A Generalised Fractional Differencing Bootstrap for Long Memory Processes

A bootstrap methodology, first proposed in a restricted form by Kapetanios and Papailias (2011), suitable for use with stationary and nonstationary fractionally integrated time series is further developed in this paper. The resampling algorithm involves estimating the degree of fractional integration, applying the fractional differencing operator, resampling the resulting approximation to the underlying short memory series and, finally, cumulating to obtain a resample of the original fractionally integrated process. While a similar approach based on differencing has been independently proposed in the literature for stationary fractionally integrated processes using the sieve bootstrap by Poskitt, Grose and Martin (2015), we extend it to allow for general bootstrap schemes including blockwise bootstraps. Further, we show that it can also be validly used for nonstationary fractionally integrated processes. We establish asymptotic validity results for the general method and provide simulation evidence which highlights a number of favourable aspects of its finite sample performance, relative to other commonly used bootstrap methods

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks

Dependent bootstrapping for value-at-risk and expected shortfall

Estimation in extreme financial risk is often faced with challenges such as the need for adequate distributional assumptions, considerations for data dependencies, and the lack of tail information. Bootstrapping provides an alternative that overcomes some of these challenges. It does not assume a distributional form and asymptotically replicates the empirical density for resampled data. Moreover, advanced bootstrapping can cater for dependencies and stationarity in the data. In this paper, we evaluate the use of dependent bootstrapping, both for the original financial time series and for its GARCH innovations (under the Gaussian and Student t noise assumptions), in forecasting value-at-risk and expected shortfall. We also assess the effect of using different window sizes for these procedures. The two datasets used are daily returns of the S & P500 from NYSE and the ALSI from JSE