Optimal Statistical Inference in Financial Engineering
CRC Press, Nov 26, 2007 - Mathematics - 384 pages
Until now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively describe actual financial data and illustrates how to properly estimate the proposed models.
After explaining the elements of probability and statistical inference for independent observations, the book discusses the testing hypothesis and discriminant analysis for independent observations. It then explores stochastic processes, many famous time series models, their asymptotically optimal inference, and the problem of prediction, followed by a chapter on statistical financial engineering that addresses option pricing theory, the statistical estimation for portfolio coefficients, and value-at-risk (VaR) problems via residual empirical return processes. The final chapters present some models for interest rates and discount bonds, discuss their no-arbitrage pricing theory, investigate problems of credit rating, and illustrate the clustering of stock returns in both the New York and Tokyo Stock Exchanges.
Basing results on a modern, unified optimal inference approach for various time series models, this reference underlines the importance of stochastic models in the area of financial engineering.
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AR(p assume asymptotic variance asymptotically efficient asymptotically optimal called CHARN model clustering coefficient condition consider consistent estimator convergence covariance D(fo defined Definition denote discount bond discuss distribution function efficient estimator ergodic Example Exercise Figure financial engineering financial time series fo(u fo(X following theorem Gaussian given Hannan Hence Henceforth implies integral interval Kakizawa Lemma linear process locally stationary processes log-likelihood ratio martingale matrix measurable function measure misclassification probabilities non-Gaussian nonlinear normal distribution option pricing periodogram probability density function probability distribution probability space random variables random vector respect return process sample satisfies second-order sequence series models spot rate stationary process statistical stochastic process strictly stationary sufficient statistic Suppose Taniguchi theory unbiased estimator unknown parameter varying spectral density window function zero