Analytic performance evaluation of cumulant-based arma system identification methods

The authors perform an analytic study of some cumulant-based methods for estimating the AR parameters of ARMA processes. The analysis includes new AR identifiability results for pure AR process and the analytic performance evaluation of system identification methods based on cumulants. The authors present examples of pure AR processes that are not identifiable via the normal equations based on the diagonal third-order cumulant slice. The results of the performance evaluation are illustrated graphically with plots of the variance of the estimates as a function of the parameters of the process.Peer ReviewedPostprint (published version

Frequency domain minimum distance inference for possibly noninvertible and noncausal arma models.

This article introduces frequency domain minimum distance procedures for performing inference in general, possibly non causal and/or noninvertible, autoregressive moving average (ARMA) models. We use information from higher order moments to achieve identification on the location of the roots of the AR and MA polynomials for non-Gaussian time series. We propose a minimum distance estimator that optimally combines the information contained in second, third, and fourth moments. Contrary to existing estimators, the proposed one is consistent under general assumptions, and may improve on the efficiency of estimators based on only second order moments. Our procedures are also applicable for processes for which either the third or the fourth order spectral density is the zero function.Supported by Ministerio Economía y Competitividad (Spain), Grants ECO2012-31748, ECO2014-57007p and MDM 2014-0431, and Comunidad de Madrid, MadEco-CM (S2015/HUM- 3444). Supported by Asociación Mexicana de Cultura and from the Mexican Consejo Nacional de Ciencia y Tecnología (CONACYT) under project Grant 151624

Credit Spread Modeling: Macro-financial versus HOC Approach

The aim of this paper is to throw light on the relationship between credit spreadn changes and past changes of U.S. macro-financial variables when invariants do not have Gaussian distribution. The first part presents the empirical analysis which is based on 10-year AAA corporate bond yields and 10-year Treasury bond yields. Explanatory variables include lagged U.S. leading index, Russell 2000 returns, BBB bond price changes interest rate swaps, exchange rates EUR/ USD, Repo rates, S& P 500 returns and S&P 500 volatility, Treasury bill changes, liquidity index-TRSW, LIBOR rates, Moody’s default rates; credit spread volatility and Treasury bills volatility. The proposed dynamical model explains 73% of the U.S. credit spread variance for the period 1999:07-2013:07. The second part of the article introduces the parameter estimation method based on higher order cumulants. It is demonstrated empirically that much of the information about variability of Credit Spread can be extracted from higher order cumulant function (85%)

A multivariate generalized independent factor GARCH model with an application to financial stock returns

We propose a new multivariate factor GARCH model, the GICA-GARCH model , where the data are assumed to be generated by a set of independent components (ICs). This model applies independent component analysis (ICA) to search the conditionally heteroskedastic latent factors. We will use two ICA approaches to estimate the ICs. The first one estimates the components maximizing their non-gaussianity, and the second one exploits the temporal structure of the data. After estimating the ICs, we fit an univariate GARCH model to the volatility of each IC. Thus, the GICA-GARCH reduces the complexity to estimate a multivariate GARCH model by transforming it into a small number of univariate volatility models. We report some simulation experiments to show the ability of ICA to discover leading factors in a multivariate vector of financial data. An empirical application to the Madrid stock market will be presented, where we compare the forecasting accuracy of the GICA-GARCH model versus the orthogonal GARCH one

Spectral identification and estimation of mixed causal-noncausal invertible-noninvertible models

This paper introduces new techniques for estimating, identifying and simulating mixed causal-noncausal invertible-noninvertible models. We propose a framework that integrates high-order cumulants, merging both the spectrum and bispectrum into a single estimation function. The model that most adequately represents the data under the assumption that the error term is i.i.d. is selected. Our Monte Carlo study reveals unbiased parameter estimates and a high frequency with which correct models are identified. We illustrate our strategy through an empirical analysis of returns from 24 Fama-French emerging market stock portfolios. The findings suggest that each portfolio displays noncausal dynamics, producing white noise residuals devoid of conditional heteroscedastic effects

A New Approach to Causality Testing

A new causality test based on Higher Order Cumulants (HOC) is proposed in this paper. The test can be applied on non Gaussian time series. The methodological novelty is the usage of a two‐  step method based on digital whitening, which is performed by ARMA‐HOC filter. To substantiate the method further, an empirical analysis of the relationship between  the interest rate spread and real gross domestic product (GDP) growth is presented for the period 1982:q1  ‐2010:q1. The spread is measured as a difference between 10‐year bond yields and three‐month Treasury bill rates in the US. The fist step applies ARMA‐HOC models to obtain white residuals from a quarterly term spread (TS) and GDP growth. The second step tests the dynamical correlation of TS and GDP growth residuals. The results show that the proposed test can capture the information about non Gaussian properties of the random variables being tested. The test is compared with the Granger‐Sims causality test. The paper questions the reliability of the Granger test

Application of higher-order spectra for signal processing in electrical power engineering

In power spectrum estimation, the signal under consideration is processed in such a way, that the distribution of power among its frequency is estimated and phase relations between the frequency components are suppressed. Higher order statistics and their associated Fourier transforms reveal not only amplitude information about a signal, but also phase information. If a non-Gaussian signal is received along with additive Gaussian noise, a transformation to higher order cumulant domain eliminates the noise. These are some methods for estimation of signal components, based on HOS. In the paper we apply the MUSIC method both for the correlation and the 4th order cumulant, to investigate the state of asynchronous running of synchronous machines and the fault operation of inverter-fed induction motors. When the investigated signal is distorted by a coloured noise, more exact results can be achieved by applying cumulants