ARCH Models and Financial ApplicationsSpringer Science & Business Media, 1997 - Počet stran: 228 1.1 The DevelopmentofARCH Models Time series models have been initially introduced either for descriptive purposes like prediction and seasonal correction or for dynamic control. In the 1970s, the researchfocusedonaspecificclassoftimeseriesmodels, theso-calledautoregres- sive moving average processes (ARMA), which were very easy to implement. In thesemodels, thecurrentvalueoftheseriesofinterestiswrittenasalinearfunction ofits own laggedvalues andcurrentandpastvaluesofsomenoiseprocess, which can be interpreted as innovations to the system. However, this approach has two major drawbacks: 1) it is essentially a linear setup, which automatically restricts the type of dynamics to be approximated; 2) it is generally applied without im- posing a priori constraintson the autoregressive and moving average parameters, which is inadequatefor structural interpretations. Among the field ofapplications where standard ARMA fit is poorare financial and monetary problems. The financial time series features various forms ofnon- lineardynamics, the crucialone being the strongdependenceofthe instantaneous variabilityoftheseriesonitsownpast. Moreover, financial theoriesbasedoncon- ceptslikeequilibriumorrationalbehavioroftheinvestorswouldnaturallysuggest including and testing some structural constraints on the parameters. In this con- text, ARCH (Autoregressive Conditionally Heteroscedastic) models, introduced by Engle (1982), arise as an appropriate framework for studying these problems. Currently, there existmorethan onehundredpapers and some dozenPh.D. theses on this topic, which reflects the importance ofthis approach for statistical theory, finance and empirical work. 2 1. Introduction From the viewpoint ofstatistical theory, the ARCH models may be considered as some specific nonlinear time series models, which allow for aquite exhaustive studyoftheunderlyingdynamics.Itisthereforepossibletoreexamineanumberof classicalquestions like the random walkhypothesis, prediction intervals building, presenceoflatentvariables [factors] etc., and to test the validity ofthe previously established results. |
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Běžně se vyskytující výrazy a sousloví
a₁ approximated arbitrage ARCH models ARMA assumption asymptotic autoregressive basic assets basic portfolios betas Bollerslev CAPM coefficients computed conditional distribution conditional expectation conditional variance constraint covariance decomposition defined denotes depends derived diag dynamic efficient portfolio endogenous factors error Exercise expected return factor model forecast function gains GARCH Gaussian white noise Gouriéroux h₁ heteroscedasticity homoscedasticity independent information set initial introduce K₁ kurtosis Let us consider likelihood function linear m₁ market portfolio martingale Max(p,q maximum likelihood moving average multivariate nonlinear null hypothesis optimal p₁ parameters past values procedure properties quantities random walk random walk hypothesis recursive equation representation residual risk risk aversion risk-free asset risk-free security Rore S₁ satisfied second order sequence solution St+1 stationary statistic stochastic Theory u₁ uncorrelated variables variance-covariance matrix vector volatility white noise Y₁ θα ᎧᎾ
Oblíbené pasáže
Strana 217 - Engle and J. Wooldridge (1988), A capital asset pricing model with time varying covariances, Journal of Political Economy, 96, 116-131.
Strana 220 - Koopmans, T. (1951), Analysis of Production as an Efficient Combination of Activities, in: T.
Strana 219 - Safety First and the Holding of Assets", Econometrica, 20, 431449.
Strana 222 - Tests of Asset Pricing with Time Varying Expected Risk Premiums and Market Betas", Journal of Finance, 42, 201-220.
Strana 220 - Potential Performance and Tests of Portfolio Efficiency," Journal of Financial Economics 10, 433-456. 8. Jobson, JD and Korkie, R. (1989). "A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning and MeanVariance Efficiency," Journal of Financial and Quantitative Analysis 24, 185-204.
Strana 222 - Multivariate Tests of Asset Pricing: The Comparative Power of Alternative Statistics", Journal of Financial and Quantitative Analysis, 25, 163-185.
Strana 218 - A Multivariate GARCH Model of International Transmission of Stock Returns and Volatility: The Case of United States and Canada", Journal of Business and Economic Statistics, 13, 11-25.
Strana 225 - Glosten, LR, R. Jagannathan, and D. Runkle. (1993). "Relationship Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.
Odkazy na tuto knihu
Time Series Analysis and Its Applications Robert H. Shumway,David S. Stoffer Náhled není k dispozici. - 2000 |