[Paper Review] Comparison of volatility distributions in the periods of booms and stagnations: an empirical study on stock price indices

Taisei Kaizoji|ArXiv.org|Jun 13, 2005

Complex Systems and Time Series Analysis12 references3 citations

TL;DR

This paper compares volatility distributions in stock market booms versus stagnation periods using daily price indices from four major markets (Nikkei 225, DJIA, S&P 500, FT 100) from 1975 to 2004. It finds that absolute log-returns follow a power-law with exponent ≈3 during booms, but an exponential distribution with scale ≈1 during stagnations, indicating fundamentally different market dynamics in each regime.

ABSTRACT

The aim of this paper is to compare statistical properties of stock price indices in periods of booms with those in periods of stagnations. We use the daily data of the four stock price indices in the major stock markets in the world: (i) the Nikkei 225 index (Nikkei 225) from January 4, 1975 to August 18, 2004, of (ii) the Dow Jones Industrial Average (DJIA) from January 2, 1946 to August 18, 2004, of (iii) Standard and Poor's 500 index (SP500) from November 22, 1982 to August 18, 2004, and of (iii) the Financial Times Stock Exchange 100 index (FT 100) from April 2, 1984 to August 18, 2004. We divide the time series of each of these indices in the two periods: booms and stagnations, and investigate the statistical properties of absolute log returns, which is a typical measure of volatility, for each period. We find that (i) the tail of the distribution of the absolute log-returns is approximated by a power-law function with the exponent close to 3 in the periods of booms while the distribution is described by an exponential function with the scale parameter close to unity in the periods of stagnations.

Motivation & Objective

• To investigate how statistical properties of stock price volatility differ between periods of market booms and stagnations.
• To analyze absolute log-returns as a proxy for volatility across multiple global stock indices.
• To determine whether volatility distributions follow power-law or exponential forms in each economic regime.
• To provide empirical evidence on regime-dependent market dynamics in financial time series.

Proposed method

• The study uses daily closing prices from four major stock indices: Nikkei 225 (1975–2004), DJIA (1946–2004), S&P 500 (1982–2004), and FT 100 (1984–2004).
• Time series are segmented into 'booms' and 'stagnations' based on market performance trends.
• Absolute log-returns are computed as a measure of volatility for each period.
• The empirical distributions of absolute log-returns are fitted to power-law and exponential functions to compare goodness of fit.
• The power-law exponent and exponential scale parameter are estimated for each regime and index.
• Statistical comparison is performed to assess whether the distributional form differs significantly between booms and stagnations.

Experimental results

Research questions

• RQ1 How do the statistical properties of volatility differ between periods of market booms and stagnations?
• RQ2 Do absolute log-returns follow a power-law or exponential distribution in boom and stagnation regimes?
• RQ3 Is the power-law exponent or exponential scale parameter significantly different between boom and stagnation periods?
• RQ4 Do these distributional differences hold consistently across multiple global stock indices?

Key findings

• In periods of market booms, the tail of the absolute log-return distribution follows a power-law with an exponent close to 3.
• In periods of stagnation, the absolute log-return distribution is best described by an exponential function with a scale parameter close to 1.
• The power-law fit in booms suggests higher tail risk and fat-tailed behavior compared to the exponential decay in stagnation periods.
• The difference in distributional form indicates that market dynamics and risk characteristics are fundamentally different in boom versus stagnation regimes.
• The results are consistent across all four major stock indices studied: Nikkei 225, DJIA, S&P 500, and FT 100.
• The study provides empirical support for regime-dependent volatility modeling in financial markets.