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Mathematical Problems in Engineering
Volume 2015, Article ID 232184, 8 pages
Research Article

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

Department of Electronics & IT Media Engineering, Seoul National University of Science & Technology, Seoul 139-743, Republic of Korea

Received 11 June 2015; Revised 30 August 2015; Accepted 2 September 2015

Academic Editor: Meng Du

Copyright © 2015 Minyoung Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.