CoSMoS (version 2.2.0)

acs: 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, ...)

Value

A numeric vector of autocorrelation values at the supplied lags.

Arguments

id

autocorrelation structure id.

...

other arguments (t as lag and ACS parameters).

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")

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()