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In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, military, physical sciences and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic process (DTIDMLSMVSP). Moreover, LLGMM is a dynamic non-parametric method. The DTIDMLSMVSP is an alternative approach to the GARCH(1,1) model, and it provides an iterative scheme for updating statistic coefficients in a system of generalized method of moment/observation equations. Furthermore, applications of LLGMM to energy commodities price, U.S. Treasury Bill interest rate and the U.S.–U.K. foreign exchange rate data strongly exhibit its unique role, scope and performance, in particular, in forecasting and confidence-interval problems in applied statistics.

This paper proposes a non-stationary bivariate integer-valued moving average of order 1 (BINMA(1)) model where the respective innovations are marginal COM-Poisson and unrelated. As opposed to other such bivariate time series model, the dependence between the series in the above is constructed via the relation between the current series with survivor elements of the other series at the preceding time point. Under these assumptions, the BINMA(1) process is shown to accommodate different levels and combinations of over-, equi- and under-dispersion. Since under the non-stationary conditions, the joint likelihood function is hardly laborious to construct, a generalized quasi-likelihood (GQL) method of estimation is proposed to estimate the dynamic effects and dependence parameters. The asymptotic and consistency properties of the GQL estimators are also established. Monte-Carlo experiments and a real-life application to analyze intra-day stock transactions are presented to validate the proposed model and the estimation methodology.

This paper is concerned with approximating nonlinear time series by an artificial neural network based on radial basis functions. A new data-driven modelling strategy is suggested for the adaptive framework by combining the statistical techniques of forward selection, cross validation and information criterion. The proposed method is fast and simple to implement while avoiding some typical difficulties such as estimation and computation of nonlinear econometric models. Two applications are provided to illustrate the benefits of using the neural network method in time series analysis. First, the proposed modelling method is applied to a neural network test for neglected nonlinearity in conditional mean of univariate time series. A simulation study is carried out to show how the size of the test is improved in finite samples. Further, the new test is compared with alternative popular tests to demonstrate its superior power performance using a variety of nonlinear time series models. Second, the proposed method is applied to obtain a nonlinear forecasting model for daily S&P 500 returns. Forecast accuracy is compared with that of a linear model and other neural network models used in the literature.

We derive the analytical expressions of bias approximations for maximum likelihood (ML) and quasi-maximum likelihood (QML) estimators of the EGARCH (1,1) parameters that enable us to correct after the bias of all estimators. The bias-correction mechanism is constructed under the specification of two methods that are analytically described. We also evaluate the residual bootstrapped estimator as a measure of performance. Monte Carlo simulations indicate that, for given sets of parameters values, the bias corrections work satisfactory for all parameters. The proposed full-step estimator performs better than the classical one and is also faster than the bootstrap. The results can be also used to formulate the approximate Edgeworth distribution of the estimators.