[Returnanalytics-commits] r2253 - in pkg/PerformanceAnalytics/sandbox/Meucci: . R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Mon Aug 20 00:16:28 CEST 2012
Author: mkshah
Date: 2012-08-20 00:16:28 +0200 (Mon, 20 Aug 2012)
New Revision: 2253
Added:
pkg/PerformanceAnalytics/sandbox/Meucci/man/FitOU.Rd
pkg/PerformanceAnalytics/sandbox/Meucci/man/GenFirstEigVect.Rd
pkg/PerformanceAnalytics/sandbox/Meucci/man/GenPCBasis.Rd
pkg/PerformanceAnalytics/sandbox/Meucci/man/MaxEntropy.Rd
pkg/PerformanceAnalytics/sandbox/Meucci/man/MeanTCEntropyFrontier.Rd
pkg/PerformanceAnalytics/sandbox/Meucci/man/OUstep.Rd
pkg/PerformanceAnalytics/sandbox/Meucci/man/OUstepEuler.Rd
Removed:
pkg/PerformanceAnalytics/sandbox/Meucci/R/EmpiricalMultivariateOUnCointegration.R
pkg/PerformanceAnalytics/sandbox/Meucci/R/TheoryMultivariateOUnCointegration.R
Modified:
pkg/PerformanceAnalytics/sandbox/Meucci/00index
pkg/PerformanceAnalytics/sandbox/Meucci/DESCRIPTION
pkg/PerformanceAnalytics/sandbox/Meucci/R/MeanDiversificationFrontier.R
pkg/PerformanceAnalytics/sandbox/Meucci/R/MultivariateOUnCointegration.R
Log:
Updating documentation
Modified: pkg/PerformanceAnalytics/sandbox/Meucci/00index
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/00index 2012-08-19 21:49:52 UTC (rev 2252)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/00index 2012-08-19 22:16:28 UTC (rev 2253)
@@ -15,9 +15,13 @@
efficientFrontier Construct the mean-variance efficient frontier using a quadratic solver
EntropyProg Entropy pooling program for blending views on scenarios with a prior
scenario-probability distribution
+FitOU Fit the Ornstein-uhlenbeck process to model the behavior for different
+ values of the timestep.
gaussHermiteMesh Generates grid reprensentation of a distribution according to the
method suggested by Meucci and inspired from Gauss-Hermite quadratures.
GenerateLogNormalDistribution Generate arbitrary distribution of a shifted-lognormal invariant
+GenFirstEigVect This function generates the first eigen vector
+GenPCBasis This function computes the conditional principal portfolios
hermitePolynomial Generate a Hermite Polynomial of order n
integrateSubIntervals Integrate the subinterval for the given cumulative distribution
function to get the equivalent probability
@@ -29,11 +33,17 @@
kernelpdf Evaluates probability distribution function for the input numeric value
linreturn Generate arithmetric returns and arithmetric covariance matrix given a
distribution of log returns
+MaxEntropy This function computes the extreme frontier
+MeanTCEntropyFrontier This function computes the mean diversification efficient frontier
MvnRnd Generates normal simulations whose sample moments match the population
moments
NoisyObservations Generate observations from a two asset covariance matrix and add
outliers
normalizeProb Generates the normalized probability for an input probability value
+OUstep Generate the next element based on Ornstein-Uhlenbeck Process
+OUstepEuler Generate the next element based on Ornstein-Uhlenbeck process using
+ antithetic concept and assuming that the Brownian motion has Euler
+ discretization
PanicCopula Copula-Marginal Algorithm (CMA)
PartialConfidencePosterior Constructs the partial confidence posterior based on a prior, sample
mu/covariance, and relative confidence in the prior
Modified: pkg/PerformanceAnalytics/sandbox/Meucci/DESCRIPTION
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/DESCRIPTION 2012-08-19 21:49:52 UTC (rev 2252)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/DESCRIPTION 2012-08-19 22:16:28 UTC (rev 2253)
@@ -1,35 +1,37 @@
-Package: Meucci
-Type: Package
-Title: Econometric tools for performance and risk analysis.
