Package 'tscopula'

Description

Compute partial autocorrelations from autocorrelations

Usage

acf2pacf(rho)

Arguments

Value

A vector of partial autocorrelation values with same length as rho.

Examples

rho <- ARMAacf(ar = -0.9, ma = 0.8, lag.max = 50)[-1]
alpha <- acf2pacf(rho)

Description

Akaike Corrected Information Criterion

Usage

AICc(object, ...)

Arguments

Value

If just one object is provided, a numeric value with the corresponding AICC value.

If multiple objects are provided, a data.frame with rows corresponding to the objects and columns representing the number of parameters in the model (df) and the AICC.

Description

Transform an armacopula into a dvinecopula or dvinecopula2 object

Usage

arma2dvine(object)

Arguments

Value

An object of class dvinecopula (for AR copulas) or class dvinecopula2 (for MA or ARMA copulas).

Examples

arma2dvine(armacopula(list(ar = 0.5, ma = 0.4)))

Description

Constructor function for ARMA copula process

Usage

armacopula(pars = list(ar = 0, ma = 0))

Arguments

Value

An object of class armacopula.

Examples

armacopula(list(ar = 0.5, ma = 0.4))

Description

Class of objects for ARMA copula processes.

Usage

## S4 method for signature 'armacopula'
coef(object)

## S4 method for signature 'armacopula'
show(object)

## S4 method for signature 'armacopula'
sim(object, n = 1000)

## S4 method for signature 'armacopula'
kendall(object, lagmax = 20)

## S4 method for signature 'armacopula'
predict(object, data, x, type = "df")

Arguments

Methods (by generic)

• coef(armacopula): Coef method for ARMA copula class

• show(armacopula): Show method for ARMA copula process

• sim(armacopula): Simulation method for armacopula class

• kendall(armacopula): Calculate Kendall's tau values for armacopula model

• predict(armacopula): Prediction method for armacopula class

Slots

name

name of ARMA copula process.

modelspec

vector containing number of AR and MA parameters.

pars

list consisting of vector of AR parameters named 'ar' and vector of MA parameters named 'ma'.

Examples

sim(armacopula(list(ar = c(0.5, 0.4), ma = -0.8)), n = 1000)
mod <- armacopula(list(ar = 0.95, ma = -0.85))
kendall(mod)

Description

Transform a fitted armacopula into a fitted dvinecopula or dvinecopula2 object

Usage

armafit2dvine(object)

Arguments

Value

An object of class tscopulafit in which the copula is a dvinecopula (for fitted AR copulas) or class dvinecopula2 (for fitted MA or ARMA copulas).

Description

Turn vector of ARMA parameters into list

Usage

armavec2list(theta, order)

Arguments

Value

a list containing ARMA parameters in components ar and ma

Description

This function begins with a model based exclusively on Gaussian pair copulas and systematically replaces a finite number of copulas with non-Gaussian alternatives that lower a specified information criterion.

Usage

auto_dvine(
  model,
  nreplace = 5,
  tautol = 1e-04,
  maxlag = Inf,
  ICtol = 0.5,
  nstrike = 3,
  criterion = "AIC",
  choices = c("gumbel", "clayton", "frank", "joe"),
  verbose = TRUE
)

Arguments

Details

The number of copulas to replace is specified by nreplace but the algorithm may stop prematurely if the information criterion is barely lowered over nstrike consecutive steps.

This is a slow function to execute. Increasing tautol or setting a value for maxlag will speed it up at the cost of some accuracy in the final model. The default choices of copula are all one-parameter but the t copula can be added if desired. For copulas without radial symmetry different rotations are tried to accommodate negative and positive dependencies.

Value

An object of class tscopulafit such that model@tscopula is of class sdvinecopula.

Description

Time series of Bitcoin closing prices from 31 December 2015 to 31 December 2019 (1044 values). This permits the calculation of 4 calendar years of returns.

Usage

data(bitcoin)

Format

An object of class "xts".

Examples

data(bitcoin)
plot(bitcoin)
X <- (diff(log(bitcoin))[-1]) * 100
plot(X)

Description

Convert tscopula object to tscm object

Usage

## S4 method for signature 'tscopula,tscm'
coerce(from, to = "tsc", strict = TRUE)

Arguments

Value

A tscm object.

Description

Convert tscopulafit object to be tscmfit object

Usage

## S4 method for signature 'tscopulafit,tscmfit'
coerce(from, to = "tscmfit", strict = TRUE)

Arguments

Value

A tscmfit object.

Description

Time series of US quarterly CPI (consumer price index) data Q4 1959 to Q4 2020 (245 values) for studying inflation. These data were sourced from the OECD webpage and represent the total ‘perspective’ on inflation, including food and energy. They have been based to have a value of 100 in 2015.

Usage

data(cpi)

Format

An object of class "xts".

Examples

data(cpi)
plot(cpi)
X <- (diff(log(cpi))[-1]) * 100
plot(X)

Description

Compute the density function of the marginal model.

Usage

dmarg(x, y, log = FALSE)

Arguments

Value

A vector of values for the density.

Examples

margmod <- margin("gauss", pars = c(mu = 0, sigma = 1))
dmarg(margmod, c(-2, 0, 2), log = TRUE)

Description

Double Weibull distribution

Usage

ddoubleweibull(x, mu = 0.05, shape = 1, scale = 1, log = FALSE)

pdoubleweibull(q, mu = 0.05, shape = 1, scale = 1)

qdoubleweibull(p, mu = 0.05, shape = 1, scale = 1)

rdoubleweibull(n, mu = 0.05, shape = 1, scale = 1)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

This function sets up a stationary d-vine process of finite order where the elements of the (finite-length) copula sequence may be any copulas that can be implemented using bicop_dist in the rvinecopulib package.

Usage

dvinecopula(family = "indep", pars = list(NULL), rotation = 0)

Arguments

Details

Copulas may also be rotated through 90, 180 and 270 degrees. If the same family or same rotation is to be used at every lag, these arguments may be scalars. The pars argument must be a list with the same length as the copula sequence.

