This paper discuses some novel results concerning the wave action conservation law for multisymplectic partial differential equations and their discretizations. We provide a method for deriving this conservation law in Fourier spectral space. A discrete wave action conservation law for a...

We present an spectral numerical method for the numerical valuation of bonds with embedded options. We use a CIR model for the short term interest rate. The method is based in a Galerkin formulation of the relevant partial differential equation for the value of the bond discretized by means of...

Using coherence analysis (which is an extensively used method to study the correlations in frequency domain, between two simultaneously measured signals) we estimate the time delay between two signals. This method is suitable for time delay estimation of narrow band coherence signals for which...

An effective and easy-to-implement frequency filter is proposed, obtained by convolving a raised-cosine window with the ideal rectangular filter response function. Three other filters, Hodrick–Prescott, Baxter–King, and Christiano–Fitzgerald, are thoroughly reviewed. A bandpass version of...

This paper presents a formula expressing Legendre polynomials in terms of their derivatives and a formula expressing a Legendre polynomial integrated k-times in terms of Legendre polynomials. In view of these formulae, the second-and fourth-order elliptic equation were solved. Moreover, the...

New time and frequency domain tests for the presence of a unit root are developed. The tests are based on generalized least squares (GLS) methods in both the time and the frequency domains. For the time domain tests, moving average processes are assumed for the error terms on the autoregression....

We consider statistical inference in the presence of serial dependence. The main focus is on use of statistics that are constructed as if no dependence were believed present, and are asymptotically normal in the presence of dependence. Typically the variance in the limit distribution is affected...