New Model And Simulation Algorithm Of Nonstationary Non-gaussian Ground Motions Based On S-transform

The seismic ground motions are nonstationary stochastic processes and vary from site to site. The time histories of synthetic ground motions are used for nonlinear inelastic structural dynamic analysis since the historical records are limit or unavailable for a particular scenario seismic event. This is especially the case for structures with multiple supports. The characteristics of the nonstationary stochastic ground motions depend on the earthquake magnitude, fault mechanism, source-to-site distance, and local site conditions. The characteristics could be represented by time-frequency (dependent) power spectral density (TFPSD) and coherence functions. The assessment of such power spectral density and coherence functions are presented by using historical records and the S-transform – a Fourier transform with time localized and frequency-dependent windows – is carried out. New models of the TFPSD function and coherence function are presented. Also, new time-frequency spectral representation methods (TFSRMs) to simulate nonstationary stochastic processes are proposed. The TFSRM is developed by taking the advantages of the orthonormal basis functions in the discrete orthogonal S-transform (DOST) and the refined time-frequency representation obtained by using the S-transform. TFSRM can be used to simulate ground motions at a single site or multiple sites. They can also be used to simulate seismic ground motions conditioned on observed ground motions. TFSRM can cope with the time-varying lagged coherence function; this is not the case with the well-known spectral representation method (SRM). Similar to the SRM, the direct use of TFSRM leads to Gaussian processes (stationary or nonstationary). However, there is indicates that the seismic ground motions may not be Gaussian. A new iterative power and amplitude correction algorithm is proposed to simulate nonstationary non-Gaussian stochastic processes. This procedure is successfully implemented and illustrated by numerical examples

Interpolation of nonstationary high frequency spatial-temporal temperature data

The Atmospheric Radiation Measurement program is a U.S. Department of Energy project that collects meteorological observations at several locations around the world in order to study how weather processes affect global climate change. As one of its initiatives, it operates a set of fixed but irregularly-spaced monitoring facilities in the Southern Great Plains region of the U.S. We describe methods for interpolating temperature records from these fixed facilities to locations at which no observations were made, which can be useful when values are required on a spatial grid. We interpolate by conditionally simulating from a fitted nonstationary Gaussian process model that accounts for the time-varying statistical characteristics of the temperatures, as well as the dependence on solar radiation. The model is fit by maximizing an approximate likelihood, and the conditional simulations result in well-calibrated confidence intervals for the predicted temperatures. We also describe methods for handling spatial-temporal jumps in the data to interpolate a slow-moving cold front.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS633 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonparametric frequency domain analysis of nonstationary multivariate time series

We analyse the properties of nonparametric spectral estimates when applied to long memory and trending nonstationary multiple time series. We show that they estimate consistently a generalized or pseudo-spectral density matrix at frequencies both close and away from the origin and we obtain the asymptotic distribution of the estimates. Using adequate data tapers this technique is consistent for observations with any degree of nonstationarity, including polynomial trends. We propose an estimate of the degree of fractional cointegration for possibly nonstationary series based on coherence estimates around zero frequency and analyse its finite sample properties in comparison with residual-based inference. We apply this new semiparametric estimate to an example vector time series.Publicad

Compression and Conditional Emulation of Climate Model Output

Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus it is important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing the conditional distribution of the full dataset given the summary statistics. The statistical model can be used to generate realizations representing the full dataset, along with characterizations of the uncertainties in the generated data. Thus, the methods are capable of both compression and conditional emulation of the climate models. Considerable attention is paid to accurately modeling the original dataset--one year of daily mean temperature data--particularly with regard to the inherent spatial nonstationarity in global fields, and to determining the statistics to be stored, so that the variation in the original data can be closely captured, while allowing for fast decompression and conditional emulation on modest computers

Gaussian semi-parametric estimation of fractional cointegration

We analyse consistent estimation of the memory parameters of a nonstationary fractionally cointegrated vector time series. Assuming that the cointegrating relationship has substantially less memory than the observed series, we show that a multi-variate Gaussian semi-parametric estimate, based on initial consistent estimates and possibly tapered observations, is asymptotically normal. The estimates of the memory parameters can rely either on original (for stationary errors) or on differenced residuals (for nonstationary errors) assuming only a convergence rate for a preliminary slope estimate. If this rate is fast enough, semi-parametric memory estimates are not affected by the use of residuals and retain the same asymptotic distribution as if the true cointegrating relationship were known. Only local conditions on the spectral densities around zero frequency for linear processes are assumed. We concentrate on a bivariate system but discuss multi-variate generalizations and show the performance of the estimates with simulated and real data.Publicad