Adaptive, locally-linear models of complex dynamics

The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based on local linear models within windows determined adaptively from the data. While the dynamics within each window are simple, consisting of exponential decay, growth and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a novel likelihood-based hierarchical clustering and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode $C. elegans$ our approach identifies fine-grained behavioral states and model dynamics which fluctuate close to an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. Finally, we analyze whole-brain imaging in $C. elegans$ and show that the stability of global brain states changes with oxygen concentration.Comment: 25 pages, 16 figure

Sources of time varying return comovements during different economic regimes: evidence from the emerging Indian equity market

We study the economic and non-economic sources of stock return comovements of the emerging Indian equity market and the developed equity markets of the US, UK, Germany, France, Canada and Japan. Our findings show that the probability of extreme comovements in the economic contraction regime is relatively higher than in the economic expansion regime. We show that international interest rates, inflation uncertainty and dividend yields are the main drivers of the asymmetric return comovements. Findings reported in the paper imply that the impact of interest rates and inflation on return comovements could be used for anticipating financial contagion and/or spillover effects. This is particularly critical since during extreme market conditions, the tail return comovements can potentially reveal critical information for active portfolio management

Arbitrage, Covered Interest Parity and Long-Term Dependence between the US Dollar and the Yen

Using a daily time series from 1983 to 2005 of currency prices in spot and forward USD/Yen markets and matching equivalent maturity short term US and Japanese interest rates, we investigate the sensitivity over the sample period of the difference between actual prices in forward markets to those calculated from short term interest rates. According to a fundamental theorem in financial economics termed covered interest parity (CIP) the actual and estimated prices should be identical once transaction and other costs are accommodated. The paper presents four important findings: First, we find evidence of considerable variation in CIP deviations from equilibrium that tends to be one way and favours those market participants with the ability to borrow US dollars (and subsequently lend yen). Second, these deviations have diminished significantly and by 2000 have been almost eliminated. We attribute this to the effects of electronic trading and pricing systems. Third, regression analysis reveals that interday negative changes in spot exchange rates, positive changes in US interest rates and negative changes in yen interest rates generally affect the deviation from CIP more than changes in interday volatility. Finally, the presence of long-term dependence in the CIP deviations over time is investigated to provide an insight into the equilibrium dynamics. Using a local Hurst exponent – a statistic used in fractal geometry - we find episodes of both positive and negative dependence over the various sample periods, which appear to be linked to episodes of dollar decline/yen appreciation, or vice versa. The presence of negative dependence is consistent with the actions of arbitrageurs successfully maintaining the long-term CIP equilibrium. Given the time varying nature of the deviations from equilibrium the sample period under investigation remains a critical issue when investigating the presence of longterm dependence.Hurst exponent; Efficient market hypothesis; covered interest parity, arbitrage