System Identification in Noisy Data Environments

This paper analyzes the systematic relationship between the stock market valuations, the nominal GDPs and the interest rates of six Asian countries, using not single equation regression, but an alternative methodology based on complete, multidirectional, least squares projections. We compare the results with the spectral analysis of the information matrices and determine the noise levels. The objective is to extract the multidimensional economic system structures from the noisy empirical observations. This complete methodology sharply contrasts with the incomplete methodology of Fama (1990), Schwert (1990), etc., who presume planal relations, fit them to the multidimensional data by only one prejudiced unidirectional projection, thereby ignoring between 75% - 92% of the available covariance information and not publishing all possibleadditional model projections. The results in this paper show that the analyzed countries are better analyzed using such complete multidirectional LS projections, even though the analysis is combinatorially much more complex. All six Asian financial-economic systems are high data noise environments, in which it is very difficult to separate the systematic signals from the noise. Because of these high noise levels, spectral analysis is very unreliable. We identify Taiwan's stock market, economy and financial market to be rationally coherent. In contrast, Malaysia, Singapore, Philippines and Indonesia show only partially coherent systems, while no coherent system can be identified among Japan's data