Package 'DMQ' reference manual

Title:	Dynamic Multiple Quantile (DMQ) Model
Description:	Perform estimation, prediction, and simulations using the Dynamic Multiple Quantile model of Catania and Luati (2023) <doi:10.1016/j.jeconom.2022.11.002>. Can be used to estimate a set of conditional time-varying quantiles of a time series that do not cross.
Authors:	Leopoldo Catania [cre, aut] , Alessandra Luati [ctb]
Maintainer:	Leopoldo Catania <[email protected]>
License:	GPL-3
Version:	0.1.2
Built:	2024-12-21 06:43:52 UTC
Source:	CRAN

Dynamic Multiple Quantiles model in R

Description

The DMQ package allows us to simulate, estimate and forecast using the Dynamic Multiple Quantile (DMQ) model of Catania, L., & Luati, A. (2022). Semiparametric modeling of multiple quantiles. Journal of Econometrics, see doi:10.1016/j.jeconom.2022.11.002.

Note

Please cite Catania and Luati (2022) in working papers and published papers that use DMQ. Use citation("DMQ").

Author(s)

Leopoldo Catania [aut,cre], Alessandra Luati [aut]

Maintainer: Leopoldo Catania <[email protected]>

References

Catania, L, and Luati, A. (2023). "Semiparametric modeling of multiple quantiles." Journal of Econometrics doi:10.1016/j.jeconom.2022.11.002.

Estimate the Dynamic Multiple Quantile (DMQ) model.

Description

Estimate the parameters of the DMQ model using the estimator detailed in Catania and Luati (2023).

Usage

EstimateDMQ(vY, vTau, iTau_star = NULL, vPn_Starting = NULL, 
                        FixReference = FALSE, FixOthers = FALSE, 
                        ScalingType = "InvSqrt",
                         vQ_0 = NULL,  
                         fn.optimizer = fn.DEoptim, 
                        cluster = NULL, smooth = NULL, ...)
EstimateDMQ(vY, vTau, iTau_star = NULL, vPn_Starting = NULL, 
                        FixReference = FALSE, FixOthers = FALSE, 
                        ScalingType = "InvSqrt",
                         vQ_0 = NULL,  
                         fn.optimizer = fn.DEoptim, 
                        cluster = NULL, smooth = NULL, ...)

Arguments

`vY`	`numeric` vector of length Tx1 containing the time series of observations.
`vTau`	`numeric` vector of length Jx1 containing probability levels at which quantiles are estimated.
`iTau_star`	Integer indicating the position in `vTau` where the reference quantile is placed. For instance, if `vTau = seq(0.01, 0.99, 0.01)` then `iTau_star = 50` means that the median is used as the reference quantile.
`vPn_Starting`	`numeric` named vector of length 4x1 with starting values for the optimizer. For example `vPn_Starting = c("phi" = 0.9, "gamma" = 0.05, "alpha" = 0.01, "beta" = 0.7)`.
`FixReference`	`logical`. Should the reference quantile be fixed? By default `FixReference = FALSE`.
`FixOthers`	`logical`. Should the quantiles other than the reference quantile be fixed? By default `FixOthers = FALSE`.
`ScalingType`	`character` Indicating the scaling mechanism for the conditional quasi score. Possible choices are `"Identity"`, `"Inv"`,`"InvSqrt"`. When `ScalingType = "InvSqrt"` quasi scores are scaled by their standard deviation. When `ScalingType = "Inv"` quasi scores are scaled by their variance. When `ScalingType = "Identity"` quasi scores are not scaled. Default value `ScalingType = "InvSqrt"`.
`vQ_0`	`numeric`. Vector of limiting quantiles evaluated at `vTau`. By default `FixOthers = NULL` meaning that empirical unconditional quantilies are used.
`fn.optimizer`	`function`. This is a generic optimization function that can be provided by the user. By default `fn.optimizer = fn.DEoptim` where fn.DEoptim is a wrapper to the DEoptim function of the package `DEoptim`. See the Details and Examples sections for user defined optimization routines.
`cluster`	A `cluster` object created calling using the `paralell` package. If supplied parallel processing is used to speed up the computations if `fn.optimizer` makes use of it. When `fn.optimizer = fn.DEoptim` parallel computation can be used.
`smooth`	`logical`. Should a smooth version of the objective function should be used? If using a gradient based optimizer like `fn.optimizer = fn.optim` is it advised to set `smooth = TRUE`. By default, when `fn.optimizer = fn.DEoptim` we set `smooth = FALSE` and when `fn.optimizer = fn.optim` or `fn.optimizer = fn.solnp` we set `smooth = TRUE`.
`...`	Additional arguments to be passed to `fn.optimizer`.

