(2) Objectives:

This paper seeks to help explain stock market volatility by investigating volatility in the crude oil market.  We examine the linkages between volatility in the futures price of crude oil and the futures price of the S&P500 contract as well as the relationship between the volatility in volume of crude oil futures and the volume of the S&P500 futures contract. We also investigate the lead/lag relationship between crude oil volatility and stock price volatility.

(3) Data/Methods:  

We analyze daily futures data from 3/30/83 through 7/10/08.The data series is obtained from Price-data.com (http://www.price-data.com ). We use frequency-domain techniques to determine the relative importance of cycles of different frequencies in accounting for the comovement among prices and volume on crude oil and the S&P500 futures contract. Further, we study how cospectra change during three periods, before and after 1987 and 2001.

The goal of spectral analysis is to determine how important cycles of different frequencies are in accounting for volatility and comovement of the time series (, 1994). According to Granger (1966), one of the advantages of spectral methods is that they do not require specification of a model and so the results are not based on any rigid modeling assumptions.

In addition to Fourier analysis, we also use wavelet analysis, which allows

for frequency analysis by scale while maintaining time position in the data series.

Mathematically this admissibility condition is written as:

                                          +∞

                                          ∫ψ(t)dt = 0                                          (1)                                             

                                          -∞

An additional condition is that the energy of the series being studied must be preserved.

This second condition is written as (see Gençay et al., 2002):

                                           +∞

                                          ∫|ψ(t)|²dt = 1                                        (2)

                                          -∞

Changing the length of the wavelet at each level of resolution gives rise to the phraseology: multiresolution analysis (MRA). Wavelets of relatively short length are particularly good at capturing the high frequency components of a time series whereas longer length wavelets capture the low frequency longer enduring components of a time series. As you proceed from one level of resolution to the next, a graphical summary of the pronounced information effects is often presented as a  wavelet power spectrum which is made up of the squared absolute value of the wavelet coefficients at each level of resolution.

(4) Results/Expected Results: Using Fourier spectral analysis and wavelet correlation

across different localized time scales, we expect to show the association between crude oil and stock prices. Also by analyzing different sub-periods of the data: pre 1987, 1987-2001, 2001-present, we expect to show the changes in the lead/lag relationship between the volatilities of crude oil and stock prices