If a t copula is included, the correlation parameter precedes the degrees of freedom in the parameter vector. This copula should be referred to as "t" rather than "Student".

Value

An object of class dvinecopula.

Examples

dvinecopula(family = c("joe", "gauss", "t"), pars = list(3, .5, c(0.4, 4)), rotation = c(180, 0, 0))

Description

Class of objects for d-vine copula processes.

Usage

## S4 method for signature 'dvinecopula'
coef(object)

## S4 method for signature 'dvinecopula'
show(object)

## S4 method for signature 'dvinecopula'
sim(object, n = 1000, innov = NA, start = NA)

## S4 method for signature 'dvinecopula'
predict(object, data, x, type = "df")

## S4 method for signature 'dvinecopula'
kendall(object, lagmax = 20)

Arguments

Methods (by generic)

• coef(dvinecopula): Coef method for dvinecopula class

• show(dvinecopula): Show method for dvinecopula class

• sim(dvinecopula): Simulation method for dvinecopula class

• predict(dvinecopula): Prediction method for dvinecopula class

• kendall(dvinecopula): Calculate Kendall's tau values for pair copulas in d-vine copula

Slots

name

name of the d-vine copula process.

modelspec

list containing the family, number of parameters and rotations

pars

list comprising of the parameters.

Examples

mixmod <- dvinecopula(family = c("gumbel", "gauss"), pars = list(1.5, -0.6))
kendall(mixmod)

Description

This function sets up a stationary d-vine process of finite or infinite order based on a single copula family from a subset of those that can be implemented using bicop_dist in the rvinecopulib package.

Usage

dvinecopula2(
  family = "gauss",
  rotation = 0,
  kpacf = "kpacf_arma",
  pars = list(ar = 0.1, ma = 0.1),
  tautol = 1e-04,
  maxlag = Inf,
  negtau = "none"
)

Arguments

Details

The copula family may be any one-parameter family or the t copula family. The basic copula from which the sequence is built may be rotated through 180 degrees using the rotation argument; the default is no rotation (0 degrees).

The copulas are parameterized using the Kendall partial autocorrelation function (kpacf) specified by the kpacf argument. The default choice is the kpacf of a standard ARMA process which is implemented in the function kpacf_arma. The parameters of the kpacf should be set as a list using the pars argument; the required parameters should usually be clear from the documentation of the chosen kpacf function and must be correctly named.

If the kpacf takes a negative value at any lag and the standard copula is unable to model a negative dependency (e.g. Clayton, Gumbel, Joe and their 180 degree rotations) then one of four different treatments may be specified using the negtau parameter: "gauss" substitutes a Gaussian copula at that lag; "frank" substitutes a Frank copula; "right" and "left" rotate the copula through 90 degrees in a clockwise or anto-clockwise direction respectively.

In practice, the sequence of copulas will be truncated at the last copula for which the kpacf exceeds tautol. The maxlag parameter is typically used to force the truncation to take place at a lower lag (to increase speed). This can also be achieved by increasing the value of tautol.

If the t copula is chosen by setting family equal to "t", the list of parameters needs to be augmented with a component named "df" which is the degrees of freedom. In this case it makes sense to set maxlag to be a finite number to avoid models with tail dependencies at arbitrary lags which are not ergodic. The class dvinecopula3 is more suitable for working with t copulas with different degrees of freedom at different lags.

Value

An object of class dvinecopula2.

Examples

dvinecopula2(family = "joe", kpacf = "kpacf_arma",
pars = list(ar = 0.95, ma = -0.85), maxlag = 30)

Description

Class of objects for d-vine copula processes. See dvinecopula2 for more details.

Usage

## S4 method for signature 'dvinecopula2'
coef(object)

## S4 method for signature 'dvinecopula2'
show(object)

## S4 method for signature 'dvinecopula2'
sim(object, n = 1000)

## S4 method for signature 'dvinecopula2'
predict(object, data, x, type = "df")

## S4 method for signature 'dvinecopula2'
kendall(object, lagmax = 20)

Arguments

Methods (by generic)

• coef(dvinecopula2): Coef Method for dvinecopula2 class

• show(dvinecopula2): Show method for dvinecopula2 class

• sim(dvinecopula2): Simulation method for dvinecopula2 class

• predict(dvinecopula2): Prediction method for dvinecopula2 class

• kendall(dvinecopula2): Calculate Kendall's tau values for pair copulas in type 2 d-vine copula

Slots

name

name of the d-vine copula process.

modelspec

list containing the family, rotation, and name of KPACF

pars

list comprising of the parameters.

Examples

copmod <- dvinecopula2(family = "joe", kpacf = "kpacf_arma",
pars = list(ar = 0.95, ma = -0.85), maxlag = 30)
kendall(copmod)

Description

This function sets up a stationary d-vine process of finite or infinite order based on a sequence of Gaussian copulas with a finite number of non-Gaussian substitutions at specified lags. The substituted families can be Gumbel, Clayton, Joe, Frank, t and BB1 copulas as implemented by the bicop_dist in the rvinecopulib package. The Gauss copula can be named in the list of substitutions but does not need to be.

Usage

dvinecopula3(
  location = 1,
  family = "gumbel",
  posrot = 0,
  negrot = 90,
  kpacf = "kpacf_arma",
  pars = list(ar = 0.1, ma = 0.1),
  auxpar = NA,
  tautol = 1e-04,
  maxlag = Inf
)

Arguments

Details

For the substituted copulas (other than t and Frank) the user must specify the rotation that should be used for positive dependencies (0 or 180) and the rotation that should be used for negative dependencies (90 or 270).

The copulas are parameterized using the Kendall partial autocorrelation function (kpacf) specified by the kpacf argument. The default choice is the kpacf of a standard ARMA process which is implemented in the function kpacf_arma. The parameters of the kpacf should be set as a list using the pars argument; the required parameters should usually be clear from the documentation of the chosen kpacf function and must be correctly named.

