acs: AutoCorrelation Structure

In CoSMoS: Complete Stochastic Modelling Solution

AutoCorrelation Structure

Description

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).

Usage

acs(id, ...)

Arguments

id	autocorrelation structure id.
...	other arguments (t as lag and ACS parameters).

Value

A numeric vector of autocorrelation values at the supplied lags.

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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.advwatres.2018.02.013")}

See Also

actpnts, fitACS, fitactf

Examples

library(CoSMoS)

## 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()

CoSMoS documentation built on May 8, 2026, 1:08 a.m.