Principal Component Analysis for the Nonlinear Portfolio Model

Abstract

The present study improves the nonlinear portfolio model by using principal component analysis. To enhance the portfolio effect of spreading risks efficiently, we aim for lower correlations among each asset movement. For this reason, we apply the principal components of assets to the nonlinear portfolio model, which uses nonlinear prediction to estimate future movements. However, because we are not sure whether these principal components have nonlinearity, we perform Fourier-shuffled surrogate tests on the principal components. Finally, we confirm the efficiency of our nonlinear principal-component portfolio model through some investment simulations with real financial data.

Improving Predictive Power and Risk Reduction of Portfolio Models Based on Principal Component Analysis

“…Here, we composed a long-only portfolio, which means that all of the allocation rates w were optimized by giving them positive values in each portfolio model. In addition, similarly to in the previous study [3], we set the historical data length T as 245, which is the number of business days in a year, and set L as 1200, i.e., about five years. For the nonlinear prediction in Sect.…”

“…However, the above portfolio models are not active enough to predict price movements. Therefore, to improve the predictive power, in our previous study we proposed the nonlinear principal component portfolio (NPCP) model [3], which uses a nonlinear time-series prediction in analogy with the nonlinear portfolio (NP) model [4]. The NPCP and NP models use historical prediction errors to estimate investment risks, but the correlation among these prediction errors has not yet been investigated.…”

Nonlinear Time-varying AR-ARCH Model Based on Chaos Prediction Model and its Statistical Significance Tests

“…All of the above models are categorized into linear models because they are based on the multivariate linear regression. However, according to some previous studies [4,5], financial markets might be so complex that linear models are not good enough to express them, and therefore it would be possible that higher order nonlinear models could work better. From this viewpoint, the present study modifies the original AR-ARCH model into its nonlinear versions by applying a local linear approximation method [6], which is one of nonlinear predictions based on the chaotic dynamical theory.…”