In practice, the sequence of copulas will be truncated at the last copula for which the kpacf exceeds tautol. The maxlag parameter is typically used to force the truncation to take place at a lower lag (to increase speed). This can also be achieved by increasing the value of tautol.

If one or more of the substituted copulas are t or BB1 copulas the argument auxpar should be used to specify the additional parameters. These are the degree-of-freedom parameter for t and the delta parameter for BB1; the former must be greater or equal 2 and the latter greater or equal 1.

Value

An object of class dvinecopula3.

Examples

dvinecopula3(location = c(1,4), family = c("Gumbel", "clayton"),
posrot = c(0, 180), negrot = c(90, 270), kpacf = "kpacf_arma",
pars = list(ar = 0.95, ma = 0.85), maxlag = 20)

Description

Class of objects for d-vine copula processes. See dvinecopula3 for more details.

Usage

## S4 method for signature 'dvinecopula3'
coef(object)

## S4 method for signature 'dvinecopula3'
kendall(object, lagmax = 20)

## S4 method for signature 'dvinecopula3'
show(object)

## S4 method for signature 'dvinecopula3'
sim(object, n = 1000)

## S4 method for signature 'dvinecopula3'
predict(object, data, x, type = "df")

Arguments

Methods (by generic)

• coef(dvinecopula3): Coef Method for dvinecopula3 class

• kendall(dvinecopula3): Calculate Kendall's tau values for pair copulas in type 3 d-vine copula

• show(dvinecopula3): Show method for dvinecopula3 class

• sim(dvinecopula3): Simulation method for dvinecopula3 class

• predict(dvinecopula3): Prediction method for dvinecopula2 class

Slots

name

name of the d-vine copula process.

modelspec

list containing the family, rotation, and name of KPACF

pars

list comprising of the parameters.

Description

This function sets up a stationary d-vine process of finite or infinite order based on a single inverse-v-transformed copula family from a subset of those that can be implemented using bicop_dist in the rvinecopulib package.

Usage

dvinecopulavt(
  family = "joe",
  rotation = 0,
  kpacf = "kpacf_arma",
  pars = list(ar = 0.1, ma = 0),
  vt1 = Vlinear(0.5),
  vt2 = Vlinear(0.5),
  tautol = 1e-04,
  maxlag = Inf,
  V2override = FALSE
)

Arguments

Details

The permitted choices of base copula family are currently Joe, Gumbel, Frank, ast or Clayton survival. If Clayton is chosen, the rotation argument must be set to 180, while if Joe, Gumbel or ast are chosen, the rotation argument must be zero (which is the default); any other options will return an error

The copulas are parameterized using the Kendall partial autocorrelation function (kpacf) of the base copula sequence specified by the kpacf argument. The default choice is the kpacf of a standard ARMA process which is implemented in the function kpacf_arma. The parameters of the kpacf should be set as a list using the pars argument; the required parameters should usually be clear from the documentation of the chosen kpacf function and must be correctly named.

The arguments vt1 and vt2 are used to enter two parametric v-transforms which may be created, for example, by Vlinear or V2p. However, the latter is very slow and the variable V2override has to be set to TRUE if you want to include 2-parameter v-transforms. While fitting is possible, residual analysis and simulation are almost always prohibitively slow.

For data showing stochastic volatility, we expect positive serial dependencies in the base copula sequence. For this reason, we do not consider models where the kpacf takes negative values.

In practice, the sequence of base copulas will be truncated at the last copula for which the kpacf exceeds tautol. The maxlag parameter is typically used to force the truncation to take place at a lower lag (to increase speed). This can also be achieved by increasing the value of tautol.

Value

An object of class dvinecopulavt.

Examples

dvinecopulavt(family = "joe", kpacf = "kpacf_arma",
pars = list(ar = 0.95, ma = -0.85), maxlag = 30)

Description

Class of objects for d-vine copula processes. See dvinecopulavt for more details.

Usage

## S4 method for signature 'dvinecopulavt'
coef(object)

## S4 method for signature 'dvinecopulavt'
show(object)

## S4 method for signature 'dvinecopulavt'
kendall(object, lagmax = 20)

## S4 method for signature 'dvinecopulavt'
sim(object, n = 1000, forcetrunc = TRUE)

## S4 method for signature 'dvinecopulavt'
predict(object, data, x, type = "df")

Arguments

Methods (by generic)

• coef(dvinecopulavt): Coef Method for dvinecopulavt class

• show(dvinecopulavt): Show method for dvinecopulavt class

• kendall(dvinecopulavt): Calculate Kendall's tau values for core pair copulas in d-vine copula model with v-transforms

• sim(dvinecopulavt): Simulation method for dvinecopulavt class

• predict(dvinecopulavt): Prediction method for dvinecopulavt class

Slots

name

name of the d-vine copula process.

modelspec

list containing the family, rotation, and name of KPACF

pars

list comprising of the parameters.

Examples

copmod <- dvinecopulavt(family = "joe", kpacf = "kpacf_arma",
pars = list(ar = 0.95, ma = -0.85), maxlag = 30)
kendall(copmod)

Description

Construct empirical margin

Usage

edf()

Value

An object of class margin signifying an empirical distribution function.

Description

Methods are available for objects of class tscopulaU, vtscopula, tscopulafit, margin and tscm.

Usage

fit(x, y, ...)

Arguments

Value

An object of the fitted model class.

Description

Fit method for margin class

Usage

## S4 method for signature 'margin'
fit(x, y, tsoptions = list(), control = list())

Arguments

Value

An object of class marginfit.

Examples

margmod <- margin("gauss", pars = c(mu = 0, sigma = 1))
data <- sim(margmod, n = 500)
fit(margmod, data)

Description

Fit method for tscm class

Usage

## S4 method for signature 'tscm'
fit(x, y, tsoptions = list(), control = list(), method = "IFM")

Arguments

Value

An object of class tscmfit.

