We consider statistical aspects of the modelling and prediction theory of time series in one and many dimensions. We discuss Lévy-based and general models, and the stationary and non-stationary cases. Our starting point is the recent pair of surveys, Szegö’s theorem and its probabilistic descendants and Multivariate prediction and matrix Szegö theory, by this author.

Functional Principal Component Analysis (FPCA) provides a powerful and natural way to model functional financial data sets (such as collections of time-indexed futures and interest rate yield curves). However, FPCA assumes each sample curve is drawn from an independent and identical distribution. This assumption is axiomatically inconsistent with financial data; rather, samples are often interl...

where {Pt, t = 0, 1, 2, . . .} is the price of a financial asset observed at time t, t can be measured in seconds, minutes, hours, days, etc. Standard examples for Pt are prices of company-shares quoted at major stock exchanges, interest rates and foreign exchange rates among different currencies. A Taylor series argument shows that Rt is close to the relative returns (Pt−Pt−1)/Pt−1 which are f...

The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. ...

The existence of forbidden patterns, i.e., certain missing sequences in a given time series, is a recently proposed instrument of potential application in the study of time series. Forbidden patterns are related to the permutation entropy, which has the basic properties of classic chaos indicators, such as Lyapunov exponent or Kolmogorov entropy, thus allowing to separate deterministic (usually...

Using the spectral regression and Gaussian semiparametric methods of estimating the long-memory parameter, we test for fractional dynamic behavior in a number of important Japanese financial time series: spot exchange rates, forward exchange rates, stock prices, currency forward premia, Euroyen deposit rates, and the Euroyen term premium. Stochastic long memory is established as a feature of th...

This paper presents an overview of the literature on applications of copulas in the modelling of …nancial time series. Copulas have been used both in multivariate time series analysis, where they are used to charaterise the (conditional) cross-sectional dependence between individual time series, and in univariate time series analysis, where they are used to characterise the dependence between a...

The paper points to a coverage of the latest research techniques and findings relating to the econometric analysis of financial markets. It contains a wealth of new materials reflecting the developments during the last decade or so. Particular attention is paid to the wide range of nonlinear models that are used to analyze financial data observed at high frequencies and to the long memory chara...