A comparison of barostats for the mechanical characterization of metal-organic frameworks

In this paper, three barostat coupling schemes for pressure control, which are commonly used in molecular dynamics simulations, are critically compared to characterize closed pore the rigid MOF-5 and flexible MIL-53(Al) metal organic frameworks. We investigate the performance of the three barostats, the Berendsen, the Martyna-Tuckerman-Tobias-Klein (MTTK), and the Langevin coupling methods, in reproducing the cell parameters and the pressure versus volume behavior in isothermal isobaric simulations. A thermodynamic integration method is used to construct the free energy profiles as a function of volume at finite temperature. It is observed that the aforementioned static properties are well-reproduced with the three barostats. However, for static properties depending nonlinearly on the pressure, the Berendsen barostat might give deviating results as it suppresses pressure fluctuations more drastically. Finally, dynamic properties, which are directly related to the fluctuations of the cell, such as the time to transition from the large-pore to the closed-pore phase, cannot be well-reproduced by any of the coupling schemes

Economic Fluctuations and Diffusion

Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and quantify the relation between trading activity - measured by the number of transactions $N_{\Delta t}$ - and the price change $G_{\Delta t}$, for a given stock, over a time interval $[t, t+\Delta t]$. To this end, we analyze a database documenting every transaction for 1000 US stocks over the two-year period 1994-1995. We find that price movements are equivalent to a complex variant of diffusion, where the diffusion coefficient fluctuates drastically in time. We relate the analog of the diffusion coefficient to two microscopic quantities: (i) the number of transactions $N_{\Delta t}$ in $\Delta t$, which is the analog of the number of collisions and (ii) the local variance $w^2_{\Delta t}$ of the price changes for all transactions in $\Delta t$, which is the analog of the local mean square displacement between collisions. We study the distributions of both $N_{\Delta t}$ and $w_{\Delta t}$, and find that they display power-law tails. Further, we find that $N_{\Delta t}$ displays long-range power-law correlations in time, whereas $w_{\Delta t}$ does not. Our results are consistent with the interpretation that the pronounced tails of the distribution of $G_{\Delta t} are due to$w_{\Delta t}$, and that the long-range correlations previously found for$| G_{\Delta t} |$are due to$N_{\Delta t}$.Comment: RevTex 2 column format. 6 pages, 36 references, 15 eps figure

Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k } is strongly mixing. More precisely {a r } is a periodic sequence of real numbers with period P \textgreater{} 0 and such that P r=1 |a r | \textgreater{} 1. The time series {u r } is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated

The merit of high-frequency data in portfolio allocation

This paper addresses the open debate about the usefulness of high-frequency (HF) data in large-scale portfolio allocation. Daily covariances are estimated based on HF data of the S&P 500 universe employing a blocked realized kernel estimator. We propose forecasting covariance matrices using a multi-scale spectral decomposition where volatilities, correlation eigenvalues and eigenvectors evolve on different frequencies. In an extensive out-of-sample forecasting study, we show that the proposed approach yields less risky and more diversified portfolio allocations as prevailing methods employing daily data. These performance gains hold over longer horizons than previous studies have shown

Unit roots in periodic autoregressions

Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model