Low-dimensional Time Series Research Articles

A semiparametric factor model for implied volatility surface dynamics

We propose a semiparametric factor model, which approximates the implied volatility surface (IVS) in a finite dimensional function space. Unlike standard principal component approaches typically used to reduce complexity, our approach is tailored to the degenerated design of IVS data. In particular, we only fit in the local neighborhood of the design points by exploiting the expiry effect present in option data. Using DAX index option data, we estimate the nonparametric components and a low-dimensional time series of latent factors. The modeling approach is completed by studying vector autoregressive models fitted to the latent factors.

Parallel implementation of a general purpose functional predictor for chaotic time series

A general purpose predictor for complex and chaotic deterministic dynamics is proposed. This consists of a functional reconstructor whose base functions are the polynomials orthonormal to the invariant measure associated to the time series, and of a preprocessing unit providing the necessary reconstruction parameters (the optimal time delay and the reconstructed phase space dimension). The proposed criterion for the estimation of these parameters is independent of the reconstruction method and is grounded on the results of chaotic signal analysis. A parallel implementation of reconstruction is discussed on the basis of a VME architecture. The applicability of the proposed method is tested by means of numerical simulations on low-dimensional time series.

Detecting chaos in a noisy time series

We propose a new method for detecting low-dimensional chaotic time series when there is dynamical noise present. The method identifies the sign of the largest Liapunov exponent and thus the presence or absence of chaos. It also shows when it is possible to assign a value to the exponent. This approach can work for short time series of only 500 points. We analyse several real time series including chickenpox and measles data from New York City. For model systems it correctly identifies important spatial scales at which noise and nonlinear effects are important. We propose a further technique for estimating the level of noise in real time series if it is difficult to detect by the former method.