Abstract
Abstract When the variance of a population of random variables is non stationary, the population kurtosis is greater than the kurtosis of the probability distribution of the individual random variables. Therefore, the high kurtosis observed in the distribution of security prices can be explained by high kurtosis in the individual price changes, non stationarity in the variances of the price changes, or any combination of these two causes. For a 100-year series of monthly changes in the Standard & Poor’s Composite Index, fluctuations in variance as forecasted by a two-parameter model explain 70 percent of the deviation of the sample kurtosis from normality. The results suggest that increments in the logarithms of security prices obey a normal distribution with predictably fluctuating variance.
Keywords
KurtosisStatisticsEconometricsMathematicsVariance (accounting)Standard deviationDistribution (mathematics)PopulationNormalityNormal distributionEconomicsDemographyMathematical analysis
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Publication Info
- Year
- 2005
- Type
- book-chapter
- Pages
- 83-108
- Citations
- 73
- Access
- Closed
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Cite This
Barr Rosenberg
(2005).
The Behavior of Random Variables with Non stationary Variance and the Distribution of Security Prices.
, 83-108.
https://doi.org/10.1093/oso/9780199257195.003.0004
Identifiers
- DOI
- 10.1093/oso/9780199257195.003.0004