Statistical learning and testing approaches for temporal dependence structures with application to financial engineering

In the finance literature, an objective way to judge whether an asset pricing model is misspecified is by statistical tests. In the past, both the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT) have been the subjects of extensive tests.; According to a recent survey by Cochrane (1999), the multi-factor APT model is gaining popularity and recognition over CAPM by the investment community. While empirical evidence shows that mutual funds can earn average returns not explained by the CAPM by following a variety of investment styles, this anomaly could be captured by APT which includes the single-factor CAPM as a special case. Yet, three aspects of APT still cannot be tested in practice.; A technique called gaussian temporal factor analysis (gaussian TFA) proposed by Xu in 2000 may be used to test the APT model under the mild assumption that the efficient market hypothesis (EMH) is violated. We are motivated to investigate statistical behaviors of the gaussian TFA model.; First, a systematic testing package is proposed for testing gaussian TFA in six dimensions, including factor number, factor loadings, residuals correlations and autoregressive conditional heteroscedasticity (ARCH) effects, economic significance and factor independence, using financial data in Hong Kong. Particularly, a new hypothesis testing approach is proposed for statistically testing independence.; Second, we investigate two extensions of the gaussian TFA model in view of ARCH in driving noise residuals. We test the extended models for ARCH as well as other aspects to ensure model specification adequacy. Furthermore, we find that ARCH effects are not quite significant driving noise residuals of the macroeconomic modulate independent state-space model. This may be due to long-term modelling of the market.; Third, we test gaussian TFA from the practical point of view in financial prediction and portfolio management. For prediction, we introduce the gaussian TFA alternative mixture experts (ME) approach for forecasting. For adaptive portfolio management, we derive the gaussian TFA adaptive algorithm for implementing the Sharpe-ratio based adaptive portfolio management under different scenarios. Empirical results reveal that APT-based portfolio management techniques are in general superior to return-based techniques.