-Version: 0.1
-Date: $Date: 2012-06-06 15:18:48 -0500 (Wed, 06 Jun 2012) $
-Author: Ram Ahluwalia, Manan Shah
-Maintainer: Brian G. Peterson <brian at braverock.com>
-Description: stub for Meucci
-Depends:
- R (>= 2.14.0),
- zoo,
- xts (>= 0.8),
- matlab,
- ggplot2,
- MASS,
- pracma,
- Hmisc,
- Matrix,
- nloptr,
- limSolve,moments,
- quadprog
-License: GPL
-URL: http://r-forge.r-project.org/projects/returnanalytics/
-Copyright: (c) 2004-2012
-Collate:
- 'CmaCopula.R'
- 'DetectOutliersviaMVE.R'
- 'EntropyProg.R'
- 'FullyFlexibleBayesNets.R'
- 'HermiteGrid.R'
- 'InvariantProjection.R'
- 'logToArithmeticCovariance.R'
- 'Prior2Posterior.R'
- 'RankingInformation.R'
- 'RobustBayesianAllocation.R'
+Package: Meucci
+Type: Package
+Title: Econometric tools for performance and risk analysis.
+Version: 0.1
+Date: $Date: 2012-06-06 15:18:48 -0500 (Wed, 06 Jun 2012) $
+Author: Ram Ahluwalia, Manan Shah
+Maintainer: Brian G. Peterson <brian at braverock.com>
+Description: stub for Meucci
+Depends:
+ R (>= 2.14.0),
+ zoo,
+ xts (>= 0.8),
+ matlab,
+ ggplot2,
+ MASS,
+ pracma,
+ Hmisc,
+ Matrix,
+ nloptr,
+ limSolve,moments,
+ quadprog
+License: GPL
+URL: http://r-forge.r-project.org/projects/returnanalytics/
+Copyright: (c) 2004-2012
+Collate:
+ 'CmaCopula.R'
+ 'DetectOutliersviaMVE.R'
+ 'EntropyProg.R'
+ 'FullyFlexibleBayesNets.R'
+ 'HermiteGrid.R'
+ 'InvariantProjection.R'
+ 'logToArithmeticCovariance.R'
+ 'Prior2Posterior.R'
+ 'RankingInformation.R'
+ 'RobustBayesianAllocation.R'
+ 'MeanDiversificationFrontier.R'
+ 'MultivariateOUnCointegration.R'
\ No newline at end of file
Deleted: pkg/PerformanceAnalytics/sandbox/Meucci/R/EmpiricalMultivariateOUnCointegration.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/R/EmpiricalMultivariateOUnCointegration.R 2012-08-19 21:49:52 UTC (rev 2252)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/R/EmpiricalMultivariateOUnCointegration.R 2012-08-19 22:16:28 UTC (rev 2253)
@@ -1,78 +0,0 @@
-FitOU = function ( Y, tau )
-{
- library(expm)
- T = nrow( Y )
- N = ncol( Y )
-
- X = Y[ -1 , ]
- F = cbind( rep( 1, T-1 ), Y [ 1:T-1 ,] )
- E_XF = t( X ) %*% F / T
- E_FF = t( F ) %*% F / T
- B = E_XF %*% solve( E_FF )
-
- Th = -logm ( B [ , -1 ] ) / tau
- Mu = solve( diag( N ) - B[ , -1 ] ) %*% B[ , 1 ]
-
- U = F %*% t( B ) - X
- Sig_tau = cov( U )
-
- N = length( Mu )
- TsT = kronecker( Th , diag( N ) ) + kronecker( diag( N ) , Th )
-
- VecSig_tau = Sig_tau
- dim( VecSig_tau ) = c( N^2 , 1 )
- VecSig = solve( diag( N^2 ) - expm( as.matrix( -TsT * tau ) ) ) %*% TsT %*% VecSig_tau
- Sig = VecSig
- dim( Sig ) = c( N , N )
-
- return( list( Mu = Mu, Th = Th, Sig = Sig ) )
-}
-
-OUstep = function( X_0 , t , Mu , Th , Sig )
-{
- NumSimul = nrow( X_0 )
- N = ncol( X_0 )
-
- # location
- ExpM = expm( as.matrix ( -Th * t ) )
-
- # repmat = function(X,m,n) - R equivalent of repmat (matlab)
- X = t( Mu - ExpM %*% Mu )
- mx = dim( X )[1]
- nx = dim( X )[2]
