Cost-Sensitive Estimation of ARMA Models for Financial Asset Return Data

Minyoung Kim

doi:10.1155/2015/232184

Abstract

The autoregressive moving average (ARMA) model is a simple but powerful model in financial engineering to represent time-series with long-range statistical dependency. However, the traditional maximum likelihood (ML) estimator aims to minimize a loss function that is inherently symmetric due to Gaussianity. The consequence is that when the data of interest are asset returns, and the main goal is to maximize profit by accurate forecasting, the ML objective may be less appropriate potentially leading to a suboptimal solution. Rather, it is more reasonable to adopt an asymmetric loss where the model's prediction, as long as it is in the same direction as the true return, is penalized less than the prediction in the opposite direction. We propose a quite sensible asymmetric cost-sensitive loss function and incorporate it into the ARMA model estimation. On the online portfolio selection problem with real stock return data, we demonstrate that the investment strategy based on predictions by the proposed estimator can be significantly more profitable than the traditional ML estimator.

Highlights

In modeling time-series data, capturing the underlying statistical dependency of the variables of interest at current time on the historic data is central to accurate forecasting and faithful data representation
The autoregressive moving average (ARMA) models appear in a wide spectrum of applications recently including filter design in signal processing [11], time-series analysis and model selection in computational statistics [12], and jump modeling for asset prices in quantitative finance [13], to name just a few
We provide an efficient optimization strategy based on the subgradient descent using the trustregion approximation, whose effectiveness is empirically demonstrated for the portfolio selection problem with realworld stock return data

Summary

Introduction

In modeling time-series data, capturing the underlying statistical dependency of the variables of interest at current time on the historic data is central to accurate forecasting and faithful data representation. We propose a reasonable cost function that effectively captures the above idea of the intrinsic asymmetric profit/loss structure regarding asset return data. Our cost function effectively encodes the goodness of matching in directions between true and model predicted asset returns, which is directly related to ultimate profits in the investment.

Objectives

Results

Conclusion