Super-Whiteness of Returns Spectra

Erhard Reschenhofer

doi:10.6339/jds.2009.07(4).499

Abstract

Until the late 70’s the spectral densities of stock returns and stock index returns exhibited a type of non-constancy that could be detected by standard tests for white noise. Since then these tests have been unable to find any substantial deviations from whiteness. But that does not mean that today’s returns spectra contain no useful information. Using several sophisticated frequency domain tests to look for specific patterns in the periodograms of returns series we find nothing or, more precisely, less than nothing. Actually, there is a striking power deficiency, which implies that these series exhibit even fewer patterns than white noise. To unveil the source of this “super-whiteness” we design a simple frequency domain test for characterless, fuzzy alternatives, which are not immediately usable for the construction of profitable trading strategies, and apply it to the same data. Because the power deficiency is now much smaller, we conclude that our puzzling findings may be due to trading activities based on excessive data snooping.

Highlights

There is abundant evidence that price changes are predictable, but there is evidence that this predictability is getting smaller over time
Predictability does not necessarily imply the existence of profitable trading strategies, if transaction costs are taken into account
Using conventional frequency domain tests, which are most powerful in the case of distinct spectral patterns, and taking explicitly into account the possibility that there may be a lack of patterns, we find even fewer distinct patterns in the periodograms of returns series than we would expect in the case of a perfect white noise process

Summary

Introduction

There is abundant evidence that price changes are predictable, but there is evidence that this predictability is getting smaller over time (see, e.g., Patro and Wu, 2004, Reschenhofer 2004a). Using conventional frequency domain tests, which are most powerful in the case of distinct spectral patterns, and taking explicitly into account the possibility that there may be a lack of patterns, we find even fewer distinct patterns in the periodograms of returns series than we would expect in the case of a perfect white noise process. It turns out that this new test is more powerful than the other tests, which indicates that a spectrum exhibiting an extremely flat and wide peak is a more realistic alternative to a constant spectrum than a spectrum with a steep and narrow peak While the latter alternative implies the presence of sinusoidal components with large amplitudes and frequencies within a narrow band, the former alternative implies cycles with small amplitudes and fuzzy periods, which cannot immediately be used for the construction of trading strategies.

Some Frequency Domain Tests for White Noise

Application to Financial Data

Concluding remarks