Abstract
AbstractThis chapter discusses actual features of financial time series data, and how to model them statistically. Because the mechanism of financial market is obviously complicated, modeling for financial time series is difficult. For this, first, we look at some empirical characteristics of financial data. Then, we review and examine various time series models (e.g., ARCH, general linear process, non-stationary process, etc.), which show plausibility. Their estimation theory is provided in a unified fashion. Optimality of the estimation and testing, etc., is described based on the local asymptotic normality (LAN) due to Le Cam. The theory and models are very general and modern.KeywordsNonlinear time series modelsVector linear processes LAN approachOption pricingClassification for time seriesLocally stationary processes
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