  We study the nature of fluctuations in variety of price indices involving
companies listed on the New York Stock Exchange. The fluctuations at multiple
scales are extracted through the use of wavelets belonging to Daubechies basis.
The fact that these basis sets satisfy vanishing moments conditions makes them
ideal to extract local polynomial trends, through the low pass or `average
coefficients'. Subtracting the trends from the original time series yields the
fluctuations, at different scales, depending on the level of low-pass
coefficients used for finding the `average behavior'. The fluctuations are then
studied using wavelet based multifractal detrended fluctuation analysis to
analyze their self-similar and non-statistical properties. Due to the
multifractality of such time series, they deviate from Gaussian behavior in
different frequency regimes. Their departure from random matrix theory
predictions in such regimes is also analyzed. These deviations and
non-statistical properties of the fluctuations can be instrumental in throwing
significant light on the dynamics of financial markets.