- Mu_t = matrix( t ( matrix( X , mx , nx*1 ) ), mx * NumSimul, nx * 1, byrow = T ) + X_0 %*% ExpM
-
- # scatter
- TsT = kronecker( Th , diag( N ) ) + kronecker( diag( N ) , Th )
-
- VecSig = Sig
- dim( VecSig ) = c( N^2 , 1 )
- VecSig_t = solve( TsT ) %*% ( diag( N^2 ) - expm( as.matrix( -TsT * t ) ) ) %*% VecSig
- Sig_t = VecSig_t
- dim( Sig_t ) = c( N , N )
- Sig_t = ( Sig_t + t( Sig_t ) ) / 2
-
- Eps = mvrnorm( NumSimul, rep( 0 , N ), Sig_t )
-
- X_t = Mu_t + Eps
- Mu_t = t( colMeans( Mu_t ) )
-
- return( list( X_t = X_t, Mu_t = Mu_t, Sig_t = Sig_t ) )
-}
-
-ProjectOU = function( x_0 , t , Mu , Th , Sig )
-{
- N = length( x_0 )
-
- # location
- Mu_t = Mu + expm( as.matrix( -Th * t ) ) %*% ( x_0 - Mu )
-
- # scatter
- TsT = kronecker( Th , diag( N ) ) + kronecker( diag( N ) , Th )
-
- VecSig = Sig
- dim( VecSig ) = c( N^2 , 1 )
- VecSig_t = solve( TsT ) %*% ( diag( N^2 ) - expm( as.matrix( -TsT * t ) ) ) %*% VecSig
- Sig_t = VecSig_t
- dim( Sig_t ) = c( N , N )
-}
\ No newline at end of file
Modified: pkg/PerformanceAnalytics/sandbox/Meucci/R/MeanDiversificationFrontier.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/R/MeanDiversificationFrontier.R 2012-08-19 21:49:52 UTC (rev 2252)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/R/MeanDiversificationFrontier.R 2012-08-19 22:16:28 UTC (rev 2253)
@@ -38,6 +38,7 @@
#' @return E a matrix containing conditional principal portfolios composition
#' @return L a matrix containing conditional principal portfolios variances
#' @return G map weights -> conditional diversification distribution (square root of, not normalized)
+#'
#' \deqn{ e_{n} \equiv argmax_{ e'e \equiv 1 } \big\{ e' \Sigma e \big\} s.t. e' \Sigma e_{j} \equiv 0 }
#' @references
#' A. Meucci - "Managing Diversification", Risk Magazine, June 2009 - Formula (12)
@@ -104,6 +105,7 @@
#' @param Constr a list containing the equality and inequality constraints
#'
#' @return x a numeric containing the maximum entropy
+#'
#' \deqn{ N_{ent} \equiv exp \big(-\sum_{n=k+1}^N p_{n} ln p_{n} \big),
#' w_{ \varphi } \equiv argmax_{w \in C, \mu'w \geq \varphi } N_{ent} \big(w\big) }
#' @references
Modified: pkg/PerformanceAnalytics/sandbox/Meucci/R/MultivariateOUnCointegration.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/R/MultivariateOUnCointegration.R 2012-08-19 21:49:52 UTC (rev 2252)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/R/MultivariateOUnCointegration.R 2012-08-19 22:16:28 UTC (rev 2253)
@@ -53,7 +53,7 @@
#' Brownian motion has Euler discretization
#'
#' @param X_0 a matrix containing the starting value of each process
-#' @param t a numeric containing the timestep
+#' @param Dt a numeric containing the timestep
#' @param Mu a vector containing the unconditional expectation of the process
#' @param Th a transition matrix, i.e., a fully generic square matrix that steers the deterministic portion
#' of the evolution of the process
