acs function

AutoCorrelation Structure

Provides a parametric function that describes the values of the linear autocorrelation up to desired lags. For more details on the parametric autocorrelation structures see section 3.2 in Papalexiou (2018).

acs(id, ...)

Arguments

• id: autocorrelation structure id
• ...: other arguments (t as lag and acs parameters)

Examples

library(CoSMoS)
library(data.table)

## specify lag
t <- 0:10

## get the ACS
f <- acs('fgn', t = t, H = .75)
b <- acs('burrXII', t = t, scale = 1, shape1 = .6, shape2 = .4)
w <- acs('weibull', t = t, scale = 2, shape = 0.8)
p <- acs('paretoII', t = t, scale = 3, shape = 0.3)

## visualize the ACS
dta <- data.table(t, f, b, w, p)

m.dta <- melt(dta, id.vars = 't')

ggplot(m.dta,
       aes(x = t,
           y = value,
           group = variable,
           colour = variable)) +
  geom_point(size = 2.5) +
  geom_line(lwd = 1) +
  scale_color_manual(values = c('steelblue4', 'red4', 'green4', 'darkorange'),
                     labels = c('FGN', 'Burr XII', 'Weibull', 'Pareto II'),
                     name = '') +
  labs(x = bquote(lag ~ tau),
       y = 'Acf') +
  scale_x_continuous(breaks = t) +
  theme_classic()

References

Papalexiou, S.M. (2018). Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency. Advances in Water Resources, 115, 234-252, tools:::Rd_expr_doi("10.1016/j.advwatres.2018.02.013")