Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data-generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and, consequently, the calculation of risk at different time scales.

This paper investigates a nonparametric modular neural network (MNN) model to price the S&P-500 European call options. The modules are based on time to maturity and moneyness of the options. The option price function of interest is homogeneous of degree one with respect to the underlying index price and the strike price. When compared to an array of parametric and nonparametric models, the MNN method consistently exerts superior out-of-sample pricing performance. We conclude that modularity improves the generalization properties of standard feedforward neural network option pricing models (with and without the homogeneity hint).

This paper analyzes the impact of economic freedom along with traditional economic factors on economic growth for a panel of European countries. The growth of the gross domestic product was observed over a twenty-year time period on a sample of 43 developing and developed countries. Based on a robust dynamic panel setting, we conclude that increases in economic freedom as expressed by the Index of Economic Freedom/Heritage Foundation (but not its levels) are related to economic growth. The EU membership status either had no effect or it curbed the effect of the economic freedom on growth. We also find that the subprime economic crisis of 2008–2009 exerted a negative impact on the growth of European economies.

This article tests the profitability of Bollinger Bands (BB) technical indicators. It is found that, after adjusting for transaction costs, the BB are consistently unable to earn profits in excess of the buy-and-hold trading strategy. However, the profitability is improved using a contrarian's approach.