Statistical Evidences for the Influence of GP's Representation on Forecasting

The research on financial engineering by means of genetic programming is gradually popular and appealing. For example, Kaboudan (1999, 2001) and Iba and Sasaki (1999), Iba and Sasaki (1999), used standard GP to evolve forecasting models. Neely, et al. (1997), Allen and Karjalainen (1999), Fyfe et al. (1999), and Neely and Weller (1999) applied standard GP to evolving trading strategies. In Wang (2000), automated defined functions (ADFs) are further included to search useful trading strategies. Iba and Nikolaev (2000) employed an enhanced GP system, STROGANOFF (Iba et al.,1994), which searches for polynomial autoregressive models to the stock price prediction. In addition, Nikolaev and Iba (2001) developed polynomial harmonic GP which outperforms the previous GP system, STROGANOFF. In the research of financial engineering, besides the determination of important explanatory variables, there are two important factors which influence our understanding about the regularity of the time series data. The first one is the inherent complexity of data series. The second one concerns how we explain the regularity, i.e., representation. In Kaboudan (1995, 1998), he gave a complexity measure (theta) for a time series data. The work of Iba and Nikolaev (2000) has implicitly pointed out the importance of representation in GP. In this paper, we try to figure out the relationship between the complexity of time series data and GP's representation