Deleted: pkg/PerformanceAnalytics/sandbox/Meucci/R/TheoryMultivariateOUnCointegration.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/R/TheoryMultivariateOUnCointegration.R 2012-08-19 21:49:52 UTC (rev 2252)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/R/TheoryMultivariateOUnCointegration.R 2012-08-19 22:16:28 UTC (rev 2253)
@@ -1,54 +0,0 @@
-OUstep = function( X_0 , t , Mu , Th , Sig )
-{
- NumSimul = nrow( X_0 )
- N = ncol( X_0 )
-
- # location
- ExpM = expm( -Th * t )
-
- # repmat = function(X,m,n) - R equivalent of repmat (matlab)
- X = t( Mu - ExpM %*% Mu )
- mx = dim( X )[1]
- nx = dim( X )[2]
- Mu_t = matrix( t ( matrix( X , mx , nx*1 ) ), mx * NumSimul, nx * 1, byrow = T ) + X_0 %*% ExpM
-
- # scatter
- TsT = kronecker( Th , diag( N ) ) + kronecker( diag( N ) , Th )
-
- VecSig = Sig
- dim( VecSig ) = c( N^2 , 1 )
- VecSig_t = solve( TsT ) %*% ( diag( N^2 ) - expm( -TsT * t ) ) %*% VecSig
- Sig_t = VecSig_t
- dim( Sig_t ) = c( N , N )
- Sig_t = ( Sig_t + t( Sig_t ) ) / 2
-
- Eps = mvrnorm( NumSimul, rep( 0 , N ), Sig_t )
-
- X_t = Mu_t + Eps
- Mu_t = t( colMeans( Mu_t ) )
-
- return( list( X_t = X_t, Mu_t = Mu_t, Sig_t = Sig_t ) )
-}
-
-OUstepEuler = function( X_0 , Dt , Mu , Th , Sig )
-{
- NumSimul = nrow( X_0 )
- N = ncol( X_0 )
-
- # location
- ExpM = expm( as.matrix( -Th %*% Dt ) )
-
- # repmat = function(X,m,n) - R equivalent of repmat (matlab)
- X = t( Mu - ExpM %*% Mu )
- mx = dim( X )[1]
- nx = dim( X )[2]
- Mu_t = matrix( t ( matrix( X , mx , nx*1 ) ), mx * NumSimul, nx * 1, byrow = T ) + X_0 %*% ExpM
-
- # scatter
- Sig_t = Sig %*% Dt
- Eps = mvrnorm( NumSimul / 2, rep( 0 , N ) , Sig_t )
- Eps = rbind( Eps, -Eps)
-
- X_t = Mu_t + Eps
- Mu_t = t( colMeans( X_t ) )
-}
\ No newline at end of file
Added: pkg/PerformanceAnalytics/sandbox/Meucci/man/FitOU.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/man/FitOU.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/man/FitOU.Rd 2012-08-19 22:16:28 UTC (rev 2253)
@@ -0,0 +1,42 @@
+\name{FitOU}
+\alias{FitOU}
+\title{Fit the Ornstein-uhlenbeck process to model the behavior for different values of the timestep.}
+\usage{
+ FitOU(Y, tau)
+}
+\arguments{
+ \item{Y}{a matrix containing the value of a process at
+ various time steps.}
+
+ \item{tau}{a numeric containing the timestep}
+}
+\value{
+ a list containing
+
+ Mu a vector containing the expectation of the process
+
+ Sig a matrix containing the covariance of the resulting
+ fitted OU process
+
+ Th a transition matrix required for defining the fitted
+ OU process
+
+ \deqn{ x_{t+ \tau } = \big(I- e^{- \theta \tau } \big)
+ \mu + e^{- \theta \tau } x_{t}, vec \big( \Sigma _{ \tau
+ } \big) \equiv \big( \Theta \oplus \Theta \big) ^{-1}
+ \big(I- e^{( \Theta \oplus \Theta ) \tau } \big) vec
+ \big( \Sigma \big) }
+}
+\description{
+ Fit the Ornstein-uhlenbeck process to model the behavior
+ for different values of the timestep.
