Academic journal article IUP Journal of Applied Economics

An Analysis of Lead-Lag Relationship between Stock Returns Using Spectral Methods

Academic journal article IUP Journal of Applied Economics

An Analysis of Lead-Lag Relationship between Stock Returns Using Spectral Methods

Article excerpt

(ProQuest: ... denotes formulae omitted.)


Spectral analysis of time series gives information about the time series in the frequency domain. Several studies based on spectral analysis try to analyze the time series in the frequency domain, which helps in obtaining valuable information that is not available in the usual time domain analysis. The use of spectral analysis as a tool to understand the dynamics of stock prices is not a new area of study. In frequency domain analysis, the disaggregation of a time series into its different periodic components allows us to determine the relative importance of different components. This paper uses the existing spectral methods to analyze the behavior of stock markets. As we are mainly dealing with more than one market, we will be interested in the lead-lag relationship between the markets.

The paper is structured as follows: it presents a brief review of the related literature, followed by description of the tools used in this analysis and their application to stock market prices. Subsequently, the results are discussed, and finally, the conclusion is offered.

Literature Review

The use of spectral analysis spans many areas in finance and economics. The tools of spectral analysis have been used a number of studies to examine the stock price behavior. A spectral analysis of New York stock prices was carried out by Granger and Morgenstern (1963). They found that the short-run movements of the series follow a simple randomwalk hypothesis as the spectrum was flat almost over the whole frequency range. Granger and Hatanaka (1964) did a comprehensive study on the applicability of spectral analysis to economic data. Power spectra and cross-spectra of Japanese economic annual series since 1887 were estimated by Suzuki (1965). The spectrum suggested that long swings and business cycle components are important in many of the time series. The lead-lag relationship between the series was verified by the cross-spectral estimates, where loans and discounts of all banks, exports and government consumption were leading all the other series and driving the growth.

Cross-spectral methods were applied by Ying (1966) to the Standard and Poor's 500 daily closing price indexes and daily volumes of stock sales on the New York Stock Exchange from January 1957 to December 1962, to analyze the short-run relationships between prices and volumes. A periodicity of length equal to around six months was chosen for the shortrun analysis. It was clear from the individual spectra of prices and volumes that most of the variations were due to the cycles of long length.

Pakko (2004) used cross-spectral analysis to study the cross-country correlation puzzle. Dynamic general equilibrium models show high cross-country consumption correlation, whereas the data reflects a high output correlation. However, spectral decomposition shows that the relative ranking of this cross-country correlation varies across frequency bands, thus explaining the discrepancy between theory and data. Following Mantegna and Stanley (2000), the spectral density of the logarithm of stock price is well described by the inverse power law, S(f)=1 f 2 , which is the prediction for the spectral density of a random walk. The spectral density of the Standard and Poor's 500 index, for the four-year period from January 1984 to December 1987, exhibits the inverse power law, in agreement with the hypothesis that the stochastic dynamics of stock prices may be described by a random walk.

Durlauf (1991) proposed a method of testing whether a time series is a martingale, using spectral distribution estimates. The null hypothesis that the spectral distribution function is a straight line is tested. The application of the proposed method based on spectral distribution estimates, to weekly and monthly stock returns, revealed some evidence against the null hypothesis that the returns are martingale differences. …

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