Wavelet Exploratory Analysis of the FTSE ALL SHARE Index

Wavelets by construction are able to show us “the forest as well as the trees”. They are compactly supported functions that allow us to localise in frequency as well as in time whereas traditional Fourier analysis focuses only on frequency. This makes wavelets useful when examining time sequences that exhibit sharp spikes and irregularities, such financial time series. In this paper we demonstrate how a wavelet semi-parametric approach can provide useful insight on the structure and behaviour of stock index prices, returns and volatility. By using wavelets we capture salient features such as changes in trend and volatility and reveal dynamic patterns at various scales