# acs: AutoCorrelation Structure In CoSMoS: Complete Stochastic Modelling Solution

## 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

 `1` ```acs(id, ...) ```

## 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, doi: 10.1016/j.advwatres.2018.02.013

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```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 30, 2021, 1:06 a.m.