Reproducing Business Cycle Features: How Important Is Nonlinearity Versus Multivariate Information?

In this paper, we consider the ability of time-series models to generate simulated data that display the same business cycle features found in U.S. real GDP. Our analysis of a range of popular time-series models allows us to investigate the extent to which multivariate information can account for the apparent univariate evidence of nonlinear dynamics in GDP. We find that certain nonlinear specifications yield an improvement over linear models in reproducing business cycle features, even when multivariate information inherent in the unemployment rate, inflation, interest rates, and the components of GDP is taken into account.

The Effects of Dollar/Sterling Exchange Rate Volatility on Futures Markets for Coffee and Cocoa

The paper investigates the extent to which the dollar/sterling exchange rate fluctuations affect coffee and cocoa futures prices on the London LIFFE and the New York CSCE by means of multivariate GARCH models - under the assumption that traders in perfectly competitive markets have equal access to all available information on changes in weather and in global demand and supply conditions. In three out of the four investigated cases, exchange rate posed as a main source of risk for the commodity futures price. The significance and form of volatility spill-over effects of a bilateral exchange rate are shown to be specific for commodity and market. A forecasting comparison on the basis of the identified models suggests that possible gains in prediction accuracy may be small.Commodity markets, Multivariate GARCH models, Exchange rates, Volatility, Forecasting

Monotonicity Results for Coherent MIMO Rician Channels

The dependence of the Gaussian input information rate on the line-of-sight (LOS) matrix in multiple-input multiple-output coherent Rician fading channels is explored. It is proved that the outage probability and the mutual information induced by a multivariate circularly symmetric Gaussian input with any covariance matrix are monotonic in the LOS matrix D, or more precisely, monotonic in D'D in the sense of the Loewner partial order. Conversely, it is also demonstrated that this ordering on the LOS matrices is a necessary condition for the uniform monotonicity over all input covariance matrices. This result is subsequently applied to prove the monotonicity of the isotropic Gaussian input information rate and channel capacity in the singular values of the LOS matrix. Extensions to multiple-access channels are also discussed.Comment: 14 pages, submitted to IEEE Transactions on Information Theor

Permutation complexity of interacting dynamical systems

The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work, we clarify the meaning of the coupling complexity by discussing in detail some cases leading to extreme values, and present examples using synthetic data to describe its properties. We also generalize the coupling complexity index to the multivariate case and derive a number of important properties by exploiting the structure of the symmetric group. The applicability of this index to the multivariate case is demonstrated with a real-world data example. Finally, we define the coupling complexity rate of random and deterministic time series. Some formal results about the multivariate coupling complexity index have been collected in an Appendix.Comment: 16 pages, 6 figure

Spectral Simplicity of Apparent Complexity, Part II: Exact Complexities and Complexity Spectra

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainty, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. An appendix presents spectral decomposition calculations for one example in full detail.Comment: 27 pages, 12 figures, 2 tables; most recent version at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt2.ht

Time and spectral domain relative entropy: A new approach to multivariate spectral estimation

The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy rates. This naturally leads to a new spectral estimation technique where a multivariate version of the Itakura-Saito distance is employed}. It may be viewed as an extension of the approach, called THREE, introduced by Byrnes, Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the form of a constrained spectrum approximation problem where the distance is equal to the processes relative entropy rate. The corresponding solution entails a complexity upper bound which improves on the one so far available in the multichannel framework. Indeed, it is equal to the one featured by THREE in the scalar case. The solution is computed via a globally convergent matricial Newton-type algorithm. Simulations suggest the effectiveness of the new technique in tackling multivariate spectral estimation tasks, especially in the case of short data records.Comment: 32 pages, submitted for publicatio