Abstract: The increased computational speed and developments in the area of algorithms have created the possibility for efficiently identifying a well-fitting time series model for the given nonstationary-nonlinear time series and use it for prediction. In this paper a new method is used for analyzing a given nonstationary-nonlinear time series. Based on the Multiresolution Analysis (MRA) and n...

Recursive non-linear Bayesian estimation is addressed using equivalence approach as motivating framework. Its specific form – tailored to a model class covering non-normal ARX (auto-regression with exogenous variables) models, models with discrete outputs and continuous-valued regression vectors and their dynamic mixtures – is presented. The resulting algorithms provide efficient solutions of d...

The present study investigates linear and volatile (nonlinear) correlations of firstorder autoregressive process with uncorrelated AR (1) and long-range correlated CAR (1) Gaussian innovations as a function of the process parameter (θ). In the light of recent findings [1], we discuss the choice of CAR (1) in modeling daily temperature records. We demonstrate that while CAR (1) is able to captur...

In the last decade alpha−stable distributions have become a standard model for impulsive data. Especially the linear symmetric alpha−stable processes have found applications in various fields. When the process parameters are time−invariant, various techniques are available for estimation. However, time−invariance is an important restriction given that in many communications applications channel...

This paper introduces nonlinear threshold time series modeling techniques that actuaries can use in pricing insurance products, analyzing the results of experience studies, and forecasting actuarial assumptions. Basic “self-exciting” threshold autoregressive (SETAR) models, as well as heteroscedastic and multivariate SETAR processes, are discussed. Modeling techniques for each class of models a...

In this paper, variable bit rate (VBR) H.261 encoded video traffic is modeled by a nonlinear time series process. A threshold autoregressive (TAR) process is of particular interest. The TAR model is comprised of a set of autoregressive (AR) processes that are switched according to the amplitude of bit rates of the time series. The TAR model is shown to capture accurately the statistical charact...

Suppose we observe a time series that alternates between different nonlinear autoregressive processes. We give conditions under which the model is locally asymptotically normal, derive a characterization of efficient estimators for differentiable functionals of the model, and use it to construct efficient estimators for the autoregression parameters and the innovation distributions. Surprisingl...

Compared to the traditional maximum likelihood regression approach, the penalized maximum likelihood estimation (PMLE) is a more rigorous method because of the adjustment for over fitting is directly built into the model development process, instead of relying on shrinkage afterwards. This paper illustrates the application of a nonlinear programming technique on PMLE to develop a prediction mod...

We study the estimation of optimal portfolios for a Reserve Fund with an endof-period target, and when the returns of the assets that constitute the Reserve Fund portfolio follow two specifications. In the first one assets are split into short memory (bonds) and long memory (equity), and the optimality of the portfolio is based on maximizing the Sharpe ratio. In the second returns follow a cond...

Abstract: In order that the nth-order Generalized Frequency Response Function (GFRF) for nonlinear systems described by a NARX model can be directly written into a more straightforward and meaningful form in terms of the first order GFRF and model parameters, the nth-order GFRF is now determined by a new mapping function based on a parametric characteristic. This can explicitly unveil the linea...