Statistical Modelling in Financial Time Series

This topic being developed is concerned with the graphics and modelling of volatility in time series. A general modelling basis for stationary time series allowing changing level and volatility is used to suggest graphics which explore the existence of volatility, its dependence on earlier values in the time series, and possible ways in which it depends on earlier values. The importance of prior decorrelation is explored. Illustrations use financial series, while simulations are employed for validation purposes. The well-known signature of volatility, the clustering of oppositely signed extremes, is captured by the plot of their squared deautocorrelated values and its autocorrelations. This prompts investigating the explicit model of squared values when the unsquared deautocorrelated values follow garch models. In fact, the squared values follow arma models except that their innovations are themselves garch-like volatile and dependent, as seen in examples from financial series. A final point concerns the usefulness of linear dependency in financial series, however slight, and motivates modifying the iconic arch and garch volatility models to include linear dependence in a natural way suggested by the previous volatility developments.

References

Volatile ARMA modelling of GARCH squares, Central European Journal of Economic Modelling and Econometrics, (2010) 2-3, 195-203.

Exploratory statistical graphics for time series volatility. Submitted (2011)