Marcelo C. Medeiros

A hybrid linear-neural model for time series forecasting

This paper considers a linear model with time varying parameters controlled by a neural network to analyze and forecast nonlinear time series.We show that this formulation, called neural coefficient smooth transition autoregressive (NCSTAR) model, is in close relation to the threshold autoregressive (TAR) model and the smooth transition autoregressive (STAR) model with the advantage of naturally incorporating linear multivariate thresholds and smooth transitions between regimes. In our proposal, the neuralnetwork output is used to induce a partition of the input space, with smooth and multivariate thresholds. This also allows the choice of good initial values for the training algorithm.

Piecewise Linear Time Series Estimation with GRASP

This paper describes a heuristic to build piecewise linear statistical models with multivariate thresholds, based on a Greedy Randomized Adaptive Search Procedure (GRASP). GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. In this paper we describe a GRASP to sequentially split an n-dimensional space in order to build a piecewise linear time series model.

State Space Arch: Forecasting Volatility with a Stochastic Coefficient Model

This article investigates the use of AR models with stochastic coefficients to describe the changes in volatility observed in time series of financial returns. Such models can reproduce the main stylised facts observed in financial series: excess kurtosis, serial correlated square returns and time-varying conditional variance. We first cast the model in a state space form. Then the EM algorithm is used to estimate the parameters of the model. With the state-space formulation one can use the Kalman filter to evaluate the conditional variance of future returns. The model is tested using daily returns of TELEBRAS-PN, one of the main stocks of the brazilian market.