Details

Starting values for the optimizer are by default set as c("phi" = 0.94, "gamma" = 0.10, "alpha" = 0.05, "beta" = 0.95).
The user is free to employ his/her own optimization routine via the fn.optimizer argument. fn.optimizer accepts a function object. The user provided optimizer has to satisfy strict requirements. The arguments of the fn.optimizer are:

par0: a vector of starting values,
vY: the data provided,
FUN: the objective function,
LB: vector of lower bounds for the parameters,
UB: vector of upper bounds for the parameters.
...: additional arguments.

The output of fn.optimizer has to be an object of the class list with four named elements:

pars: a numeric vector where the estimated parameters are stored,
value: a numeric containing the value of the objective function evaluated at its minimum,
hessian: a numeric matrix containing the Hessian matrix evaluated at the minimum of the objective function, this is used for inferential purposes,
convergence: a numeric variable reporting information about the convergence of the optimization. convergence = 0 has to indicate successful completion.

The user is allowed to not include the last two elements of the output of the fn.optimizer function, that is, the values hessian = NULL and convergence = NULL are admissible. In the case of hessian = NULL, no standard errors will be computed.

Value

A list with, among others, elements:

`lFilter`	A `list` containing the output from the filtering procedure. For instance filtered quantiles, hit variables, and losses.
`vPn`	`numeric` named vector of estimated parameters.
`optimizer`	A `list` with the output from `fn.optimizer`.
`Inference`	A `list` with output from the inferential procedure.

Author(s)

Leopoldo Catania

References

Catania, L, and Luati, A. (2023). "Semiparametric modeling of multiple quantiles." Journal of Econometrics doi:10.1016/j.jeconom.2022.11.002.

Examples

# Load Microsoft Corporation logarithmic percentage returns from December 8, 
# 2010 to November 15, 2018 for a total of T = 2000 observation
data("MSFT")

##############################################################
######################## Estimate DMQ ########################
##############################################################

# Deciles
vTau = seq(0.1, 0.9, 0.1)

# Reference quantile to the median
iTau_star = 5

# Fix the reference quantile to a constant
FixReference = TRUE

# Estimate DMQ
Fit_solnp = EstimateDMQ(vY = vY,
                  vTau = vTau,
                  iTau_star = iTau_star,
                  FixReference = FixReference,
                  fn.optimizer = fn.solnp,
                  cluster = cluster)

Fit_solnp$vPn
Fit_solnp$optimizer$value

## Not run: 
#### Estimate DMQ using different optimizers

# With the DEoptim optimizer

# parallel computation
iG = 7
cluster = makeCluster(iG)

set.seed(123)

# Estimate DMQ
Fit_DEoptim = EstimateDMQ(vY = vY,
                  vTau = vTau,
                  iTau_star = iTau_star,
                  FixReference = FixReference,
                  fn.optimizer = fn.DEoptim,
                  cluster = cluster)

Fit_DEoptim$vPn
Fit_DEoptim$optimizer$value

# Estimate the model with a user defined optimizer.
# Let's use the gosolnp() optimizer from the Rsolnp package.

library("Rsolnp")
fn.gosolnp <- function(par0, vY, FUN, LB, UB, ...) {
  
  foo = list(...)
  if (!is.null(foo$cluster)) {
    cluster = foo$cluster
    clusterEvalQ(cluster, library(DMQ))
  } 
  
  optimiser = gosolnp(
    pars = par0,
    fun = FUN, vY = vY, 
    n.sim = 1000,
    n.restarts = 5,
    LB = LB,
    UB = UB, control = list(trace = 1), 
    ...)
  
  out = list(pars = optimiser$pars,
             value = tail(optimiser$values, 1),
             hessian = optimiser$hessian,
             convergence = optimiser$convergence)
  
  return(out)
  
}

set.seed(123)
# Estimate DMQ
Fit_gosolnp = EstimateDMQ(vY = vY,
                  vTau = vTau,
                  iTau_star = iTau_star,
                  FixReference = FixReference,
                  fn.optimizer = fn.gosolnp,
                  cluster = cluster,
                  smooth = TRUE) 

Fit_gosolnp$vPn
Fit_gosolnp$optimizer$value

stopCluster(cluster)