Examples

mod <- tscm(dvinecopula(family = "gauss", pars = 0.5), margin("doubleweibull"))
y <- sim(mod)
fit(mod, y)

Description

Fit method for tscopulafit class

Usage

## S4 method for signature 'tscopulafit'
fit(x, y, tsoptions = list(), control = list(warn.1d.NelderMead = FALSE))

Arguments

Value

An object of class tscopulafit.

Examples

ar1 <- armacopula(list(ar = 0.7))
data <- sim(ar1, 1000)
ar1fit <- fit(fit(ar1, data), sim(ar1, 1000))

Description

Fit method for tscopulaU class

Usage

## S4 method for signature 'tscopulaU'
fit(x, y, tsoptions = list(), control = list())

Arguments

Value

An object of class tscopulafit.

Examples

data <- sim(armacopula(list(ar = 0.5, ma = 0.4)), n = 1000)
fit(armacopula(list(ar = 0.5, ma = 0.4)), data)

Description

Fit object of class vtscopula to data using maximum likelihood.

Usage

## S4 method for signature 'vtscopula'
fit(
  x,
  y,
  tsoptions = list(),
  control = list(maxit = 2000, warn.1d.NelderMead = FALSE)
)

Arguments

Value

An object of class tscopulafit.

Examples

copobject <- armacopula(pars = list(ar = 0.6, ma = 0.2))
vtcop <- vtscopula(copobject, Vtransform = V2p())
y <- sim(vtcop)
fit(vtcop, y)

Description

Gaussian distribution

Usage

dgauss(x, mu = 0, sigma = 1, log = FALSE)

pgauss(q, mu = 0, sigma = 1)

qgauss(p, mu = 0, sigma = 1)

rgauss(n, mu = 0, sigma = 1)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Centred Gaussian distribution

Usage

dgauss0(x, sigma = 1, log = FALSE)

pgauss0(q, sigma = 1)

qgauss0(p, sigma = 1)

rgauss0(n, sigma = 1)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Generalized hyperbolic distribution

Usage

pgh(q, lambda = 0, shape = 1, gamma = 0, mu = 0, sigma = 1)

qgh(p, lambda, shape = 1, gamma = 0, mu = 0, sigma = 1)

dgh(x, lambda, shape = 1, gamma = 0, mu = 0, sigma = 1, log = FALSE)

rgh(n, lambda, shape = 1, gamma = 0, mu = 0, sigma = 0)

Arguments

Description

Generalized lagging function

Usage

glag(x, lagmax = 20, glagplot = FALSE)

Arguments

Value

If glagplot is TRUE a list of generalized lagged datasets of maximum length 9 is returned to facilitate a generalized lagplot. If glagplot is FALSE a vector of length lagmax containing the Kendall rank correlations for the generalized lagged datasets is returned.

Description

Hyperbolic distribution

Usage

phyp(q, shape = 1, gamma = 0, mu = 0, sigma = 1)

qhyp(p, shape = 1, gamma = 0, mu = 0, sigma = 1)

dhyp(x, shape = 1, gamma = 0, mu = 0, sigma = 1, log = FALSE)

rhyp(n, shape = 1, gamma = 0, mu = 0, sigma = 0)

Arguments

Description

Johnson's SU distribution

Usage

pjsu(q, delta = 2, mu = 0, sigma = 1, gamma = 0)

qjsu(p, delta, mu, sigma, gamma)

djsu(x, delta, mu, sigma, gamma, log = FALSE)

rjsu(n, delta, mu, sigma, gamma)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Methods are available for objects of class armacopula, dvinecopula, dvinecopula2 and vtscopula.

Usage

kendall(object, ...)

Arguments

Value

A vector of Kendall correlations.

Description

Kalman filter for ARMA copula model

Usage

kfilter(x, y)

Arguments

Value

A matrix or multivariate time series with columns consisting of conditional mean, standard deviation and residuals.

Examples

data <- sim(armacopula(list(ar = c(0.5, 0.4), ma = -0.8)), n = 1000)
kfilter(armacopula(list(ar = c(0.5, 0.4), ma = -0.8)), data)

Description

KPACF of ARFIMA process

Usage

kpacf_arfima(k, theta)

Arguments

Value

A vector of Kendall partial autocorrelations of length k.

Description

KPACF of ARMA process

Usage

kpacf_arma(k, theta)

Arguments

Value

A vector of Kendall partial autocorrelations of length k.

Description

KPACF of fractional Brownian noise

Usage

kpacf_fbn(k, theta)

Arguments

Value

A vector of Kendall partial autocorrelations of length k.

Description

KPACF of monthly seasonal ARMA process

Usage

kpacf_sarma12(k, theta)

Arguments

Value

A vector of Kendall partial autocorrelations of length k.

Description

KPACF of quarterly seasonal ARMA process

Usage

kpacf_sarma4(k, theta)

Arguments

Value

A vector of Kendall partial autocorrelations of length k.

Description

Laplace distribution

Usage

dlaplace(x, mu = 0, scale = 1, log = FALSE)

plaplace(q, mu = 0, scale = 1)

qlaplace(p, mu = 0, scale = 1)

rlaplace(n, mu = 0, scale = 1)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Centred Laplace distribution

Usage

dlaplace0(x, scale = 1, log = FALSE)

plaplace0(q, scale = 1)

qlaplace0(p, scale = 1)

rlaplace0(n, scale = 1)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Constructor function for margin

Usage

margin(name, pars = NULL)

Arguments

Value

An object of class margin.

Examples

margin("sst")

Description

Class of objects for marginal models for stationary time series. The object is given a name and there must exist functions pname, qname, dname and rname. As well as the parameters of the distribution, dname must have the logical argument log specifying whether log density should be computed.

