique plot can be derived for all parameters in a chain graph model, and is easy to implement using the output of posterior sampling.
Title:
Maxima of Multivariate Data: Theory, Applications and Algorithms
Speaker: Professor Hwang Hsien-Kuei, Institute of Statistical Science, Academia Sinica, Taiwan
Date: 3 April 2009 (Friday)
Time: 11:00am - 12:00pm
Venue:
S16-05-102, DSAP Computer Lab 2
Abstract
Maximal elements of given multidimensional point samples are naturally encountered in many scientific disciplines and have been widely used under different names such as noninferiority, Pareto optimality, admissibility, efficiency, elite, skyline, etc. A survey will be given of the diverse aspects of maxima in connection with probabilistic properties, applications, and efficient algorithms for finding them.
Title:
Statistical analysis of Illness Death and Semi-competing Risks Data
Speaker: Professor Jack Kalbfleisch, University of Michigan
Date: 1 April 2009 (Wednesday)
Time: 4:00pm - 5:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
Semi-competing risks data frequently arise in clinical and observational studies. In these cases, the subject can experience both non-terminal and terminal events where the terminal event (e.g., death) censors the non-terminal event (e.g., relapse) but not vice-versa. Typically, the two events are correlated. An approach based on latent failure times has been advocated for the analysis of such data, where the joint survival function of two event times is assumed to follow a copula function over the positive quadrant with observation restricted to the upper wedge. We argue, that similar to models for competing risks, latent failure times should generally be avoided in modeling such data. We consider an illness-death process which circumvents any need for latent times and provides for easy incorporation of covariates. Nonparametric maximum likelihood estimation is used for inference, a simple iterative procedure is developed and needed asymptotic results are obtained. Simulation studies are conducted to assess the finite sample performance of the proposed estimators and compare them with other approaches in the literature. The methods are illustrated in an analysis of data on nasopharyngeal cancer from a randomized clinical trial.
This is joint work with Jinfeng Xu and Beechoo Tai.
BIO
Jack Kalbfleisch is Professor of Biostatistics. He received his Ph.D. in statistics in 1969 from the University of Waterloo. He was Assistant Professor in the Department of Statistics at the State University of New York at Buffalo (1970-73) and on faculty at the University of Waterloo (1973-2002). At Waterloo, he served as Chair of the Department of Statistics and Actuarial Science (1984-1990) and as Dean of the Faculty of Mathematics (1990-1998). He has held visiting appointments as Professor at the University of Washington, the University of Michigan, the University of California at San Francisco, the University of Auckland, and the National University of Singapore. He has worked in various areas of statistics and biostatistics including failure time and survival analysis, likelihood methods of inference, bootstrapping and estimating equations, mixture and mixed effects models and medical applications. Dr. Kalbfleisch is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics. He is also an elected member of the International Statistical Institute, a Fellow of the Royal Society of Canada and Gold Medalist of the Statistical Society of Canada.
Title:
Extremes and Data Assimilation in Epidemiology: Two Influenza Case Studies
Speaker: Dr Hans Wackernagel, Ecole des Mines Paris
Date: 18 March 2009 (Wednesday)
Time: 4:00pm - 5:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
The talk will present two case studies, one dealing with the problem of the early detection of an influenza epidemic using particle filtering for assimilating morbidity data, the other tackling the problem of evaluating the risk of a major pandemic by performing an extreme value analysis of pneumonia and influenza mortality data.
1) Sentinel networks of general practitioners, as set up in France since over 20 years (www.sentiweb.org), collect data about contagious disease cases for infuenza, acute diarrhea, chickenpox and others. Influenza infects from 5% to 20% of the population of France during an epidemic episode, which typically lasts a few weeks, and, as the conditions leading to an outbreak are not well understood, the moment of its start during winter is difficult to foresee. The early detection of an epidemic can however make it possible to limit its impact by adopting appropriate actions this is particularly desirable in account of the threat of a major pandemic. We describe ways of setting up such a system based on a stochastic epidemic model with spatialization into which the sentinel network data is assimilated online. As second product provided by this forecasting system is an assessment of the total number of infected people in each region at every time step, together with an error estimate.
2) Past influenza pandemics, notably the Spanish influenza (1918-1919) with a death toll of more than 40 million people, and other pandemics such as Asian influenza (1957), Hong Kong influenza (1968), Russian influenza (1977), have greatly impacted humans all around the world.
