Changes to Location-Dispersion Ellipsoid Plot

R/PerformIidAnalysis.R

@@ -1,62 +1,63 @@
-#' @title Performs simple invariance (i.i.d.) tests on a time series.
-#'
-#' @description This function performs simple invariance (i.i.d.) tests on a time series, as described in
-#' A. Meucci "Risk and Asset Allocation", Springer, 2005
-#'
-#'  @param	Dates : [vector] (T x 1) dates
-#'	@param	Data  : [matrix] (T x N) data
-#'  @param	Str   : [string]  title for the plot 
-#'  
-#'  @note it checks the evolution over time
-#'
-#'   it checks that the variables are identically distributed by looking at the histogram of two subsamples
-#'
-#'   it checks that the variables are independent by looking at the 1-lag scatter plot
-#'
-#'   under i.i.d. the location-dispersion ellipsoid should be a circle
-#'
-#' @references
-#' A. Meucci - "Exercises in Advanced Risk and Portfolio Management" \url{http://symmys.com/node/170}.
-#'
-#' See Meucci's script for "PerformIidAnalysis.m"
-#'
-#' @author Xavier Valls \email{flamejat@@gmail.com}
-#' @export
-
-PerformIidAnalysis = function( Dates = dim( Data)[1], Data, Str = "")
-{
-
-	##########################################################################################################
-	### Time series over time
-	dev.new(); 
-	plot( Dates, Data, main = Str ); 
-	#datetick( 'x', 'mmmyy', 'keeplimits', 'keepticks' );
-
-
-	##########################################################################################################
-	### Test "identically distributed hypothesis": split observations into two sub-samples and plot histogram
-	Sample_1 = Data[ 1:round(length(Data) / 2) ];
-	Sample_2 = Data[(round(length(Data)/2) + 1) : length(Data) ];
-	num_bins_1 = round(5 * log(length(Sample_1)));
-	num_bins_2 = round(5 * log(length(Sample_2)));
-	X_lim = c( min(Data) - .1 * (max(Data) - min(Data)), max(Data) + .1 * (max(Data) - min(Data)));
-
-	dev.new();
-
-	layout( matrix(c(1,1,2,2,0,3,3,0), 2, 4, byrow = TRUE), heights=c(1,1,1));
-	hist(Sample_1, num_bins_1, xlab = "", ylab = "", main = "first half" );
-	hist(Sample_2, num_bins_2, xlab = "", ylab = "", main = "second half" );
-
-	##########################################################################################################
-	### Test "independently distributed hypothesis": scatter plot of observations at lagged times
-
-
-	X = Data[ 1 : length(Data)-1 ];
-	Y = Data[ 2 : length(Data) ];
-	plot(X, Y, main="changes in implied vol");
-
-	m = cbind( apply( cbind( X, Y ), 2, mean ));
-	S = cov( cbind( X, Y ));
-	TwoDimEllipsoid( m, S, 2, FALSE, FALSE);
-
-}
+#' @title Performs simple invariance (i.i.d.) tests on a time series.
+#'
+#' @description This function performs simple invariance (i.i.d.) tests on a time series, as described in
+#' A. Meucci "Risk and Asset Allocation", Springer, 2005
+#'
+#'  @param	Dates : [vector] (T x 1) dates
+#'	@param	Data  : [matrix] (T x N) data
+#'  @param	Str   : [string]  title for the plot 
+#'  
+#'  @note it checks the evolution over time
+#'
+#'   it checks that the variables are identically distributed by looking at the histogram of two subsamples
+#'
+#'   it checks that the variables are independent by looking at the 1-lag scatter plot
+#'
+#'   under i.i.d. the location-dispersion ellipsoid should be a circle
+#'
+#' @references
+#' A. Meucci - "Exercises in Advanced Risk and Portfolio Management" \url{http://symmys.com/node/170}.
+#'
+#' See Meucci's script for "PerformIidAnalysis.m"
+#'
+#' @author Xavier Valls \email{flamejat@@gmail.com}
+#' @export
+
+PerformIidAnalysis = function( Dates = dim( Data)[1], Data, Str = "")
+{
+
+	##########################################################################################################
+	### Time series over time
+	dev.new(); 
+	plot( Dates, Data, main = Str ); 
+	#datetick( 'x', 'mmmyy', 'keeplimits', 'keepticks' );
+
+
+	##########################################################################################################
+	### Test "identically distributed hypothesis": split observations into two sub-samples and plot histogram
+	Sample_1 = Data[ 1:round(length(Data) / 2) ];
+	Sample_2 = Data[(round(length(Data)/2) + 1) : length(Data) ];
+	num_bins_1 = round(5 * log(length(Sample_1)));
+	num_bins_2 = round(5 * log(length(Sample_2)));
+	X_lim = c( min(Data) - .1 * (max(Data) - min(Data)), max(Data) + .1 * (max(Data) - min(Data)));
+
+	dev.new();
+
+	layout( matrix(c(1,1,2,2,0,3,3,0), 2, 4, byrow = TRUE), heights=c(1,1,1));
+	hist(Sample_1, num_bins_1, xlab = "", ylab = "", main = "first half" );
+	hist(Sample_2, num_bins_2, xlab = "", ylab = "", main = "second half" );
+
+	##########################################################################################################
+	### Test "independently distributed hypothesis": scatter plot of observations at lagged times
+
+
+	X = Data[ 1 : length(Data)-1 ];
+	Y = Data[ 2 : length(Data) ];
+    	par(pty = "s");
+    	plot(X, Y, main = "Location-Dispersion Ellipsoid", asp = 1);
+
+	m = cbind( apply( cbind( X, Y ), 2, mean ));
+	S = cov( cbind( X, Y ));
+	TwoDimEllipsoid( m, S, 2, FALSE, FALSE);
+
+}