ABSTRACT
Diomidis Spinellis Department of Management Science and Technology, Athens University of Economics and Business
Nick Nassuphis 31 St. Martin’s Lane, London
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 11.2 Finding Robust Autocorrelation Portfolios . . . . . . . . . . . . . . . . . . . . . . 239
11.2.1 Financial Time Series: Notation and Definitions . . . . . . . . 239 11.2.2 Regularization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 11.2.3 Interpretation of the Case →∞ . . . . . . . . . . . . . . . . . . . . . . . 241 11.2.4 Connection to Slow Feature Analysis . . . . . . . . . . . . . . . . . . . 242
11.3 Optimization Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 11.4 Robust Canonical Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 244 11.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
11.5.1 Synthetic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 11.5.2 S&P 500 Stock Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
11.6 Conclusion and Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 11.7 Appendix: Robust cca Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
Vector
11.1 Introduction Given a vector-valued time series, we study the problem of learning the
weights of a linear combination of the series’ components (e.g., a portfolio), which has large autocorrelation, and discuss the extension to the problem of learning two combinations, which have large cross-correlation. Both problems have been studied from different perspectives in various areas, ranging from computational neuroscience [27], to computer vision [20, 14], to information retrieval [15], among others. In this chapter, we address these problems from the point of view of robust optimization (see, e.g., [5, 8] and references therein) and regularization, and highlight their application to the context of financial time series analysis; see, e.g., [25].