## End(Not run)
# Load Microsoft Corporation logarithmic percentage returns from December 8, 
# 2010 to November 15, 2018 for a total of T = 2000 observation
data("MSFT")

##############################################################
######################## Estimate DMQ ########################
##############################################################

# Deciles
vTau = seq(0.1, 0.9, 0.1)

# Reference quantile to the median
iTau_star = 5

# Fix the reference quantile to a constant
FixReference = TRUE

# Estimate DMQ
Fit_solnp = EstimateDMQ(vY = vY,
                  vTau = vTau,
                  iTau_star = iTau_star,
                  FixReference = FixReference,
                  fn.optimizer = fn.solnp,
                  cluster = cluster)

Fit_solnp$vPn
Fit_solnp$optimizer$value

## Not run: 
#### Estimate DMQ using different optimizers

# With the DEoptim optimizer

# parallel computation
iG = 7
cluster = makeCluster(iG)

set.seed(123)

# Estimate DMQ
Fit_DEoptim = EstimateDMQ(vY = vY,
                  vTau = vTau,
                  iTau_star = iTau_star,
                  FixReference = FixReference,
                  fn.optimizer = fn.DEoptim,
                  cluster = cluster)

Fit_DEoptim$vPn
Fit_DEoptim$optimizer$value

# Estimate the model with a user defined optimizer.
# Let's use the gosolnp() optimizer from the Rsolnp package.

library("Rsolnp")
fn.gosolnp <- function(par0, vY, FUN, LB, UB, ...) {
  
  foo = list(...)
  if (!is.null(foo$cluster)) {
    cluster = foo$cluster
    clusterEvalQ(cluster, library(DMQ))
  } 
  
  optimiser = gosolnp(
    pars = par0,
    fun = FUN, vY = vY, 
    n.sim = 1000,
    n.restarts = 5,
    LB = LB,
    UB = UB, control = list(trace = 1), 
    ...)
  
  out = list(pars = optimiser$pars,
             value = tail(optimiser$values, 1),
             hessian = optimiser$hessian,
             convergence = optimiser$convergence)
  
  return(out)
  
}

set.seed(123)
# Estimate DMQ
Fit_gosolnp = EstimateDMQ(vY = vY,
                  vTau = vTau,
                  iTau_star = iTau_star,
                  FixReference = FixReference,
                  fn.optimizer = fn.gosolnp,
                  cluster = cluster,
                  smooth = TRUE) 

Fit_gosolnp$vPn
Fit_gosolnp$optimizer$value

stopCluster(cluster)


## End(Not run)

A wrapper to the DEoptim function of the `DEoptim` package of Mullen et al. (2011).

Description

This function is a wrapper to the DEoptim function of the DEoptim package of Mullen et al. (2011).

Usage

 fn.DEoptim(par0, vY, FUN, LB, UB, ...)
fn.DEoptim(par0, vY, FUN, LB, UB, ...)

Arguments

`par0`	`numeric` vector of named model coefficients.
`vY`	`numeric` vector or matrix of data.
`FUN`	A function to optimize.
`LB`	A vector of lower bounds for the parameters.
`UB`	A vector of upper bounds for the parameters.
`...`	Additional arguments to provide to DEoptim.

Details

The following control parameters are used: trace = 0, rho = 1, outer.iter = 400, inner.iter = 1800, delta = 1e-08, tol = 1e-08. See the documentation of DEoptim.

Value

It returns a named list with four elements: i) pars: a numeric vector where the estimated parameters are stored, ii) value: a numeric containing the value of the objective function evaluated at its minumum, iii) hessian, a numeric matrix containing the Hessian matrix evaluated at the minimum of the objective function, and iv) convergence a numeric element indicating the convergence (convergence is always reached by DEoptim, i.e. convergence = 1).

Author(s)

Leopoldo Catania

References

Katharine Mullen, David Ardia, David Gil, Donald Windover, James Cline (2011). 'DEoptim': An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software, 40(6), 1-26. doi:10.18637/jss.v040.i06.

Ardia, D., Boudt, K., Carl, P., Mullen, K.M., Peterson, B.G. (2010). Differential Evolution with 'DEoptim': An Application to Non-Convex Portfolio Optimization. R Journal, 3(1), 27-34. doi:10.32614/RJ-2011-005.

A wrapper to the optim function.

Description

This function is a wrapper to the standard optim optimizer with method = "BFGS".

Usage

 fn.optim(par0, vY, FUN, LB, UB, ...)
fn.optim(par0, vY, FUN, LB, UB, ...)

