Financial Time Series - And In China's Capital Market

The history of autoregressive conditional heteroskedasticity(ARCH) model is indeed a very short one.For they first introduced by Robert Engle(1982) only a decade ago.Within this brief period,however,the ARCH literature has grown in a spectacular fashion.The numerous application of ARCH models defies observed trends in scientific advancement. Usually, applications lag theoretical development,but Engle's original ARCH model and its various generalization have been applied to numerous economic and financial data series of many countries.while it has seen relatively few theoretical advancement.The concept of ARCH might be only a decade old.but its roots go far into the past.possiblely as far as Bachelier(1900),who was the first to conduct a rigorous study of the behavior of speculative price.There was then a period of long silence. Mandelbrot(1963)reviewed the interest in the time series properties of asset prices with his theory that 'random variables with an infinite population variance are indispensable for a workable description of price change. His observations such as that unconditional distribution have thicker tails, variance change over time and large (small) change tend to be followed by large (small)change of either sign are 'stylized facts' for many economic and financial variables. Prior to the introduction of ARCH, researchers are very much aware of changes in variance, but used only informal procedures to take account of this .For example, Mandelbrot(1963) used recursive estimates about a ten-period moving sample mean. Engle's(1982) ARCH model was the first formal model which seemed to capture the stylized facts mentioned above.The ARCH model is used not only because it capture some stylized facts, but also because it has applications to numerous and diverse areas. For examples, it has been used in asset pricing model and arbitrage pricing theory, to develop volatility test for market efficiency and to estimate the time-varying systematic risk in the context of the market models. It has been use to measure the term structure of interest rate; To develop optimal dynamic hedging strategies; to examine how information flow across countries market and assets; to price options; and to model risk premium. In macroeconomics, it has been successfully used to construct debt portfolios of developing countries to measure inflationary uncertainty, to examine the relation between exchange rate uncertainty and trade, to study the effect of central bank interventions, and to characterize the relations between the macroeconomy and the stock market.The plan of the paper is as follows. The basic ARCH model are described in the part of Introduction. I introduce the original ARCH model of Engle(1982). I begin by defining the ARCH process. An ARCH process can be defined as follows: the dependent variable is assumed to be generated by t=1,2,.....T where is a vector of exogenous variables. is a vector of regression parameters. The ARCH model characterized the distribution of the stochastic error conditional on the realized values of the set of variables . Specifically, Engle's(1982) original ARCH model assumes where And heuristically describe its properties. I emphasized the properties of the ARCH model that make it appealing for modeling the volatility of economic time series. Subsequently, I introduce the generalized ARCH(GARCH) model of Bollerslev(1986),which provides a parsimonious parameterization for the conditional variance. The properties of ARCH process are then formally characterized by describing its unconditional moments.In chapter one first I will discuss the property of conditional and unconditional moments of ARCH in the section one. Then I describe the estimate procedure of ARCH, including the maxlikehood method and other methods such as GMM, kernel methods. A very important use of ARCH is evaluation of the accuracy of forecasts, it is described in section three. In last section, s...