The exchange rate and purchasing power parity: extending the theory and tests.

This paper analyzes the exchange rate in a ``no-arbitrage' or ``real business cycle' equilibrium model and provides empirical evidence for this model vis-a-vis PPP. Our contribution is to show, based on a generalization of the equilibrium model of exchange rates, that (i) the test equation linking the exchange rate to fundamentals should allow for international heterogeneity in time preferences or risk attitudes, as well as noise---that is, the model should not be tested as an exact relation; (ii) empirical work should use levels of variables rather than first differences; (iii) tests on the existence of long-run relations should be complemented by tests on the signs of the coefficients; (iv) the specification of the regression should offer demonstrated advantages over alternatives, and the significance tests should not rely on asymptotic distributions; and (v) the tests should steer clear of countries that have imposed, for most of the period, capital restrictions or exchange controls, thus violating the integrated-markets assumption of the model. Our empirical work shows that, as a long-run relation, the generalized model outperforms PPP.Purchasing; Purchasing power; Theory; Equilibrium; Model; International; Risk; Variables; Advantages; Distribution;

The equilibrium approach to exchange rates: theory and tests.

We characterize the equilibrium exchange rate in a general equilibrium economy without imposing strong restrictions on the output processes, preferences, or commodity market imperfections. The nomial exchange rate is determined by differences in initial wealths - the currencies of richer countries tend to be overvalued, by PPP standards - and by differences of marginal indirect utilities of total nominal spending. Changes in the exchange rate mirror differences in growth rates of real spending weighted by relative risk-aversion (which can be time-varying and can differ across countries), and, in the case of non-homothetic utility functions, differences in inflation rates computed from marginal spending weights. Thus, standard regression or cointegration tests of PPP suffer from missing-variables biases and ignore variations in risk aversions across countries and over time. We also present cointegration test of the homothecy/ CRRA version of the model. When nominal spending is given an independent role (next to prices) in the short-term dynamics, both PPP and the CRRA model become acceptable.Equilibrium; Theory; Trade;

Angular Resolution of an EAS Array for Gamma Ray Astronomy at Energies Greater Than 5 x 10 (13) Ev

A 24 detector extensive air shower array is being operated at Ootacamund (2300 m altitude, 11.4 deg N latitude) in southern India for a study of arrival directions of showers of energies greater than 5 x 10 to the 13th power eV. Various configurations of the array of detectors have been used to estimate the accuracy in determination of arrival angle of showers with such an array. These studies show that it is possible to achieve an angular resolution of better than 2 deg with the Ooty array for search for point sources of Cosmic gamma rays at energies above 5 x 10 to the 13th power eV

Degenerate Kalman filter error covariances and their convergence onto the unstable subspace

The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters. In particular, as emphasized in the seminal work of Anna Trevisan and coauthors, the error covariance matrix is asymptotically supported by the unstable-neutral subspace only, i.e., it is spanned by the backward Lyapunov vectors with nonnegative exponents. This behavior is at the core of algorithms known as assimilation in the unstable subspace, although a formal proof was still missing. This paper provides the analytical proof of the convergence of the Kalman filter covariance matrix onto the unstable-neutral subspace when the dynamics and the observation operator are linear and when the dynamical model is error free, for any, possibly rank-deficient, initial error covariance matrix. The rate of convergence is provided as well. The derivation is based on an expression that explicitly relates the error covariances at an arbitrary time to the initial ones. It is also shown that if the unstable and neutral directions of the model are sufficiently observed and if the column space of the initial covariance matrix has a nonzero projection onto all of the forward Lyapunov vectors associated with the unstable and neutral directions of the dynamics, the covariance matrix of the Kalman filter collapses onto an asymptotic sequence which is independent of the initial covariances. Numerical results are also shown to illustrate and support the theoretical findings

A Bayesian approach to Lagrangian data assimilation

Lagrangian data arise from instruments that are carried by the flow in a fluid field. Assimilation of such data into ocean models presents a challenge due to the potential complexity of Lagrangian trajectories in relatively simple flow fields. We adopt a Bayesian perspective on this problem and thereby take account of the fully non-linear features of the underlying model. In the perfect model scenario, the posterior distribution for the initial state of the system contains all the information that can be extracted from a given realization of observations and the model dynamics. We work in the smoothing context in which the posterior on the initial conditions is determined by future observations. This posterior distribution gives the optimal ensemble to be used in data assimilation. The issue then is sampling this distribution. We develop, implement, and test sampling methods, based on Markov-chain Monte Carlo (MCMC), which are particularly well suited to the low-dimensional, but highly non-linear, nature of Lagrangian data. We compare these methods to the well-established ensemble Kalman filter (EnKF) approach. It is seen that the MCMC based methods correctly sample the desired posterior distribution whereas the EnKF may fail due to infrequent observations or non-linear structures in the underlying flow

Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution

We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case

Growth of CaF2 buffer on Si using low energy cluster beam deposition technique and study of its properties

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