Higher-Order Volatility: Time Series

Time Series Analysis by Higher Order Crossings

Higher order variation and stochastic volatility models

Limit distribution results on quadratic and higher order variation quantities are derived for certain types of continuous local martingales, in particular for a class of OU-based stochastic volatility models. Some key words: Mixed asymptotic normality; Realised volatility; Quadratic variation.

Artificial Higher Order Neural Networks in Time Series Prediction

Real world problems are described by nonlinear and chaotic processes, which makes them hard to model and predict. This chapter first compares the neural network (NN) and the artificial higher order neural network (HONN) and then presents commonly known neural network architectures and a number of HONN architectures. The time series prediction problem is formulated as a system identification pro...

Higher order neural networks for financial time series prediction

Generalized correlation higher order neural network designs are developed. Their performance is compared with that of first order networks, conventional higher order neural network designs, and higher order linear regression networks for financial time series prediction. The correlation higher order neural network design is shown to give the highest accuracy for prediction of stock market share...

Volatility of linear and nonlinear time series.

Previous studies indicated that nonlinear properties of Gaussian distributed time series with long-range correlations, u(i), can be detected and quantified by studying the correlations in the magnitude series |u(i)|, the "volatility." However, the origin for this empirical observation still remains unclear and the exact relation between the correlations in u(i) and the correlations in |u(i)| is...