Data atlas / stock index
Dow Monthly Log Return for 80 Years
Monthly sampling lowers kurtosis to about 11. The shape still fits, which suggests a normal cascade kernel at this interval.
The Dow monthly log return has a much smaller kurtosis, about 11, than the daily log return. The kurtosis is still significant. The general shape fits the skew lognormal cascade distribution well.
This indicates that the cascade kernel of monthly log returns is normal, unlike the daily distribution. The change with sampling interval is part of the scaling behavior studied in the papers.
Data source: Yahoo Finance.
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Data and further reading
- Yahoo FinanceMarket data and historical quotes used for several series.
- Nasdaq CompositeOfficial index information for the Nasdaq Composite.
- Nikkei marketsJapanese market data and index information from Nikkei.
- FTSE Russell US indicesIndex information for the Russell 2000 and related benchmarks.
- Federal Reserve Economic DataEconomic time series from the Federal Reserve Bank of St. Louis.
- Lihn 2008 on SSRNThe 2008 working paper on the scale invariant Brownian motion model.
- Lihn 2009 on SSRNThe working paper on higher order lognormal cascade distributions.
- Clark 1973Subordinated stochastic process model for speculative prices.
- Fernholz 2002Stochastic portfolio theory and the diversity index.
- Heavy tailed distributionsA reference overview of distributions with heavy tails.
- Lognormal distributionDefinition and properties of the lognormal distribution.
- Stochastic portfolio theoryA reference overview of stochastic portfolio theory.