[Returnanalytics-commits] r2244 - pkg/PerformanceAnalytics/sandbox/Meucci/demo

[noreply at r-forge.r-project.org]

Author: mkshah
Date: 2012-08-19 04:14:36 +0200 (Sun, 19 Aug 2012)
New Revision: 2244

Added:
   pkg/PerformanceAnalytics/sandbox/Meucci/demo/S_DeterministicEvolution.R
Log:
Additional demo for Theoretical Multivariate OU and Cointegration

Added: pkg/PerformanceAnalytics/sandbox/Meucci/demo/S_DeterministicEvolution.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/demo/S_DeterministicEvolution.R	                        (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/demo/S_DeterministicEvolution.R	2012-08-19 02:14:36 UTC (rev 2244)
@@ -0,0 +1,51 @@
+# This script animates the evolution of the determinstic component of an OU process 
+# see A. Meucci (2009) 
+# "Review of Statistical Arbitrage, Cointegration, and Multivariate Ornstein-Uhlenbeck"
+# available at ssrn.com
+
+# Code by A. Meucci, April 2009
+# Most recent version available at www.symmys.com > Teaching > MATLAB
+
+# input parameters of multivariate OU process
+K = 1
+J = 1
+
+x0 = rep( 1, K + 2*J )
+
+Mu = 0 * matrix( runif(K + 2*J), ncol = 1 )
+
+A = rbind( c(1,0,0), c(0,1,0), c(0,0,1) )
+
+ls = -10
+gs = 10
+os = 100
+
+ts_0 = .001 * as.matrix( seq( from = 0, to = 300, by = 1 ) )
+
+# process inputs
+Gamma = diag( ls, nrow = length( ls ) )
+for( j in 1:J )
+{
+  G = rbind( cbind( gs[j], os[j] ), cbind( -os[j], gs[j] ) )
+  Gamma = as.matrix( bdiag( Gamma , G ) )
+}
+
+Theta = A %*% Gamma %*% solve( A )
+
+# process dynamics 
+S = 0 * matrix( runif( ( K + 2*J )^2 ), nrow = K + 2*J, byrow = T )
+Sigma = S %*% t( S )
+X_t = matrix(0, nrow = nrow( Theta ), ncol = length( ts_0 ) )
+for( j in 1 : length( ts_0 ) )
+{
+  t = ts_0[ j ]
+  X_t[ , j ] = OUstep( t( x0 ) , t , Mu , Theta , Sigma )$X_t
+}
+
+# plots
+plot( ts_0 , X_t[ 1 , ] )
+plot( ts_0 , X_t[ 2 , ] )
+plot( ts_0 , X_t[ 3 , ] )
+
+# t = 0:pi/50:10*pi;
+# AnimateTrajectory(X_t(1,:),X_t(2,:),X_t(3,:))