Arguments

`par0`	`numeric` vector of named model coefficients.
`vY`	`numeric` vector of data.
`FUN`	A function to optimize.
`LB`	A vector of lower bounds for the parameters.
`UB`	A vector of upper bounds for the parameters.
`...`	Additional arguments to provide to optim.

Details

The following control parameters are used for control:

trace = 0
abstol = 1e-8

See the documentation of optim.

Value

It returns a named list with four elements: i) pars: a numeric vector where the estimated parameters are stored, ii) value: a numeric containing the value of the objective function evaluated at its minumum, iii) hessian, a numeric matrix containing the Hessian matrix evaluated at the minimum of objective function, iv) convergence a numeric element indicating the convergence results of optim.

Author(s)

Leopoldo Catania

A wrapper to the solnp function of the `Rsolnp` package of Ghalanos and Theussl (2016).

Description

This function is a wrapper to the solnp function of the Rsolnp package of Ghalanos and Theussl (2016).

Usage

 fn.solnp(par0, vY, FUN, LB, UB, ...)
fn.solnp(par0, vY, FUN, LB, UB, ...)

Arguments

`par0`	`numeric` vector of named model coefficients.
`vY`	`numeric` vector or matrix of data.
`FUN`	A function to optimize.
`LB`	A vector of lower bounds for the parameters.
`UB`	A vector of upper bounds for the parameters.
`...`	Additional arguments to provide to solnp.

Details

The following control parameters are used: trace = 0, rho = 1, outer.iter = 400, inner.iter = 1800, delta = 1e-08, tol = 1e-08. See the documentation of solnp.

Value

Author(s)

Leopoldo Catania

References

Alexios Ghalanos and Stefan Theussl (2015). "Rsolnp: General Non-linear Optimization Using Augmented Lagrange Multiplier Method". R package version 1.16.

Forecast with univariate DMQ model

Description

Compute the H-steap ahead prediction of the quantile processes.

Usage

ForecastDMQ(Fit, H) 
ForecastDMQ(Fit, H)

Arguments

`Fit`	The output of the function EstimateDMQ.
`H`	`numeric`, forecast horizon.

Value

A numeric matrix of dimension HxJ, where J is the number of quantiles.

Author(s)

Leopoldo Catania

Examples

# Load Microsoft Corporation logarithmic percentage returns from December 8, 
# 2010 to November 15, 2018 for a total of T = 2000 observation
data("MSFT")

##############################################################
######################## Estimate DMQ ########################
##############################################################

# Estimate DMQ at tau_j = 0.05, 0.10, ..., 0.95
# with fixed median as reference quantile.
Fit = EstimateDMQ(vY = vY,
                  vTau = seq(0.05, 0.95, 0.05),
                  iTau_star = 10,
                  FixReference = TRUE,
                  fn.optimizer = fn.solnp)

# Compute 20-step ahead predictions
mQ_pred = ForecastDMQ(Fit, H = 20) 

mQ_pred
# Load Microsoft Corporation logarithmic percentage returns from December 8, 
# 2010 to November 15, 2018 for a total of T = 2000 observation
data("MSFT")

##############################################################
######################## Estimate DMQ ########################
##############################################################

# Estimate DMQ at tau_j = 0.05, 0.10, ..., 0.95
# with fixed median as reference quantile.
Fit = EstimateDMQ(vY = vY,
                  vTau = seq(0.05, 0.95, 0.05),
                  iTau_star = 10,
                  FixReference = TRUE,
                  fn.optimizer = fn.solnp)

# Compute 20-step ahead predictions
mQ_pred = ForecastDMQ(Fit, H = 20) 

mQ_pred

Estimate conditional moments using DMQ

Description

Compute DMQ implied conditional moments. At each point in time moments are computed using the discretized distribution implied by the estimated conditional quantiles.

Usage

MomentsDMQ(Fit)
MomentsDMQ(Fit)

Arguments

Fit

The output of the function EstimateDMQ or UpdateDMQ.

Details

Moments are computed using the following approximation:

$\mathbb{E}[g(x)] \approx \sum_{j = 1}^J (\tau_j - \tau_{j-1}) g(\hat q_t^{\tau_j}),$

with $\tau_0 = 0$ , where $\hat q_t^{\tau_j}$ are estimated quantiles.

Value

A list of four elements:

`mMoments`	a Tx4 `numeric` matrix with columns containing first, second, third, and fourth moments.
`mCenterdMoments`	a Tx4 `numeric` matrix with columns containing first, second, third, and fourth central moments.
`vSkew`	a `numeric` vector of length T of estimated skewness coefficients.
`vKurt`	a `numeric` vector of length T estimated kurtosis coefficients.