+}
+\author{
+ Manan Shah \email{mkshah at cmu.edu}
+}
+\references{
+ A. Meucci - "Review of Statistical Arbitrage,
+ Cointegration, and Multivariate Ornstein-Uhlenbeck" -
+ Formula (8),(9) \url{http://ssrn.com/abstract=1404905}
+}
+
Added: pkg/PerformanceAnalytics/sandbox/Meucci/man/GenFirstEigVect.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/man/GenFirstEigVect.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/man/GenFirstEigVect.Rd 2012-08-19 22:16:28 UTC (rev 2253)
@@ -0,0 +1,25 @@
+\name{GenFirstEigVect}
+\alias{GenFirstEigVect}
+\title{This function generates the first eigen vector}
+\usage{
+ GenFirstEigVect(S, A)
+}
+\arguments{
+ \item{S}{Covariance Matrix}
+
+ \item{A}{Conditioning Matrix}
+}
+\value{
+ e First Eigen Vector
+}
+\description{
+ This function generates the first eigen vector
+}
+\author{
+ Manan Shah \email{mkshah at cmu.edu}
+}
+\references{
+ A. Meucci - "Managing Diversification", Risk Magazine,
+ June 2009 \url{http://ssrn.com/abstract=1358533}
+}
+
Added: pkg/PerformanceAnalytics/sandbox/Meucci/man/GenPCBasis.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/man/GenPCBasis.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/man/GenPCBasis.Rd 2012-08-19 22:16:28 UTC (rev 2253)
@@ -0,0 +1,39 @@
+\name{GenPCBasis}
+\alias{GenPCBasis}
+\title{This function computes the conditional principal portfolios}
+\usage{
+ GenPCBasis(S, A)
+}
+\arguments{
+ \item{S}{Covariance Matrix}
+
+ \item{A}{Conditioning Matrix}
+}
+\value{
+ a list containing
+
+ E a matrix containing conditional principal portfolios
+ composition
+
+ L a matrix containing conditional principal portfolios
+ variances
+
+ G map weights -> conditional diversification distribution
+ (square root of, not normalized)
+
+ \deqn{ e_{n} \equiv argmax_{ e'e \equiv 1 } \big\{ e'
+ \Sigma e \big\} s.t. e' \Sigma e_{j} \equiv 0 }
+}
+\description{
+ This function computes the conditional principal
+ portfolios
+}
+\author{
+ Manan Shah \email{mkshah at cmu.edu}
+}
+\references{
+ A. Meucci - "Managing Diversification", Risk Magazine,
+ June 2009 - Formula (12)
+ \url{http://ssrn.com/abstract=1358533}
+}
+
Added: pkg/PerformanceAnalytics/sandbox/Meucci/man/MaxEntropy.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/man/MaxEntropy.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/man/MaxEntropy.Rd 2012-08-19 22:16:28 UTC (rev 2253)
@@ -0,0 +1,37 @@
+\name{MaxEntropy}
+\alias{MaxEntropy}
+\title{This function computes the extreme frontier}
+\usage{
+ MaxEntropy(G, w_b, w_0, Constr)
+}
+\arguments{
+ \item{G}{map weights -> conditional diversification
+ distribution (square root of, not normalized)}
+
+ \item{w_b}{a matrix containing the benchmark weights}
+
+ \item{w_0}{a matrix containing the initial portfolio
+ weights}
+
+ \item{Constr}{a list containing the equality and
+ inequality constraints}
+}
+\value{
+ x a numeric containing the maximum entropy
+
+ \deqn{ N_{ent} \equiv exp \big(-\sum_{n=k+1}^N p_{n} ln
+ p_{n} \big), w_{ \varphi } \equiv argmax_{w \in C, \mu'w
+ \geq \varphi } N_{ent} \big(w\big) }
+}
+\description{
+ This function computes the extreme frontier
+}
+\author{
+ Manan Shah \email{mkshah at cmu.edu}
+}
+\references{
+ A. Meucci - "Managing Diversification", Risk Magazine,
+ June 2009 - Formula (18,19)
+ \url{http://ssrn.com/abstract=1358533}
+}
+
Added: pkg/PerformanceAnalytics/sandbox/Meucci/man/MeanTCEntropyFrontier.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/man/MeanTCEntropyFrontier.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/man/MeanTCEntropyFrontier.Rd 2012-08-19 22:16:28 UTC (rev 2253)
@@ -0,0 +1,44 @@
+\name{MeanTCEntropyFrontier}
+\alias{MeanTCEntropyFrontier}
+\title{This function computes the mean diversification efficient frontier}
+\usage{
+ MeanTCEntropyFrontier(S, Mu, w_b, w_0, Constr)
+}
+\arguments{
+ \item{S}{Covariance Matrix}
+
