How Can We Define The Concept of Long Memory? An Econometric Survey

In this paper we discuss different aspects of long mzmory behavior and specify what kinds of parametric models follow them. We discuss the confusion which can arise when empirical autocorrelation function of a short memory process decreases in an hyperbolic way.Long-memory, Switching, Estimation theory, Spectral

On the Necessity of Five Risk Measures

The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an important role in computing the capital for both approaches. In this paper we analyze the errors produced by using this measure. We discuss other measures, demonstrating their strengths and shortcomings. We give examples, showing the need for the information from multiple risk measures in order to determine a bank's loss distribution. We conclude by suggesting a regulatory requirement of multiple risk measures being reported by banks, giving specific recommendations.Comment: 23 pages, 9 figure

Forecasting chaotic systems: The role of local Lyapunov exponents.

We propose a novel methodology for forecasting chaotic systems which is based on the nearest-neighbor predictor and improves upon it by incorporating local Lyapunov exponents to correct for its inevitable bias. Using simulated data, we show that gains in prediction accuracy can be substantial. The general intuition behind the proposed method can readily be applied to other non-parametric predictors.

Dynamics of 8CB confined into porous silicon probed by incoherent neutron backscattering experiments

Confinement in the nanochannels of porous silicon strongly affects the phase behavior of the archetype liquid-crystal 4-n-octyl-4-cyanobiphenyl (8CB). A very striking phenom- enon is the development of a short-range smectic order, which occurs on a very broad temperature range. It suggests in this case that quenched disorder effects add to usual finite size and surface interaction effects. We have monitored the temperature variation of the molecular dynamics of the confined fluid by incoherent quasielastic neutron scat- tering. A strongly reduced mobility is observed at the highest temperatures in the liquid phase, which suggests that the interfacial molecular dynamics is strongly hindered. A continuously increasing slowdown appears on cooling together with a progressive growth of the static correlation lengt

Further evidence on the impact of economic news on interest rates

US interest rates’ overnight reaction to macroeconomic announcements is of tremendous importance when trading fixed income securities. Most of the empirical studies achieved so far either assumed that the interest rates’ reaction to announcements is linear or independent to the state of the economy. We investigate the shape of the term structure reaction of the swap rates to announcements using several linear and non-linear time series models. The empirical results yield several not-so-well-known stylized facts about the bond market. First, and although we used a daily dataset, we find that the introduction of non linear models leads to the finding of a significant number of macroeconomic figures that actually produce an effect over the yield curve. Most of the studies using daily datasets did not corroborate so far this conclusion. Second, we find that the term structure response to announcements can be much more complicated that what is generally found: we noticed at least four types of patterns in the term structure reaction of interest rates across maturities, including the hump-shaped one that is generally considered. Third, by comparing the shapes of the rates’ term structure reaction to announcements with the first four factors obtained when performing a principal component analysis of the daily changes in the swap rates, we propose a first interpretation and classification of these different shapes. Fourth we find that the existence of some outliers in the one-day changes in interest rates usually leads to a strong underestimation of the reaction of interest rates to announcements, explaining the different results obtained between high-frequency and daily datasets: the first type of study seems to lead to the finding of fewer market mover announcements.Macroeconomic Announcements; Interest Rates Dynamic; Outliers; Reaction Function; Principal Component Analysis

Local Lyapunov exponents: Zero plays no role in Forecasting chaotic systems

We propose a novel methodology for forecasting chaotic systems which uses information on local Lyapunov exponents (LLEs) to improve upon existing predictors by correcting for their inevitable bias. Using simulated data on the nearest-neighbor predictor, we show that accuracy gains can be substantial and that the candidate selection problem identified in Guégan and Leroux (2009) can be solved irrespective of the value of LLEs. An important corollary follows: the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems.Chaos theory, Lyapunov exponent, Lorenz attractor Rössler attractor, Monte Carlo Simulations.

Business surveys modelling with Seasonal-Cyclical Long Memory models.

Business surveys are an important element in the analysis of the short-term economic situation because of the timeliness and nature of the information they convey. Especially, surveys are often involved in econometric models in order to provide an early assessment of the current state of the economy, which is of great interest for policy-makers. In this paper, we focus on non-seasonally adjusted business surveys relative to the Euro area released by the European Commission. We introduce an innovative way for modelling those series taking the persistence of the seasonal roots into account through seasonal-cyclical long memory models. We empirically prove that such models produce more accurate forecasts than classical seasonal linear models.Euro area ; business surveys ; seasonal ; long memory.

Portfolio Symmetry and Momentum

This paper presents a theoretical framework to model the evolution of a portfolio whose weights vary over time. Such a portfolio is called a dynamic portfolio. In a first step, considering a given investment policy, we define the set of the investable portfolios. Then, considering portfolio vicinity in terms of turnover, we represent the investment policy as a graph. It permits us to model the evolution of a dynamic portfolio as a stochastic process in the set of the investable portfolios. Our first model for the evolution of a dynamic portfolio is a random walk on the graph corresponding to the investment policy chosen. Next, using graph theory and quantum probability, we compute the probabilities for a dynamic portfolio to be in the different regions of the graph. The resulting distribution is called spectral distribution. It depends on the geometrical properties of the graph and thus in those of the investment policy. The framework is next applied to an investment policy similar to the Jeegadeesh and Titman's momentum strategy. We define the optimal dynamic portfolio as the sequence of portfolios, from the set of the investable portfolios, which gives the best returns over a respective sequence of time periods. Under the assumption that the optimal dynamic portfolio follows a random walk, we can compute its spectral distribution. We found then that the strategy symmetry is a source of momentum.Graph Theory, Momentum, Dynamic Portfolio, Quantum Probability, Spectral Analysis