Usage

## S4 method for signature 'margin'
coef(object)

## S4 method for signature 'margin'
sim(object, n = 1000)

## S4 method for signature 'margin'
show(object)

Arguments

Methods (by generic)

• coef(margin): Coef method for margin class

• sim(margin): Simulation method for margin class

• show(margin): Show method for margin class

Slots

name

name of the marginal model class.

pars

a numeric vector containing the named parameters of the distribution which are passed as arguments to pname, qname, dname and rname.

Examples

new("margin", name = "gauss", pars = c(mu = 0, sigma = 1))
margmod <- margin("gauss", pars = c(mu = 0, sigma = 1))
sim(margmod, n = 500)

Description

Fitted marginal model for time series

Usage

## S4 method for signature 'marginfit'
logLik(object)

Arguments

Methods (by generic)

• logLik(marginfit): logLik method for marginfit class

Slots

margin

an object of class margin.

data

numeric vector or time series of data.

fit

a list containing details of the maximum likelihood fit.

Description

Normal inverse Gaussian distribution

Usage

pnig(q, shape = 1, gamma = 0, mu = 0, sigma = 1)

qnig(p, shape = 1, gamma = 0, mu = 0, sigma = 1)

dnig(x, shape = 1, gamma = 0, mu = 0, sigma = 1, log = FALSE)

rnig(n, shape = 1, gamma = 0, mu = 0, sigma = 0)

Arguments

Description

Check for invertibility of ARMA process

Usage

non_invert(ma)

Arguments

Value

A logical variable stating whether ARMA process is invertible.

Description

Check for causality of ARMA process

Usage

non_stat(ar)

Arguments

Value

A logical variable stating whether ARMA process is causal.

Description

Compute autocorrelations from partial autocorrelations

Usage

pacf2acf(alpha)

Arguments

Value

A vector of autocorrelation values with same length as alpha.

Examples

alpha <- ARMAacf(ar = -0.9, ma = 0.8, lag.max = 50, pacf = TRUE)
rho <- pacf2acf(alpha)

Description

Compute autoregressive coefficients from partial autocorrelations

Usage

pacf2ar(alpha)

Arguments

Value

A vector of autoregressive coefficients with same length as alpha.

Examples

alpha <- ARMAacf(ar = -0.9, ma = 0.8, lag.max = 50, pacf = TRUE)
phi <- pacf2ar(alpha)

Description

Computes the probability that if we v-transform a uniform random variable and then stochastically invert the v-transform, we get back to the original value.

Usage

pcoincide(x)

Arguments

Value

The probability of coincidence.

Examples

pcoincide(Vlinear(delta = 0.4))
pcoincide(V3p(delta = 0.45, kappa = 0.5, xi = 1.3))

Description

Adjusted empirical distribution function

Usage

pedf(x, data, proper = FALSE)

Arguments

Value

a vector of same length as x

Description

Plot method for marginfit class

Usage

## S4 method for signature 'marginfit,missing'
plot(x, bw = FALSE)

Arguments

Value

No return value, generates plot.

Description

Plot method for tscmfit class

Usage

## S4 method for signature 'tscmfit,missing'
plot(x, plottype = "residual", bw = FALSE, lagmax = 30)

Arguments

Value

No return value, generates plot.

Description

Plot method for tscopulafit class

Usage

## S4 method for signature 'tscopulafit,missing'
plot(x, plottype = "residual", bw = FALSE, lagmax = 30)

Arguments

Value

No return value, generates plot.

Examples

data <- sim(armacopula(list(ar = 0.5, ma = 0.4)), n = 1000)
fit <- fit(armacopula(list(ar = 0.5, ma = 0.4)), data)
plot(fit)

Description

Plots the v-transform as well as its gradient or inverse. Can also plot the conditional probability that a series PIT falls below the fulcrum for a given volatility PIT value v.

Usage

## S4 method for signature 'Vtransform,missing'
plot(
  x,
  type = "transform",
  shading = TRUE,
  npoints = 200,
  lower = 0,
  upper = 1
)

Arguments

Value

No return value, generates plot.

Examples

plot(Vsymmetric())
plot(V2p(delta = 0.45, kappa = 0.8), type = "inverse")
plot(V2p(delta = 0.45, kappa = 0.8), type = "gradient")

Description

Compute the cumulative distribution function of the marginal model.

Usage

pmarg(x, q)

Arguments

Value

A vector of values for the CDF.

Examples

margmod <- margin("gauss", pars = c(mu = 0, sigma = 1))
pmarg(margmod, c(-2, 0, 2))

Description

Profile likelihood for fulcrum parameter

Usage

profilefulcrum(
  data,
  tscopula = dvinecopula(family = 1, pars = list(0.1)),
  locations = seq(0, 1, by = 0.1),
  plot = TRUE
)

Arguments

Value

A matrix containing fulcrum values and log likelihood values.

Examples

copobject <- armacopula(pars = list(ar = 0.6, ma = 0.2))
vtcop <- vtscopula(copobject, Vtransform = V2p())
y <- sim(vtcop)
profilefulcrum(y, vtcop)

Description

Compute the quantile function of the marginal model.

Usage

qmarg(x, p)

Arguments

Value

A vector of values for the quantile function.

Examples

margmod <- margin("gauss", pars = c(mu = 0, sigma = 1))
qmarg(margmod, c(0.05, 0.5, 0.95))

Description

Quantile calculation method for VT-ARMA models

Usage

## S4 method for signature 'tscmfit'
quantile(x, alpha, last = FALSE)

Arguments

Value

a vector of the same length as the data embedded in the tscmfit object.

Description

Rosenblatt backward function with v-transforms

Usage

Rbackward(x, u, pcs, vt1, vt2)

Arguments

Value

vector of same length as x

Description

Inverse Rosenblatt forward function with v-transforms

Usage

RforwardI(x, u, pcs, vt1, vt2)

Arguments

Value

vector of same length as x

Description

Calculate standard errors safely

Usage

safe_ses(hess)

Arguments

Value

a vector of standard errors.

