A new Poisson subordinated distribution is proposed to capture major leptokurtic features in log-return time series of financial data. This distribution is intuitive, easy to calculate, and converge quickly. It fits well to the historical daily log-return distributions of currencies, commodities, Treasury yields, VIX, and, most difficult of all, DJIA. It serves as a viable alternative to the more sophisticated truncated stable distribution.
Stephen Horng-Twu Lihn <[email protected]>
On a Poisson Subordinated Distribution for Precise Statistical Measurement of Leptokurtic Financial Data, SSRN 2032762, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2032762.
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# Load the daily log-return data of DJIA data(dji_logr) # Construct the S3 object for PSD dist <- list( sigma= 0.004625, alpha= 0.292645, gamma= 0.482744, beta= -0.154049, location= 0.002968 ) class(dist) <- "LIHNPSD" dist <- rawmean(dist) # A simple graph of the distribution's log PDF x <- seq(-0.1,0.1,by=0.1/1000) plot( x, log(rawdensity(dist,x)), pch=".") # The more sophisticated fit and graphs dt <- LIHNPSD_prepare_data(dji_logr, breaks=160, merge_tails=c(4,2)) th <- LIHNPSD_theoretical_result(dist, dt) LIHNPSD_plot_std4gr(th, dt)
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