Simulated Likelihood Estimation of Non-Linear Diffusion Processes Through Non-Parametric Procedure With an Application to the Portuguese Interest Rate

In this article we present a new model of the spot interest rate and a new method of estimation of nonlinear stochastic differential equations. We show how an integrated discrete time process in an econometric sense can be modelled by a continuous time ergodic process. We make an application to the Portuguese spot interest rate.

Stressing the Boundaries of Mobile Accessibility

Mobile devices gather the communication capabilities as no other gadget. Plus, they now comprise a wider set of applications while still maintaining reduced size and weight. They have started to include accessibility features that enable the inclusion of disabled people. However, these inclusive efforts still fall short considering the possibilities of such devices. This is mainly due to the lack of interoperability and extensibility of current mobile operating systems (OS). In this paper, we present a case study of a multi-impaired person where access to basic mobile applications was provided in an applicational basis. We outline the main flaws in current mobile OS and suggest how these could further empower developers to provide accessibility components. These could then be compounded to provide system-wide inclusion to a wider range of (multi)-impairments.Comment: 3 pages, two figures, ACM CHI 2013 Mobile Accessibility Worksho

Method for simulating non-linear stochastic differential equations in R¹

Very few specific stochastic differential equations have explicitly known solutions. The most common procedure to obtain a simulated path of a solution is based on a discretization of the stochastic differential equations. However, there are some cases where the discrete-time discretization cannot be used. In this article, we propose a new method to simulate the solution of a non-linear stochastic differential equation, which, in principle, is exempt from error of simulation and can be widely applied including in cases where the discrete-time discretization cannot be used.info:eu-repo/semantics/publishedVersio

Purchasing power parity analyzed through a continuous-time version of the ESTAR model

From the discrete-time Exponential Smooth Autoregressive model, we obtain a continuous-time version that provides new tools for analyzing the Purchasing Power Parity hypothesis.info:eu-repo/semantics/publishedVersio

Bias reduction in nonparametric diffusion coefficient estimation

In this paper, we quantify the asymptotic bias of the Florens-Zmirou (1993, Journal of Applied Probability 30, 790–804) and Jiang and Knight (1997, Econometric Theory 13, 615–645) estimator for the diffusion coefficient when the step of discretization is fixed, and then we propose a bias adjustment that partially compensates for the distortion. Also, we show that our estimators have all the asymptotic properties of the Florens-Zmirou and Jiang and Knight estimator when the step of discretization goes to zero. We provide some examples.info:eu-repo/semantics/publishedVersio

Nonparametric density forecast based on time- and state-domain

We propose a new nonparametric density forecast based on time- and state-domain smoothing. We analyze some of its asymptotic properties and provide an empirical illustration.info:eu-repo/semantics/publishedVersio

Structural change test in duration of bull and bear markets

We propose a recursive test to analyze structural changes in duration of bull and bear markets. Using the Dow Jones Industrial Average index, we detected a single structural break in the bull market duration in April, 1942.info:eu-repo/semantics/publishedVersio

A new model for multivariate Markov chains

We propose a new model for multivariate Markov chains of order one or higher on the basis of the mixture transition distribution (MTD) model. We call it the MTD-Probit. The proposed model presents two attractive features: it is completely free of constraints, thereby facilitating the estimation procedure, and it is more precise at estimating the transition probabilities of a multivariate or higher-order Markov chain than the standard MTD model.info:eu-repo/semantics/publishedVersio

Stationary processes that look like random walks : the bounded random walk process in discrete and continuous time

Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks are limitless with probability one (as time goes to infinity). Yet, some of these time series behave just like random walks. In this paper we propose a new approach that takes into account these ideas. We propose a discrete-time and a continuous-time process (diffusion process) that generate bounded random walks. These paths are almost indistinguishable from random walks, although they are stochastically bounded by an upper and lower finite limit. We derive for both cases the ergodic conditions, and for the diffusion process we present a closed expression for the stationary distribution. This approach suggests that many time series with random walk behavior can in fact be stationarity processes.info:eu-repo/semantics/publishedVersio

Transition density and simulated likelihood estimation for time-inhomogeneous diffusions

We propose a method to estimate the transition density of a non-linear time-inhomogeneous diffusion. Expressing the transition density as a functional of a Brownian bridge, allows us to estimate the density through Monte Carlo simulations with any level of precision. We show how these transition density estimates can be effectively used to estimate the parameters of the time-inhomogeneous diffusion and the conditional moments of the process. In this paper we prove that our method is asymptotically equivalent to the maximum likelihood estimator and more reliable than the closed-form approximation approach largely used in the literature.info:eu-repo/semantics/publishedVersio