Description

Transform a sarmacopula object into an armacopula object

Usage

sarma2arma(object)

Arguments

Value

An object of class armacopula.

Examples

sarma2arma(sarmacopula(list(ar = 0.5, ma = 0.4, sar = 0.2, sma = 0.6), period = 4))

Description

Transform a sarmacopula into a dvinecopula2 object

Usage

sarma2dvine(object)

Arguments

Value

An object of class dvinecopula2.

Examples

sarma2dvine(sarmacopula(list(ar = 0.5, ma = 0.4, sar = 0.2, sma = 0.6), period = 4))

Description

Constructor function for SARMA copula process

Usage

sarmacopula(pars = list(ar = 0, ma = 0, sar = 0, sma = 0), period = 4)

Arguments

Value

An object of class sarmacopula.

Examples

sarmacopula(list(ar = 0.5, ma = 0.4, sar = 0.2, sma = 0.6), period = 4)

Description

Class of objects for seasonal ARMA copula processes.

Usage

## S4 method for signature 'sarmacopula'
coef(object)

## S4 method for signature 'sarmacopula'
show(object)

## S4 method for signature 'sarmacopula'
sim(object, n = 1000)

## S4 method for signature 'sarmacopula'
kendall(object, lagmax = 20)

## S4 method for signature 'sarmacopula'
predict(object, data, x, type = "df")

Arguments

Methods (by generic)

• coef(sarmacopula): Coef method for SARMA copula class

• show(sarmacopula): Show method for SARMA copula process

• sim(sarmacopula): Simulation method for sarmacopula class

• kendall(sarmacopula): Calculate Kendall's tau values for sarmacopula model

• predict(sarmacopula): Prediction method for sarmacopula class

Slots

name

name of seasonal ARMA copula process.

modelspec

vector containing number of AR, MA, SAR and SMA parameters as well as the order D of seasonal differencing.

pars

list consisting of vector of AR parameters named 'ar' and vector of MA parameters named 'ma', SAR parameters named 'sar' and vector of SMA parameters named 'sma'.

Examples

sim(sarma2arma(sarmacopula(list(ar = 0.5, ma = 0.4, sar = 0.2, sma = 0.6), period = 4)))
mod <- sarmacopula(list(ar = 0.5, ma = 0.4, sar = 0.2, sma = 0.6), period = 4)
kendall(mod)

Description

Turn vector of SARMA parameters into list

Usage

sarmavec2list(theta, order)

Arguments

Value

a list containing SARMA parameters in components ar, ma, sar and sma

Description

Skew double Weibull distribution

Usage

dsdoubleweibull(x, mu = 0.05, shape = 1, scale = 1, gamma = 1, log = FALSE)

psdoubleweibull(q, mu = 0.05, shape = 1, scale = 1, gamma = 1)

qsdoubleweibull(p, mu = 0.05, shape = 1, scale = 1, gamma = 1)

rsdoubleweibull(n, mu = 0.05, shape = 1, scale = 1, gamma = 1)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

This function sets up a stationary d-vine process of finite or infinite order. In general, models models consist of base copulas and substituted copulas, which form a copula sequence. The copulas are parameterized using the Kendall partial autocorrelation function (kpacf) specified by the kpacf argument.

Usage

sdvinecopula(
  pars = list(ar = 0, ma = 0),
  kpacf = "kpacf_arma",
  family = NULL,
  posrot = 0,
  negrot = 90,
  basefamily = "gauss",
  baseposrot = 0,
  basenegrot = 0,
  auxpar = NA,
  tautol = 1e-04,
  maxlag = Inf
)

Arguments

Details

The default choice is the kpacf of a standard ARMA process which is implemented in the function kpacf_arma. The parameters of the kpacf should be set as a named list using the pars argument; the required parameters should usually be clear from the documentation of the chosen kpacf function and must be correctly named.

The base copula sequence is specified by the name of a single 1-parameter copula in basefamily, which can be Gauss, Frank, Gumbel, Clayton or Joe. For choices other than Gauss or Frank, the user must specify the rotation that should be used for positive dependencies (0 or 180) and the rotation that should be used for negative dependencies (90 or 270). These are specified by the arguments baseposrot and basenegrot respectively.

The number of copulas to be replaced is determined by the length of the family vector, which should be a vector of character strings representing copula names. The default value is NULL meaning no substitutions. If family has length one, the same copula name is repeated for all substitutions. The substituted families can be Gauss, Gumbel, Clayton, Joe, Frank, t and BB1 copulas as implemented by the bicop_dist in the rvinecopulib package.

For the substituted copulas (other than Gauss, t and Frank) the user should specify the rotation that should be used for positive dependencies (0 or 180) and the rotation that should be used for negative dependencies (90 or 270). These are specified by the arguments posrot and negrot respectively, which have default values 0 and 90. These vectors should be the same length as family or length one, in which case the values are repeated.

In practice, the sequence of copulas will be truncated at the last copula for which the kpacf exceeds tautol. The maxlag parameter is typically used to force the truncation to take place at a lower lag (to increase speed). This can also be achieved by increasing the value of tautol.

If one or more of the substituted copulas are t or BB1 copulas the argument auxpar should be used to specify the additional parameters. These are the degree-of-freedom parameter for t and the delta parameter for BB1; the former must be greater or equal 2 and the latter greater or equal 1.

Value

An object of class sdvinecopula.

Examples

sdvinecopula(pars = list(ar = 0.95, ma = 0.85), kpacf = "kpacf_arma",
family = c("Gumbel", "clayton"), posrot = c(0, 180), negrot = c(90, 270),
tautol = 1e-04)

Description

Class of objects for stationary d-vine copula processes. See sdvinecopula for more details.

