LIHNPSD (version 0.2.1)

LIHNPSD-package: Poisson Subordinated Distribution

Description

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.

References

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.

See Also

dji_logr, rawmean, rawdensity, LIHNPSD_prepare_data, LIHNPSD_theoretical_result, LIHNPSD_plot_std4gr

Examples

  # 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)