Author(s)

Leopoldo Catania

Examples


# Load Microsoft Corporation logarithmic percentage returns from December 8, 
# 2010 to November 15, 2018 for a total of T = 2000 observation
data("MSFT")

##############################################################
######################## Estimate DMQ ########################
##############################################################

# Estimate DMQ on the in sample period
Fit = EstimateDMQ(vY = vY,
                  vTau = seq(0.01, 0.99, 0.01),
                  iTau_star = 50,
                  FixReference = TRUE,
                  fn.optimizer = fn.solnp)

# Compute estimated moments

Moments = MomentsDMQ(Fit)

# Load Microsoft Corporation logarithmic percentage returns from December 8, 
# 2010 to November 15, 2018 for a total of T = 2000 observation
data("MSFT")

##############################################################
######################## Estimate DMQ ########################
##############################################################

# Estimate DMQ on the in sample period
Fit = EstimateDMQ(vY = vY,
                  vTau = seq(0.01, 0.99, 0.01),
                  iTau_star = 50,
                  FixReference = TRUE,
                  fn.optimizer = fn.solnp)

# Compute estimated moments

Moments = MomentsDMQ(Fit)

data: Microsoft Corporation logarithmic percentage returns from December 8, 2010 to November 15, 2018 for a total of T = 2000 observation downloaded from Yahoo finance.

Description

This dataset is the one used in Catania and Luati (2023).

Dow Jones 30 Constituents closing value log returns from 1987-03-16 to 2009-02-03 from Yahoo Finance. Note that AIG was replaced by KFT (Kraft Foods) on September 22, 2008. This is not reflected in this data set as that would bring the starting date of the data to 2001.

Usage

data("MSFT")data("MSFT")

Format

An xts object of 2000 logarithmic percentage returns.

Source

Yahoo Finance

References

Catania, L, and Luati, A. (2023). "Semiparametric modeling of multiple quantiles." Journal of Econometrics doi:10.1016/j.jeconom.2022.11.002.

Simulate from the DMQ model

Description

Approximate simulation from the DMQ model. Allows to simulate quantiles and observations.

Usage

SimulateDMQ(iT, vQ_0, vTau, iTau_star, vPn, ScalingType = "InvSqrt", fSim = NULL)
SimulateDMQ(iT, vQ_0, vTau, iTau_star, vPn, ScalingType = "InvSqrt", fSim = NULL)

Arguments

`iT`	Number of observations to simulate.
`vQ_0`	`numeric` vector of limiting quantiles.
`vTau`	`numeric` vector of length Jx1 containing probability levels at which quantiles are estimated.
`iTau_star`	Integer indicating the position in `vTau` where the reference quantile is placed. For instance, if `vTau = seq(0.01, 0.99, 0.01)` then `iTau_star = 50` means that the median is used as the reference quantile.
`vPn`	`numeric` named vector of length 4x1 with starting values for the optimizer. For example `vPn = c("phi" = 0.9, "gamma" = 0.05, "alpha" = 0.01, "beta" = 0.7)`.
`ScalingType`	`character` Indicating the scaling mechanism for the conditional quasi score. Possible choices are `"Identity"`, `"Inv"`,`"InvSqrt"`. When `ScalingType = "InvSqrt"` quasi scores are scaled by their standard deviation. When `ScalingType = "Inv"` quasi scores are scaled by their variance. When `ScalingType = "Identity"` quasi scores are not scaled. Default value `ScalingType = "InvSqrt"`.
`fSim`	`function` to simulate from the discretized distribution implied by the simulated quantiles. By default `fSim = NULL` meaning that an internal simulation scheme is employed. See details.

Details

Given a set of simulated quantiles a Uniform variable drawn. The discretized quantile function is linearly interpoled at the simulated Uniform draw to obtain an observations. When the Uniform draw is outside the range spanned by vTau a Gaussian quantile function is used. The mean and variance of the Gaussian quantile distribution are set to those implied by the simulated quantiles using the same scheme of MomentsDMQ.

Value

A list with two elements:

`vY`	A `numeric` vector of T simulated observations.
`mQ`	A `numeric` TxJ matrix of simulated quantiles.

