Nonlinear Analysis: Real World Applications

A new set of methodologies extracts key nonlinearities in the dynamics of financial markets from data that would appear to be completely random with ordinary linear time series methods. The understanding acquired from this analysis forms a basis for modeling conflicting and competing motivations in market decisions. By standardizing the daily changes using the mean and standard deviation, it then becomes possible to compare the quantitative impact of very different variables such as price trend and valuation, and the nonlinear relationship between them. The analysis of a large data set of closing stock prices provides strong statistical evidence that relative daily price change is positively influenced by valuation, recent price trend, short term volatility, volume trend and the M2 money supply. However, there is a strong nonlinearity in the influence of the price trend, so that a significantly large recent uptrend has a negative influence on the subsequent day’s relative price change. The nonlinearity is the key to understanding the conflicting role of price trend, since a single large data set exhibits both underreaction and overreaction in different regimes of the independent variables. The role of long term volatility is not a clear-cut risk/return inverse relation. But rather there is an ambiguous and complicated relationship between volatility and return. There is limited support for resistance when prices near the quarterly high. Mixed effects regressions are used after standardizing the data by subtracting the mean and dividing by one standard deviation individually for each of the 119 closed-end funds. A valuation variable is constructed in terms of the recent history of net asset value. © 2010 Elsevier Ltd. All rights reserved.