Influenza leads to pneumonia in the more serious cases, and most influenza deaths result from secondary bacterial pneumonia. This occurs more often in the > 65 age group compared to the other age groups. The combined cause-of-death category pneumonia and influenza (P&I) ranks as the seventh leading cause of death in the United States, only to be preceded by heart disease, cancer, stroke, chronic lower respiratory diseases, unintentional injuries and diabetes. Thus, the prediction of future outbreaks of pneumonia and influenza is essential for prevention and control of the magnitude of epidemics. In this case study we discuss the possibility and associated difficulties in applying methods of statistical analysis of extreme values to US mortality data. We also take care to carefully analyze demographic effects, in particular that of increased aging of the population over the last decades, in order to integrate them into the analysis. Finally, we examine the problem of estimating decadal and centennial return values for large epidemics.
Title:
Multivariate Normal Approximation Using Exchangeable Pairs
Speaker: Dr Adrian Roellin, Department of Mathematics, National University of Singapore
Date: 17 February 2009 (Tuesday)
Time: 4:30pm - 5:30pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
The method introduced by Charles Stein in the early 70s for distributional approximation has now become a powerful tool in probability theory and statistics. It not only yields convergence and rates of convergence, but explicit bounds for finite sample sizes with respect to a variety of probability metrics. One variant of Stein's method uses exchangeable pairs to express the error of approximation.
Although successfully used for univariate distributions, it has been a long standing problem on how to develop this approach for multivariate normal approximation. We present and discuss our new results in this topic along with several examples and present the so-called 'embedding method', a tool that allows for wider applicability of the approach.
Title:
Tactical Asset Allocation Imbedded with Investors' Subjective
Speaker: Mr Li Zhaohui, Department of Statistics and Applied Probability, National University of Singapore
Date: 16 February 2009 (Monday)
Time: 2:00pm - 3:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
This presentation walks through the tactical asset allocation literature and focuses especially on the implementation of Black-litterman model on global equity index portfolio. We do find that Black-litterman is superior to traditional mean-variance allocation model in terms of sharp ratio and avoiding ”corner points”, even though our forecasting model is quite simple and forecasting power is low. Besides, we extend Black-litterman model in a way that one can put the business cycle views into the market equilibrium model. We found that the added business cycle information greatly enhanced the performance of the portfolio in the out of sample test, especially when the forecasting power on the asset returns is not very strong (with a R-square less than 10 percent for example). Also we proposed an equity forecasting model based on the 6 month P/B Moving Average and found that it is not worse than the interest rate surprise model when it is applied to the SPX 500 index in the out of sample test.
In addition, in our sensitivity analysis, we found that the tricky parameter “Tau” is best calibrated as 1/(Tau*m). As “Tau” grows larger than 5, the Black-litterman model becomes”out of control” in a way that the sharp ratio is exceptionally good while there exist many corner points in the allocated weights. Among others, the variance of investors’ views does not affect much of out of sample performance once “Tau” and “Lambda” are fixed. Finally, the use of daily decayed data for estimating covariance matrix has much larger impact on the traditional Mean-Variance model than on the Black-litterman model, which is evidence that Black-litterman has superiorities over Mean-Variance model in terms of parameter robustness.
Title:
Spatial Isotropy-Anisotropy Tests for Detecting White
Matter Regions Based on Diffusion-Tensor MRI
Speaker: Dr Tao Yu, Department of Statistics, University of Wisconsin-Madison
Date: 10 February 2009 (Tuesday)
Time: 4:00pm - 5:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) provides promising in-
formation about the anatomical structure in human brain. One important and widely
studied topic is how to identify white matter regions, which play important roles in
diagnosing neuro-diseases, analyzing brain anatomical structures and so on.
In this talk, I will first introduce a procedure of constructing statistical scalars
for each voxel of the whole brain based on DT-MRI data. Under mild regularity
conditions, the constructed scalars can be demonstrated asymptotically following a
χ² distribution, which provides us clear calibrate criteria for identifying white mat-
ter regions in human brain. Furthermore, because of the large testing number and
the spatial structure, we propose a spatial false discovery rate (FDR) controlling
procedure.
Simulation studies and real-data applications on the DT-MRI data are provided
to illustrate the performance of the proposed methods.