Author(s)

Leopoldo Catania

Examples


set.seed(123)

# Simulate 500 observations from the DMQ model.

# Use the percentiles
vTau = seq(0.01, 0.99, 0.01)

# Median as reference quantile
iTau_star = 50

# Standard Gaussian limiting distribution
vQ_0 = qnorm(vTau)

# vector of parameters
vPn = c("phi" = 0.95, "gamma" = 0.10, "alpha" = 0.01, "beta" = 0.7)

lSim = SimulateDMQ(iT = 500, vQ_0, vTau, iTau_star, vPn)

plot.ts(lSim$vY)
plot.ts(lSim$mQ, plot.type = "single")
set.seed(123)

# Simulate 500 observations from the DMQ model.

# Use the percentiles
vTau = seq(0.01, 0.99, 0.01)

# Median as reference quantile
iTau_star = 50

# Standard Gaussian limiting distribution
vQ_0 = qnorm(vTau)

# vector of parameters
vPn = c("phi" = 0.95, "gamma" = 0.10, "alpha" = 0.01, "beta" = 0.7)

lSim = SimulateDMQ(iT = 500, vQ_0, vTau, iTau_star, vPn)

plot.ts(lSim$vY)
plot.ts(lSim$mQ, plot.type = "single")

Update filtered quantiles

Description

Filter dynamic quantiles using an estimated model and an updated dataset.

Usage

UpdateDMQ(Fit, vY) 
UpdateDMQ(Fit, vY)

Arguments

`Fit`	The output of the function EstimateDMQ.
`vY`	`numeric` vector containing past and new observations.

Details

The function can be used to compute a sequence of one-step-ahead rolling predictions, without updating the parameters of the model, see Examples.

Value

An output like the one of EstimateDMQ with updated quantile estimated.

Author(s)

Leopoldo Catania

Examples

# Load Microsoft Corporation logarithmic percentage returns from December 8, 
# 2010 to November 15, 2018 for a total of T = 2000 observation
data("MSFT")

# Divide the sample in two equal parts
vY_is  = vY[1:1000]

##############################################################
######################## Estimate DMQ ########################
##############################################################

# Estimate DMQ over the deciles on the in sample period
Fit = EstimateDMQ(vY = vY_is,
                  vTau = seq(0.1, 0.9, 0.1),
                  iTau_star = 5,
                  FixReference = TRUE,
                  fn.optimizer = fn.solnp)

# compute a sequence of one-step-ahead rolling predictions over the out of sample

Roll = UpdateDMQ(Fit, vY) 

# one steap ahead predictions from time t = 1001 to 2001 are
mForecast = t(Roll$lFilter$mQ)[1001:2001, ]

# Load Microsoft Corporation logarithmic percentage returns from December 8, 
# 2010 to November 15, 2018 for a total of T = 2000 observation
data("MSFT")

# Divide the sample in two equal parts
vY_is  = vY[1:1000]

##############################################################
######################## Estimate DMQ ########################
##############################################################

# Estimate DMQ over the deciles on the in sample period
Fit = EstimateDMQ(vY = vY_is,
                  vTau = seq(0.1, 0.9, 0.1),
                  iTau_star = 5,
                  FixReference = TRUE,
                  fn.optimizer = fn.solnp)

# compute a sequence of one-step-ahead rolling predictions over the out of sample

Roll = UpdateDMQ(Fit, vY) 

# one steap ahead predictions from time t = 1001 to 2001 are
mForecast = t(Roll$lFilter$mQ)[1001:2001, ]

Package 'DMQ'

Help Index

Dynamic Multiple Quantiles model in R

Description

Note

Author(s)

References

Estimate the Dynamic Multiple Quantile (DMQ) model.

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

A wrapper to the DEoptim function of the DEoptim package of Mullen et al. (2011).

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

A wrapper to the optim function.

Description

Usage

Arguments

Details

Value

Author(s)

See Also

A wrapper to the solnp function of the Rsolnp package of Ghalanos and Theussl (2016).

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Forecast with univariate DMQ model

Description

Usage

Arguments

Value

Author(s)

Examples

Estimate conditional moments using DMQ

Description

Usage

Arguments

Details

Value

Author(s)

Examples

data: Microsoft Corporation logarithmic percentage returns from December 8, 2010 to November 15, 2018 for a total of T = 2000 observation downloaded from Yahoo finance.

Description

Usage

Format

Source

References

Simulate from the DMQ model

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Update filtered quantiles

Description

Usage

Arguments

Details

Value

Author(s)

Examples

A wrapper to the DEoptim function of the `DEoptim` package of Mullen et al. (2011).

A wrapper to the solnp function of the `Rsolnp` package of Ghalanos and Theussl (2016).