spGARCH: An R-Package for Spatial and Spatiotemporal ARCH models

In this paper, a general overview on spatial and spatiotemporal ARCH models is provided. In particular, we distinguish between three different spatial ARCH-type models. In addition to the original definition of Otto et al. (2016), we introduce an exponential spatial ARCH model in this paper. For this new model, maximum-likelihood estimators for the parameters are proposed. In addition, we consider a new complex-valued definition of the spatial ARCH process. From a practical point of view, the use of the R-package spGARCH is demonstrated. To be precise, we show how the proposed spatial ARCH models can be simulated and summarize the variety of spatial models, which can be estimated by the estimation functions provided in the package. Eventually, we apply all procedures to a real-data example

Exact Rational Expectations, Cointegration, and Reduced Rank Regression

We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role in the calculation of maximum likelihood estimation of the restricted parameters.

Parametric modeling of photometric signals

This paper studies a new model for photometric signals under high flux assumption. Photometric signals are modeled by Gaussian autoregressive processes having the same mean and variance denoted Constraint Gaussian Autoregressive Processes (CGARP's). The estimation of the CGARP parameters is discussed. The Cramér Rao lower bounds for these parameters are studied and compared to the estimator mean square errors. The CGARP is intended to model the signal received by a satellite designed for extrasolar planets detection. A transit of a planet in front of a star results in an abrupt change in the mean and variance of the CGARP. The Neyman–Pearson detector for this changepoint detection problem is derived when the abrupt change parameters are known. Closed form expressions for the Receiver Operating Characteristics (ROC) are provided. The Neyman–Pearson detector combined with the maximum likelihood estimator for CGARP parameters allows to study the generalized likelihood ratio detector. ROC curves are then determined using computer simulations

Estimating persistence in the volatility of asset returns with signal plus noise models

This paper examines the degree of persistence in the volatility of financial time series using a Long Memory Stochastic Volatility (LMSV) model. Specifically, it employs a Gaussian semiparametric (or local Whittle) estimator of the memory parameter, based on the frequency domain, proposed by Robinson (1995a), and shown by Arteche (2004) to be consistent and asymptotically normal in the context of signal plus noise models. Daily data on the NASDAQ index are analysed. The results suggest that volatility has a component of longmemory behaviour, the order of integration ranging between 0.3 and 0.5, the series being therefore stationary and mean-reverting.The second-named author gratefully acknowledges financial support from the Ministerio de Ciencia y Tecnología (ECO2008-03035 ECON Y FINANZAS, Spain) and from a PIUNA project at the University of Navarra

Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semi-parametric estimate of the long memory parameter is also explored. Higher-order improvements yielded by both forms of re-sampling are demonstrated using Edgeworth expansions for a broad class of statistics that includes first- and second-order moments, the discrete Fourier transform and regression coefficients. The methods are then applied to the problem of estimating the sampling distributions of the sample mean and of selected sample autocorrelation coefficients, in experimental settings. In the case of the sample mean, the pre-filtered version of the bootstrap is shown to avoid the distinct underestimation of the sampling variance of the mean which the raw sieve method demonstrates in finite samples, higher order accuracy of the latter notwithstanding. Pre-filtering also produces gains in terms of the accuracy with which the sampling distributions of the sample autocorrelations are reproduced, most notably in the part of the parameter space in which asymptotic normality does not obtain. Most importantly, the sieve bootstrap is shown to reproduce the (empirically infeasible) Edgeworth expansion of the sampling distribution of the autocorrelation coefficients, in the part of the parameter space in which the expansion is valid