Usage

## S4 method for signature 'sdvinecopula'
coef(object)

## S4 method for signature 'sdvinecopula'
kendall(object, lagmax = 20)

## S4 method for signature 'sdvinecopula'
show(object)

## S4 method for signature 'sdvinecopula'
sim(object, n = 1000)

## S4 method for signature 'sdvinecopula'
predict(object, data, x, type = "df")

Arguments

Methods (by generic)

• coef(sdvinecopula): Coef Method for sdvinecopula class

• kendall(sdvinecopula): Calculate Kendall's tau values for pair copulas in type 3 d-vine copula

• show(sdvinecopula): Show method for sdvinecopula class

• sim(sdvinecopula): Simulation method for sdvinecopula class

• predict(sdvinecopula): Prediction method for sdvinecopula class

Slots

name

name of the stationary d-vine copula process.

modelspec

list containing the family, rotation, and name of KPACF

pars

list comprising of the parameters.

Description

Uses the function tacvfARMA in the ltsa library.

Usage

sigmastarma(x)

Arguments

Value

The standard deviation of the standardized ARMA innovation distribution.

Examples

sigmastarma(armacopula(list(ar = c(0.5, 0.4), ma = -0.8)))

Description

Methods are available for objects of class swncopula, armacopula, dvinecopula, dvinecopula2, margin and tscm.

Usage

sim(object, ...)

Arguments

Value

A simulated realization from the time series model.

Description

Skew Laplace distribution

Usage

dslaplace(x, mu = 0.05, scale = 1, gamma = 1, log = FALSE)

pslaplace(q, mu = 0.05, scale = 1, gamma = 1)

qslaplace(p, mu = 0.05, scale = 1, gamma = 1)

rslaplace(n, mu = 0.05, scale = 1, gamma = 1)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Skew Student t distribution

Usage

psst(q, df = 10, gamma = 1, mu = 0, sigma = 1)

qsst(p, df, gamma, mu, sigma)

dsst(x, df, gamma, mu, sigma, log = FALSE)

rsst(n, df, gamma, mu, sigma)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Student t distribution

Usage

pst(q, df = 10, mu = 0, sigma = 1)

qst(p, df, mu, sigma)

dst(x, df, mu, sigma, log = FALSE)

rst(n, df, mu, sigma)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Centred Student t distribution

Usage

pst0(q, df = 10, sigma = 1)

qst0(p, df, sigma)

dst0(x, df, sigma, log = FALSE)

rst0(n, df, sigma)

Arguments

Value

A vector of density, distribution function, quantile or random values.

Description

Stochastic inverse of a v-transform

Usage

stochinverse(x, v, tscopula = NULL, tol = .Machine$double.eps^0.75)

Arguments

Value

A vector, matrix or time series with values in [0, 1].

Examples

stochinverse(Vsymmetric(), c(0, 0.25, 0.5, 0.75, 1))

Description

Calculate standardized ranks of data

Usage

strank(x)

Arguments

Value

A vector or time series of standardized ranks in the interval (0,1)

Examples

strank(rnorm(100))

Description

Constructor function for strict white noise copula process

Usage

swncopula()

Value

Object of class swncopula.

Examples

swncopula()

Description

Strict white noise copula process

Usage

## S4 method for signature 'swncopula'
sim(object, n = 1000)

## S4 method for signature 'swncopula'
coef(object)

## S4 method for signature 'swncopula'
show(object)

Arguments

Methods (by generic)

• sim(swncopula): Simulation method for strict white noise copula

• coef(swncopula): Coef method for strict white noise copula

• show(swncopula): Show method for strict white noise copula

Examples

sim(swncopula())

Description

Constructor function for time series

Usage

tscm(tscopula, margin = new("margin", name = "unif"))

Arguments

Value

An object of class tscm.

Examples

tscm(dvinecopula(family = "gauss", pars = 0.5), margin("doubleweibull"))

Description

Class of objects for composite time series models consisting of stationary copula processes and marginal distributions.

Usage

## S4 method for signature 'tscm'
show(object)

## S4 method for signature 'tscm'
coef(object)

## S4 method for signature 'tscm'
sim(object, n = 1000)

## S4 method for signature 'tscm'
predict(object, data, x, type = "df", qtype = 7, proper = FALSE)

## S4 method for signature 'tscm'
kendall(object, lagmax = 20)

Arguments

Methods (by generic)

• show(tscm): Show method for tscm class

• coef(tscm): Coefficient method for tscm class

• sim(tscm): Simulation method for tscm class

• predict(tscm): Prediction method for tscm class

• kendall(tscm): Calculate Kendall's tau values for pair copulas for tscm class

Slots

tscopula

an object of class tscopula.

margin

an object of class margin.

Examples

mod <- tscm(dvinecopula(family = "gauss", pars = 0.5), margin("doubleweibull"))
sim(mod)

Description

Class of objects for fitted tscm models.

Usage

## S4 method for signature 'tscmfit'
logLik(object)

## S4 method for signature 'tscmfit'
resid(object, trace = FALSE)

## S4 method for signature 'tscmfit'
predict(object, x, type = "df", qtype = 7, proper = FALSE)

Arguments

Methods (by generic)

• logLik(tscmfit): method for tscmfit class

• resid(tscmfit): Residual method for tscmfit class

• predict(tscmfit): Prediction method for tscmfit class

Slots

tscopula

an object of class tscopula.

margin

an object of class margin.

data

a vector or time series of data to which process has been fitted.

fit

a list containing details of the fit.

Description

Class of objects for time series copula processes.

Description

Class of objects for fitted time series copula processes.

Usage

## S4 method for signature 'tscopulafit'
sim(object, n = 1000)

## S4 method for signature 'tscopulafit'
kendall(object, lagmax = 20)

## S4 method for signature 'tscopulafit'
coef(object)

## S4 method for signature 'tscopulafit'
show(object)

## S4 method for signature 'tscopulafit'
logLik(object)

## S4 method for signature 'tscopulafit'
resid(object, trace = FALSE)

## S4 method for signature 'tscopulafit'
predict(object, x, type = "df")

Arguments

Methods (by generic)

• sim(tscopulafit): Simulation method for tscopulafit class

• kendall(tscopulafit): Calculate Kendall's tau values for pair copulas for tscopulafit class

• coef(tscopulafit): Coef method for tscopulafit class

• show(tscopulafit): Show method for tscopulafit objects

• logLik(tscopulafit): logLik method for tscopulafit class

• resid(tscopulafit): Residual method for tscopulafit class

• predict(tscopulafit): Prediction method for tscopulafit class

Slots

tscopula

an object of class tscopula.

data

a vector or time series of data.

fit

a list containing details of the fit.

