Common functional component modelling

Functional data analysis (FDA) has become a popular technique in applied statistics. In particular, this methodology has received considerable attention in recent studies in empirical finance. In this talk we discuss selected topics of functional principal components analysis that are motivated by financial data.nonparametric risk management, generalized hyperbolic distribution, functional data analysis

Common Functional Implied Volatility Analysis

Trading, hedging and risk analysis of complex option portfolios depend on accurate pricing models. The modelling of implied volatilities (IV) plays an important role, since volatility is the crucial parameter in the Black-Scholes (BS) pricing formula. It is well known from empirical studies that the volatilities implied by observed market prices exhibit patterns known as volatility smiles or smirks that contradict the assumption of constant volatility in the BS pricing model. On the other hand, the IV is a function of two parameters: the strike price and the time to maturity and it is desirable in practice to reduce the dimension of this object and characterize the IV surface through a small number of factors. Clearly, a dimension reduced pricing-model that should reflect the dynamics of the IV surface needs to contain factors and factor loadings that characterize the IV surface itself and their movements across time.implied volatility, Black-Scholes, option portfolio, pricing

Common Functional Principal Components

Functional principal component analysis (FPCA) based on the Karhunen-Lo`eve decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation but also by the actual question of dynamics of implied volatility (IV) functions. For different maturities the logreturns of IVs are samples of (smooth) random functions and the methods proposed here study the similarities of their stochastic behavior. Firstly we present a new method for estimation of functional principal components from discrete noisy data. Next we present the two sample inference for FPCA and develop two sample theory. We propose bootstrap tests for testing the equality of eigenvalues, eigenfunctions, and mean functions of two functional samples, illustrate the test-properties by simulation study and apply the method to the IV analysis.Functional Principal Components, Nonparametric Regression, Bootstrap, Two Sample Problem

Higijena u proizvodnji mlijeka

U okviru ovog članka ne možemo raspraviti o hranjivoj vrijednosti pojedinih vrsta suhe krme, što smo ih gore nabrojili. Samo ćemo općenito spomenuti, da je dobro sijeno najidealnija, najprirodnija, a općenito uzevši i najjeftinija krma za stoku, dakako, i za krave muzare