Time-Series Forecast with Adaptive Feedback Controlled Predictor

Mark A Pinsky

doi:10.13189/ujcmj.2013.010203

Abstract

This paper describes a novel approach to predicting time-series which blends techniques developed in the areas of observer design and numerical solvers for ODEs. The developed predictor is based on a novel feedback control architecture which leads to computationally efficient and a fairly accurate forecast even for volatile economic series. Application to series of various kinds shows that the developed forecaster possesses some basic properties of numerical solvers for ODE. In the same time it prediction horizon is favorably compared with a time step attaining in numerical simulations for the series with precisely known models whereas no knowledge of the series' global model is assumed in our forecast. We demonstrate that for noisy series the accuracy of prediction reduces to the level of noise to signal ratio as well as that reduction of noise by smoothing the series comparably increases the accuracy of prediction. It is also shown that the developed approach provides practically valuable forecast in application to volatile economic series.

Highlights

The study of fixed points for multi - valued contraction mappings using the Hausdorff metric was initiated by Nadler [9].Let (X, d) be a metric space
The concept of coupled fixed point for multi - valued mapping was introduced by Samet and Vetro [2] and later several authors namely Hussain and Alotaibi [6] and Aydi et al.[3] proved coupled coincidence point theorems in partially ordered metric spaces
Le{t (X, d) be a metric space endowed with a partia}l order ≼ and G : X → X

Summary

Introduction

The study of fixed points for multi - valued contraction mappings using the Hausdorff metric was initiated by Nadler [9].Let (X, d) be a metric space. The existence of fixed points for various multi - valued contractive mappings has been studied by many authors under different conditions. The concept of coupled fixed point for multi - valued mapping was introduced by Samet and Vetro [2] and later several authors namely Hussain and Alotaibi [6] and Aydi et al.[3] proved coupled coincidence point theorems in partially ordered metric spaces.

Results

Conclusion