Damage classification and estimation in experimental structures using time series analysis and pattern recognition

Peer reviewedPreprin

Real-time extraction of the Madden-Julian oscillation using empirical mode decomposition and statistical forecasting with a VARMA model

A simple guide to the new technique of empirical mode decomposition (EMD) in a meteorological-climate forecasting context is presented. A single application of EMD to a time series essentially acts as a local high-pass filter. Hence, successive applications can be used to produce a bandpass filter that is highly efficient at extracting a broadband signal such as the Madden-Julian Oscillation (MJO). The basic EMD method is adapted to minimize end effects, such that it is suitable for use in real time. The EMD process is then used to efficiently extract the MJO signal from gridded time series of outgoing longwave radiation (OLR) data. A range of statistical models from the general class of vector autoregressive moving average (VARMA) models was then tested for their suitability in forecasting the MJO signal, as isolated by the EMD. A VARMA (5, 1) model was selected and its parameters determined by a maximum likelihood method using 17 yr of OLR data from 1980 to 1996. Forecasts were then made on the remaining independent data from 1998 to 2004. These were made in real time, as only data up to the date the forecast was made were used. The median skill of forecasts was accurate (defined as an anomaly correlation above 0.6) at lead times up to 25 days

A numerically efficient implementation of the expectation maximization algorithm for state space models

Peer reviewedPostprin

Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.Comment: Published at http://dx.doi.org/10.1214/009053604000000021 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org