Title:
Memory Indicators and Their Incorporation into Dynamic Models
Speaker: Dr Wen Li, Department of Statistics, Iowa State University
Date: 05 February 2009 (Thursday)
Time: 4:00pm - 5:00pm
Venue:
S16-05-101, DSAP Computer Lab1
Abstract
Data collected over time exhibit some type of memory structure, such as a short or long term memory. Two commonly used indicators of memory are the Hurst exponent and the self-similarity index. We investigate the relationship between the Hurst exponent and the self-similarity index and show that the two are connected for some time series such as fractional Brownian motion. For time series with a constant self-similarity index, we compare the statistical properties of various estimators of the self-similarity index via simulation for a range of nominal H-values between 0 and 1. We also employ windowing techniques to study the over-time behavior of the memory structure in a subset of the S&P500 series.
Further, we incorporate the memory indicators into dynamical models. In particular, and due to their popularity in terms of use, we look at two continuous-timed dynamical systems – the Log Ornstein-Uhlenbeck (LogOU) and the Cox-Ingersoll-Ross (CIR) models and investigate how to extend them by substituting the standard Brownian motion driver for a fractional driver in order to allow more flexibility in their memory structures. From the point of view of Young’s integrals we confirm the well-definedness of the two new models by noticing that the smoothness of the CIR and fractional LogOU solutions is similar to the smoothness of their random drivers. We also explore the memory structures underlying these two updated models and develop related results through analytical and numerical approaches. Finally, we discuss how to estimate the memory indicators and other model parameters simultaneously in the two model systems within a Bayesian framework.
Title:
GARCH Model With Ergodic and Stationary Rescaled Errors
Speaker: Dr Kazuhiko Shinki, Department of Statistics, University of Wisconsin-Madison
Date: 04 February 2009 (Wednesday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
Various kinds of time series such as asset returns in financial markets have time-varying variance, and the generalized autoregressive conditional heteroscedasticity (GARCH) model has been widely used to estimate the variance. While rescaled (standardized) time series are conventionally assumed to be IID in most existing studies, the iidness is not always satisfied in practice. This work gives empirical evidence that the rescaled errors have dependence structure in foreign exchange data by utilizing a test based on the extreme value theory. Then the asymptotics of GARCH estimator is proved with only assuming the rescaled errors are ergodic and stationary. The efficiency of the estimator is illustrated using a simulated example.
Title:
The CLT for Random Plancherel Young Diagrams [Joint Seminar Between DSAP and Department of Mathematics]
Speaker: Professor Su Zhonggen, Department of Mathematics, Zhejiang University, China
Date: 22 January 2009 (Thursday)
Time: 4:00pm - 5:00pm - Change to 11:00am to 12:00noon
Venue:
S16-05-101, Computer Lab 1
Abstract
Let n ≥ 1 be an positive integer, consider the set {Pn} of all partitions
of n, assign a probability, Plancherel probability to each partition. A natural
geometric object associated with a partition is its Young diagram. In this talk
I shall report a recent work jointly with Bogachev on the central limit theorem
for Young diagrams around its limit shape as n →1. This partly solves the
problem first put forward by Logan and Shepp (Adv. Math.) in 1977.
Title:
Efficient Estimation of a Multivariate Multiplicative Volatility Model
Speaker: Professor Oliver Linton, Professor of Econometrics in London School of Economics
Date: 08 January 2009 (Thursday)
Time: 3:00pm - 4:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We suggest various estimation procedures for the parametric and nonparametric components, and derive the asymptotic properties thereof. For the parametric part of the model, we obtain the semiparametric efficiency bound. Our method is applied to a bivariate stock index series.
Title:
Inference in Covariance Graph Models
Speaker: Dr Kshitij Deepak Khare, Department of Statistics, Stanford University, CA
Date: 05 January 2009 (Monday)
Time: 4:00pm - 5:00pm
Venue:
S16-06-118, DSAP Seminar Room
Abstract
Gaussian covariance graph models encode marginal independence among random variables that are represented by the vertices of a graph $G$. Inference for these models is challenging both in the frequentist and Bayesian frameworks, since the models give rise to a curved exponential family.
Maximum likelihood estimation for these models in the frequentist framework has received much attetion recently. In this talk, we address the issue of Bayesian inference for these models, and present a rich family of Wishart distributions which act as a conjugate family of priors for Gaussian covariance graph models. We present various useful properties of this class of distributions, which enable inference in high dimensions. Our techniques will be illustrated using two simulated examples and one real life example.
