generateTS {CoSMoS}

Generate timeseries

Description

Generates timeseries with given properties, just provide (1) the target marginal distribution and its parameters, (2) the target autocorrelation structure or individual autocorrelation values up to a desired lag, and (3) the probablility zero if you wish to simulate an intermittent process.

Usage

generateTS(
  n,
  margdist,
  margarg,
  p = NULL,
  p0 = 0,
  TSn = 1,
  distbounds = c(-Inf, Inf),
  acsvalue = NULL
)

Arguments

n

number of values

margdist

target marginal distribution

margarg

list of marginal distribution arguments

p

integer - model order (if NULL - limits maximum model order according to auto-correlation structure values)

p0

probability zero

TSn

number of timeseries to be generated

distbounds

distribution bounds (default set to c(-Inf, Inf))

acsvalue

target auto-correlation structure (from lag 0)

Details

A step-by-step guide:

• First define the target marginal (margdist), that is, the probability distribution of the generated data. For example set margdist = 'ggamma' if you wish to generate data following the Generalized Gamma distribution, margidst = 'burrXII' for Burr type XII distribution etc. For a full list of the distributions we support see the help vignette. In general, the package supports all build-in distribution functions of R and of other packages.

• Define the parameters' values (margarg) of the distribution you selected. For example the Generalized Gamma has one scale and two shape parameters so set the desired value, e.g., margarg = list(scale = 2, shape1 = 0.9, shape2 = 0.8). Note distributions might have different number of parameters and different type of parameters (location, scale, shape). See the help vignette for details on the parameters of each distribution we support.

• If you wish your time series to be intermittent (e.g., precipitation), then define the probability zero. For example, set p0 = 0.9, if you wish your generated data to have 90% of zero values (dry days).

• Define your linear autocorrelations.

  • You can supply specific lag autocorrelations starting from lag 0 and up to a desired lag, e.g., acs = c(1, 0.9, 0.8, 0.7); this will generate a process with lag1, 2 and 3 autocorrelations equal with 0.9, 0.8 and 0.7.

  • Alternatively, you can use a parametric autocorrelation structure (see section 3.2 in Papalexiou (2018). We support the following autocorrelation structures (acs) weibull, paretoII, fgn and burrXII. See also acs examples.

• Define the order to the autoregressive model p. For example if you aim to preserve the first 10 lag autocorrelations then just set p = 10. Otherwise set it p = NULL and the model will decide the value of p in order to preserve the whole autocorrelation structure.

• Lastly just define the time series length, e.g., n = 1000 and number of time series you wish to generate, e.g., TSn = 10.

Play around with the following given examples which will make the whole process a piece of cake.

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

library(CoSMoS)

## Case1:
## You wish to generate 3 time series of size 1000 each
## that follow the Generalized Gamma distribution with parameters
## scale = 1, shape1 = 0.8, shape2 = 0.8
## and autocorrelation structure the ParetoII
## with parameters scale = 1 and shape = .75
x <- generateTS(margdist = 'ggamma',
                margarg = list(scale = 1,
                               shape1 = .8,
                               shape2 = .8),
                acsvalue = acs(id = 'paretoII',
                               t = 0:30,
                               scale = 1,
                               shape = .75),
                n = 1000,
                p = 30,
                TSn = 3)

## see the results
plot(x)



## Case2:
## You wish to generate time series the same distribution
## and autocorrelations as is Case1 but intermittent
## with probability zero equal to 90%
y <- generateTS(margdist = 'ggamma',
                margarg = list(scale = 1,
                               shape1 = .8,
                               shape2 = .8),
                acsvalue = acs(id = 'paretoII',
                               t = 0:30,
                               scale = 1,
                               shape = .75),
                p0 = .9,
                n = 1000,
                p = 30,
                TSn = 3)

## see the results
plot(y)

## Case3:
## You wish to generate a time series of size 1000
## that follows the Beta distribution
## (e.g., relative humidity ranging from 0 to 1)
## with parameters shape1 = 0.8, shape2 = 0.8, is defined from 0 to 1
## and autocorrelation structure the ParetoII
## with parameters scale = 1 and shape = .75
z <- generateTS(margdist = 'beta',
                margarg = list(shape1 = .6,
                               shape2 = .8),
                distbounds = c(0, 1),
                acsvalue = acs(id = 'paretoII',
                               t = 0:30,
                               scale = 1,
                               shape = .75),
                n = 1000,
                p = 20)

## see the results
plot(z)

## Case4:
## Same in previous case but now you provide specific
## autocorrelation values for the first three lags,
## ie.., lag 1 to 3 equal to 0.9, 0.8 and 0.7

z <- generateTS(margdist = 'beta',
                margarg = list(shape1 = .6,
                               shape2 = .8),
                distbounds = c(0, 1),
                acsvalue = c(1, .9, .8, .7),
                n = 1000,
                p = TRUE)

## see the results
plot(z)