+ \item{Mu}{a matrix containing the expectations}
+
+ \item{w_b}{a matrix containing the benchmark weights}
+
+ \item{w_0}{a matrix containing the initial portfolio
+ weights}
+
+ \item{Constr}{a list containing the equality and
+ inequality constraints}
+}
+\value{
+ a list containing
+
+ Weights
+
+ Ne_s
+
+ R_2_s
+
+ m_s
+
+ s_S
+}
+\description{
+ This function computes the mean diversification efficient
+ frontier
+}
+\author{
+ Manan Shah \email{mkshah at cmu.edu}
+}
+\references{
+ A. Meucci - "Managing Diversification", Risk Magazine,
+ June 2009 \url{http://ssrn.com/abstract=1358533}
+}
+
Added: pkg/PerformanceAnalytics/sandbox/Meucci/man/OUstep.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/man/OUstep.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/man/OUstep.Rd 2012-08-19 22:16:28 UTC (rev 2253)
@@ -0,0 +1,50 @@
+\name{OUstep}
+\alias{OUstep}
+\title{Generate the next element based on Ornstein-Uhlenbeck Process}
+\usage{
+ OUstep(X_0, t, Mu, Th, Sig)
+}
+\arguments{
+ \item{X_0}{a matrix containing the starting value of each
+ process}
+
+ \item{t}{a numeric containing the timestep}
+
+ \item{Mu}{a vector containing the unconditional
+ expectation of the process}
+
+ \item{Th}{a transition matrix, i.e., a fully generic
+ square matrix that steers the deterministic portion of
+ the evolution of the process}
+
+ \item{Sig}{a square matrix that drives the dispersion of
+ the process}
+}
+\value{
+ a list containing
+
+ X_t a vector containing the value of the process after
+ the given timestep
+
+ Mu_t a vector containing the conditional expectation of
+ the process
+
+ Sig_t a matrix containing the covariance after the time
+ step
+
+ \deqn{ X_{t+ \tau } = \big(I- e^{- \theta \tau } \big)
+ \mu + e^{- \theta \tau } X_{t} + \epsilon _{t, \tau } }
+}
+\description{
+ Generate the next element based on Ornstein-Uhlenbeck
+ Process
+}
+\author{
+ Manan Shah \email{mkshah at cmu.edu}
+}
+\references{
+ A. Meucci - "Review of Statistical Arbitrage,
+ Cointegration, and Multivariate Ornstein-Uhlenbeck" -
+ Formula (2) \url{http://ssrn.com/abstract=1404905}
+}
+
Added: pkg/PerformanceAnalytics/sandbox/Meucci/man/OUstepEuler.Rd
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/man/OUstepEuler.Rd (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/man/OUstepEuler.Rd 2012-08-19 22:16:28 UTC (rev 2253)
@@ -0,0 +1,52 @@
+\name{OUstepEuler}
+\alias{OUstepEuler}
+\title{Generate the next element based on Ornstein-Uhlenbeck process using antithetic concept and assuming that the
+Brownian motion has Euler discretization}
+\usage{
+ OUstepEuler(X_0, Dt, Mu, Th, Sig)
+}
+\arguments{
+ \item{X_0}{a matrix containing the starting value of each
+ process}
+
+ \item{Dt}{a numeric containing the timestep}
+
+ \item{Mu}{a vector containing the unconditional
+ expectation of the process}
+
+ \item{Th}{a transition matrix, i.e., a fully generic
+ square matrix that steers the deterministic portion of
+ the evolution of the process}
+
+ \item{Sig}{a square matrix that drives the dispersion of
+ the process}
+}
+\value{
+ a list containing
+
+ X_t a vector containing the value of the process after
+ the given timestep
+
+ Mu_t a vector containing the conditional expectation of
+ the process
+
+ Sig_t a matrix containing the covariance after the time
+ step
+
+ \deqn{ X_{t+ \tau } = \big(I- e^{- \theta \tau } \big)
+ \mu + e^{- \theta \tau } X_{t} + \epsilon _{t, \tau } }
+}
+\description{
+ Generate the next element based on Ornstein-Uhlenbeck
+ process using antithetic concept and assuming that the
+ Brownian motion has Euler discretization
+}
+\author{
+ Manan Shah \email{mkshah at cmu.edu}
+}
+\references{
+ A. Meucci - "Review of Statistical Arbitrage,
+ Cointegration, and Multivariate Ornstein-Uhlenbeck" -
+ Formula (2) \url{http://ssrn.com/abstract=1404905}
+}
+
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