用S-Plus做金融數(shù)據(jù)統(tǒng)計分析

前言

This book grew out of lectures notes written for a one-semester junior statisticscourse offered to the undergraduate students majoring in the Department of Oper-ations Research and Financial Engineering at Princeton University. Tidbits of thehistory of this course will shed light on the nature and spirit of the book.The purpose of the course is to introduce the students to modem data analysiswith an emphasis on a domain of application that is of interest to most of them:financial engineering. The prerequisites for this course are minimal, however it isfair to say that all of the students have already taken a basic introductory statisticscourse. Thus the elementary notions of random variables, expectation and correlationare taken for granted, and earlier exposure to statistical inference （estimation, testsand confidence intervals） is assumed. It is also expected that the students are familiarwith a minimum of linear algebra as well as vector and matrix calculus.Because of my background, the course is both computational and mathematicalin nature. Most problems considered are formulated in a rigorous manner. Mathe-matical facts are motivated by applications, stated precisely, justified at an intuitivelevel, but essentially never proven rigorously. The emphasis is more on the relevanceof concepts and on the practical use of tools, rather than on their theoretical under-pinnings.

內(nèi)容概要

This book grew out of lectures notes written for a one-semester junior statistics course offered to the undergraduate students majoring in the Department of Oper-ations Research and Financial Engineering at Princeton University. Tidbits of the history of this course will shed light on the nature and spirit of the book.

作者簡介

作者：（美國）卡莫納（Rene A.Carmona）

書籍目錄

part i data exploration, estimation and simulatioi~   1 univariate exploratory data analysis     1.1 data, random variables and their distributions     1.2 first exploratory data analysis tools     1.3 more nonparametric density estimation     1.4 quantiles and q-q plots     1.5 estimation from empirical data     1.6 random generators and monte carlo samples     1.7 extremes and heavy tail distributions     problems     notes & complements   2 multivariate data exploration     2.1 multivariate data and first measure of dependence     2.2 the multivariate normal distribution     2.3 marginals and more measures of dependence     2.4 copulas and random simulations     2.5 principal component analysis     appendix 1: calculus with random vectors and matrices     appendix 2: families of copulas     problems     notes & complements part ii regression   3 parametric regression     3.1 simple linear regression     3.2 regression for prediction & sensitivities     3.3 smoothing versus distribution theory     3.4 multiple regression     3.5 matrix formulation and linearmodels     3.6 polynomial regression     3.7 nonlinear regression     3.8 term structure of interest rates: a crash course     3.9 parametric yield curve estimation     appendix: cautionary notes on some s- plus idiosyncracies     problems     notes & complements   4 local & nonparametric regression     4.1 review of the regression setup     4.2 natural splines as local smoothers     4.3 nonparametric scatterplot smoothers     4.4 more yield curve estimation     4.5 multivariate kernel regression     4.6 projection pursuit regression     4.7 nonparametric option pricing     appendix: kernel density estimation & kernel regression     problems     notes & complements part iii time series & state space models   5 time series models: ar, ma, arma, & all that     5.1 notation and first definitions     5.2 high frequency data     5.3 time dependent statistics and stationarity     5.4 first examples of models     5.5 fitting models to data     5.6 putting a price on temperature     appendix: more s- plus icliosyncracies     problems     notes & complements   6 multivariate time series, linear systems & kalman filtering     6.1 multivariate time series     6.2 state space models     6.3 factor models as hidden markov processes     6.4 kalman filtering of linear systems     6.5 applications to linear models     6.6 state space representation of time series     6.7 example: prediction of quarterly earnings     problems     notes & complements   7 nonlinear time series: models and simulation     7.1 first nonlinear time series models     7.2 more nonlinear models: arch, garch & all that     7.3 stochastic volatility models     7.4 discretization of stochastic differential equations     7.5 random simulation and scenario generation     7.6 filtering of nonlinear systems     appendix: preparing index data.     problems     notes & complements     appendix: an introduction to s and s - plus     references     notation index     data set index     s-plus index     author index     subject index

章節(jié)摘錄

插圖：The look of a histogram can change significantly when the number of bins andthe origin of the bins are changed. The reader is encouraged to produce differenthistograms for the same data sample by setting the value of the parameter nclassto different integers.Remark. The commands given above （as well as most of the commands in thisbook） can be used both on a Unix/Linux platform and under Windows. There aremany other ways to produce plots, especially under Windows. For example, one canselect the columns of the variables to be plotted, and then click on the appropriatebutton of the 2-D plot palette. In fact, some of these alternative methods give plotsof better quality. Nevertheless, our approach will remain to provide S-plus com-mands and function codes which can be used on any platform supported by S- Plus,and essentially with any version of the program.A good part of classical parametric estimation theory can be recast in the frameworkof density estimation: indeed, estimating the mean and the variance of a normalpopulation is just estimating the density of a normal population. Indeed, a Gaussiandistribution is entirely determined by its first two moments, and knowing its meanand variance is enough to determine the entire distribution. Similarly, estimatingthe mean of an exponential population is the same as estimating the density of thepopulation since the exponential distribution is completely determined by its rateparameter, which in turn is determined by the mean of the distribution. We are notinterested in these forms of parametric density estimation in this section. Instead, weconcentrate on nonparametric procedures.Like most nonparametric function estimation procedures, the histogram relieson the choice of some parameters, two to be precise. Indeed, in order to produce ahistogram, one has to choose the width of the bins, and the origin from which thebins are defined. The dependence of the histogram upon the choice of the origin isan undesirable artifact of the method. In order to circumvent this shortcoming, thenotion of averaged histogram was introduced: one histogram is computed for eachof a certain number of choices of the origin, and all these histograms are averagedout to produce a smoother curve expected to be robust to shifts in the origin. Thisestimate is called the ASH estimate of the density of the population, the three initialsA,S and H standing for "average shifted histogram". See the Notes & Complementsat the end of this chapter for references.Even though ASH estimates are free of the artificial dependence on the choice ofthe origin, they are still dependent on the particular choice of the bin width, the latterbeing responsible for the look of the final product: ragged curves from a choice ofsmall bin widths, and smoother looking blocks from a choice of larger bin widths.The decisive influence of this parameter should be kept in mind as we inch our waytoward the introduction of our favorite density estimation procedure.

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