MomentsDMQ {DMQ}

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)

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)