Impulse response

Abstract: Building on Koop, [Koop et al. (1996) Impulse response analysis in nonlinear multivariate models. Journal of Econometrics 74, 119–147] we propose the `generalized' impulse response analysis for unrestricted vector autoregressive (VAR) and cointegrated VAR models. Unlike the traditional impulse response analysis, our approach does not require orthogonalization of shocks and is invariant to the ordering of the variables in the VAR. The approach is also used in the construction of order-invariant forecast error variance decompositions.

Abstract: Image methods are commonly used for the analysis of the acoustic properties of enclosures. In this paper we discuss the theoretical and practical use of image techniques for simulating, on a digital computer, the impulse response between two points in a small rectangular room. The resulting impulse response, when convolved with any desired input signal, such as speech, simulates room reverberation of the input signal. This technique is useful in signal processing or psychoacoustic studies. The entire process is carried out on a digital computer so that a wide range of room parameters can be studied with accurate control over the experimental conditions. A fortran implementation of this model has been included.

Abstract: This paper presents a unified approach to impulse response analysis which can be used for both linear and nonlinear multivariate models. After discussing the advantages and disadvantages of traditional impulse response functions for nonlinear models, we introduce the concept of a generalized impulse response function which, we argue, is applicable to both linear and nonlinear models. We develop measures of shock persistence and asymmetric effects of shocks derived from the generalized impulse response function. We illustrate the use of these measures for a nonlinear bivariate model of US output and the unemployment rate.

Abstract: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems. >

Abstract: This paper describes the performance characteristics of the LMS adaptive filter, a digital filter composed of a tapped delay line and adjustable weights, whose impulse response is controlled by an adaptive algorithm. For stationary stochastic inputs, the mean-square error, the difference between the filter output and an externally supplied input called the "desired response," is a quadratic function of the weights, a paraboloid with a single fixed minimum point that can be sought by gradient techniques. The gradient estimation process is shown to introduce noise into the weight vector that is proportional to the speed of adaptation and number of weights. The effect of this noise is expressed in terms of a dimensionless quantity "misadjustment" that is a measure of the deviation from optimal Wiener performance. Analysis of a simple nonstationary case, in which the minimum point of the error surface is moving according to an assumed first-order Markov process, shows that an additional contribution to misadjustment arises from "lag" of the adaptive process in tracking the moving minimum point. This contribution, which is additive, is proportional to the number of weights but inversely proportional to the speed of adaptation. The sum of the misadjustments can be minimized by choosing the speed of adaptation to make equal the two contributions. It is further shown, in Appendix A, that for stationary inputs the LMS adaptive algorithm, based on the method of steepest descent, approaches the theoretical limit of efficiency in terms of misadjustment and speed of adaptation when the eigenvalues of the input correlation matrix are equal or close in value. When the eigenvalues are highly disparate (λ max /λ min > 10), an algorithm similar to LMS but based on Newton's method would approach this theoretical limit very closely.