Examples

ar1 <- armacopula(list(ar = 0.7))
data <- sim(ar1, 1000)
ar1fit <- fit(ar1, data)
sim(ar1fit)

Description

S4 Class union for basic time series copula types. These are armacopula, dvinecopula and dvinecopula2,

Description

Constructor function for 2-parameter beta v-transform

Usage

V2b(delta = 0.5, kappa = 1)

Arguments

Value

An object of class Vtransform.

Examples

V2b(delta = 0.45, kappa = 1.2)

Description

Constructor function for 2-parameter v-transform

Usage

V2p(delta = 0.5, kappa = 1)

Arguments

Value

An object of class Vtransform.

Examples

V2p(delta = 0.45, kappa = 1.2)

Description

Constructor function for 3-parameter beta v-transform

Usage

V3b(delta = 0.5, kappa = 1, xi = 1)

Arguments

Value

An object of class Vtransform.

Examples

V3b(delta = 0.45, kappa = 1.2, xi = 1.2)

Description

Constructor function for 3-parameter v-transform

Usage

V3p(delta = 0.5, kappa = 1, xi = 1)

Arguments

Value

An object of class Vtransform.

Examples

V3p(delta = 0.45, kappa = 0.8, xi = 1.1)

Description

Constructor function for degenerate v-transform

Usage

Vdegenerate()

Value

An object of class VtransformI.

Examples

Vdegenerate()

Description

Calculate conditional down probability of v-transform

Usage

vdownprob(x, v)

Arguments

Value

A vector or time series of values of gradient.

Examples

vdownprob(V2p(delta = 0.55, kapp = 1.2), c(0, 0.25, 0.5, 0.75, 1))

Description

Calculate gradient of v-transform

Usage

vgradient(x, u)

Arguments

Value

A vector or time series of values of gradient.

Examples

vgradient(Vsymmetric(), c(0, 0.25, 0.5, 0.75, 1))

Description

If the Vtransform object is also a VtransformI object (an invertible v-transform) then the analytical inverse is used. Otherwise an inverse is found by numerical root finding with uniroot.

Usage

vinverse(x, v, tol = .Machine$double.eps^0.75)

Arguments

Value

A vector or time series with values in [0, 1].

Examples

vinverse(Vsymmetric(), c(0, 0.25, 0.5, 0.75, 1))

Description

Constructor function for linear v-transform

Usage

Vlinear(delta = 0.5)

Arguments

Value

An object of class VtransformI.

Examples

Vlinear(delta = 0.45)

Description

Constructor function for symmetric v-transform

Usage

Vsymmetric()

Value

An object of class VtransformI.

Examples

Vsymmetric()

Description

Evaluate a v-transform

Usage

vtrans(x, u)

Arguments

Value

A vector or time series with values in [0, 1].

Examples

vtrans(Vsymmetric(), c(0, 0.25, 0.5, 0.75, 1))

Description

This is the class of v-transforms. It contains the VtransformI subclass consisting of v-transforms with an analytical expression for the inverse.

Usage

## S4 method for signature 'Vtransform'
show(object)

## S4 method for signature 'Vtransform'
coef(object)

Arguments

Methods (by generic)

• show(Vtransform): Show method for Vtransform class

• coef(Vtransform): Coef method for Vtransform class

Slots

name

a name for the v-transform of class character.

Vtrans

function to evaluate the v-transform.

pars

vector containing the named parameters of the v-transform.

gradient

function to evaluate the gradient of the v-transform.

Examples

V2p(delta = 0.5, kappa = 1.2)

Description

This class inherits from the Vtransform class and contains v-transforms with an analytical expression for the inverse.

Slots

name

a name for the v-transform of class character.

Vtrans

function to evaluate the v-transform.

pars

vector containing the named parameters of the v-transform.

gradient

function to evaluate the gradient of the v-transform.

inverse

function to evaluate the inverse of the v-transform.

Examples

Vlinear(delta = 0.55)

Description

Constructor function for vtscopula object

Usage

vtscopula(tscopulaU, Vtransform = Vlinear(), Wcopula = swncopula())

Arguments

Value

An object of class vtscopula.

Examples

copobject <- armacopula(pars = list(ar = 0.6, ma = 0.2))
vtscopula(copobject, Vtransform = V2p())

Description

Class of objects for v-transformed time series copula processes.

Usage

## S4 method for signature 'vtscopula'
show(object)

## S4 method for signature 'vtscopula'
coef(object)

## S4 method for signature 'vtscopula'
predict(object, data, x, type = "df")

## S4 method for signature 'vtscopula'
sim(object, n = 1000)

## S4 method for signature 'vtscopula'
kendall(object, lagmax = 20)

Arguments

Methods (by generic)

• show(vtscopula): Show method for vtscopula objects

• coef(vtscopula): Coef method for vtscopula class

• predict(vtscopula): Prediction method for vtscopula class

• sim(vtscopula): Simulation method for vtscopula class

• kendall(vtscopula): Calculate Kendall's tau values for vtscopula model

Slots

Vcopula

object of class tscopulaU.

Vtransform

object of class Vtransform.

Wcopula

object of class tscopula.

Examples

copobject <- armacopula(pars = list(ar = 0.6, ma = 0.2))
sim(vtscopula(copobject, Vtransform = V2p()))
mod <- vtscopula(armacopula(list(ar = 0.95, ma = -0.85)))
kendall(mod)