FPCA real data analysis

FPCAcomponents/FPCAcomponents

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+% clear variables and close windows
+clear all;
+close all;
+clc;
+
+%%% Start READ REAL DATA
+load Results.mat % the workspace results are generated by the code FPCAreal_data.m
+load('xData.txt','-ascii');
+load('Is.txt','-ascii');
+load('tickdatayear.txt','-ascii');
+
+%%% End READ REAL DATA
+
+%%% Start PLOT FIGURE
+
+% define axis
+axis_x=linspace(min(mx),max(mx),50); % maturity
+axis_y=linspace(min(my),max(my),50); % moneyness
+[Xa,Ya] = meshgrid(axis_x,axis_y);
+
+% interpolate data for the functional components
+FFun1 = TriScatteredInterp(mx,my,V2b(:,1), 'linear');
+FFun2 = TriScatteredInterp(mx,my,V2b(:,2), 'linear');
+FFun3 = TriScatteredInterp(mx,my,V2b(:,3), 'linear');
+FFun4 = TriScatteredInterp(mx,my,V2b(:,4), 'linear');
+FFun5 = TriScatteredInterp(mx,my,V2b(:,5), 'linear');
+FFun6 = TriScatteredInterp(mx,my,V2b(:,6), 'linear');
+FFun7 = TriScatteredInterp(mx,my,V2b(:,7), 'linear');
+FFun8 = TriScatteredInterp(mx,my,V2b(:,8), 'linear');
+
+Za1b=FFun1(Xa,Ya);
+Za2b=FFun2(Xa,Ya);
+Za3b=FFun3(Xa,Ya);
+Za4b=FFun4(Xa,Ya);
+Za5b=FFun5(Xa,Ya);
+Za6b=FFun6(Xa,Ya);
+Za7b=FFun7(Xa,Ya);
+Za8b=FFun8(Xa,Ya);
+
+figure(2)
+hFig = figure(2);
+set(hFig, 'Position', 0.8*[500 500 1000 900])
+
+subplot(3,2,1)
+surfl(Xa,Ya,-Za1b);
+set(gca,'XTick',[0.50 0.75 1 1.25 1.50])
+set(gca,'YTick',[0 0.25 0.50 0.75 1 ])
+xh=xlabel('Moneyness')
+yh=ylabel('Maturity')
+zh=zlabel('$$\hat{\gamma}^{(d)}_{1,T}$$')
+set(zh,'Interpreter','latex')
+set([xh,yh,zh],'fontsize',10)
+set(gca, 'fontsize',10)
+
+subplot(3,2,2)
+plot(xData,-loadsb(1,Is),'blue')
+xlim([min(xData) max(xData)])
+zh=ylabel('$$\hat{\delta}_{1,T}$$')
+set(zh,'Interpreter','latex')
+set(gca,'XTick',tickdatayear([1,3,5,7,9,11]))
+set(gca,'XTickLabel',[2002 2004  2006 2008 2010 2012])
+set(gca, 'LooseInset', get(gca, 'TightInset'));
+set([xh,yh],'fontsize',10)
+set(gca, 'fontsize',10)
+
+subplot(3,2,5)
+surfl(Xa,Ya,-Za7b);
+set(gca,'XTick',[0.50 0.75 1 1.25 1.50])
+set(gca,'YTick',[0 0.25 0.50 0.75 1 ])
+xh=xlabel('Moneyness')
+yh=ylabel('Maturity')
+zh=zlabel('$$\hat{\gamma}^{(d)}_{7,T}$$')
+set(zh,'Interpreter','latex')
+set([xh,yh,zh],'fontsize',10)
+set(gca, 'fontsize',10)
+
+subplot(3,2,6)
+plot(xData,-loadsb(7,Is),'blue')
+xlim([min(xData) max(xData)])
+zh=ylabel('$$\hat{\delta}_{7,T}$$')
+set(zh,'Interpreter','latex')
+set(gca,'XTick',tickdatayear([1,3,5,7,9,11]))
+set(gca,'XTickLabel',[2002 2004  2006 2008 2010 2012])
+set(gca, 'LooseInset', get(gca, 'TightInset'));
+set([xh,yh],'fontsize',10)
+set(gca, 'fontsize',10)
+
+subplot(3,2,3)
+surfl(Xa,Ya,-Za3b);
+set(gca,'XTick',[0.50 0.75 1 1.25 1.50])
+set(gca,'YTick',[0 0.25 0.50 0.75 1 ])
+xh=xlabel('Moneyness')
+yh=ylabel('Maturity')
+zh=zlabel('$$\hat{\gamma}^{(d)}_{3,T}$$')
+set(zh,'Interpreter','latex')
+set([xh,yh,zh],'fontsize',10)
+set(gca, 'fontsize',10)
+
+subplot(3,2,4)
+plot(xData,-loadsb(3,Is),'blue')
+xlim([min(xData) max(xData)])
+zh=ylabel('$$\hat{\delta}_{3,T}$$')
+set(zh,'Interpreter','latex')
+set(gca,'XTick',tickdatayear([1,3,5,7,9,11]))
+set(gca,'XTickLabel',[2002 2004  2006 2008 2010 2012])
+set(gca, 'LooseInset', get(gca, 'TightInset'));
+set([xh,yh],'fontsize',10)
+set(gca, 'fontsize',10)
+
+%%% End PLOT FIGURE

FPCAcomponents/Metainfo.txt

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+Name of Quantlet: FPCAcomponents
+
+Published in: 'Functional Principal Component Analysis for Derivatives of High-Dimensional Spatial Curves'
+
+Description: 'It interpolates the estimated functional components at a common grid and plots them, together with the estimates loadings time series.''
+
+Keywords: estimation, FPCA, call prices, derivative, density, state price density, risk neutral density, functional components, time series, loadings
+
+See also: FPCAgpu, FPCAepan, FPCAmultiloc, FPCAsimulate_input, FPCAindividual, FPCAvariance, FPCAexpiration, FPCAcomponents, FPCAloadings
+
+Author: Maria Grith
+
+Submitted:  Maria Grith
+
+Input:
+            - Results.mat          : Output of FPCAreal_data.m
+            - vdaxm.txt            : VDAX index time series (same date as the loadings)
+            - xData.txt            : date time series
+            - Is.txt               : index for the time series of loadings
+            - tickdatayear.txt     : tick years
+
+Output: 'It plots the functional components and the corresponding loadings.''

FPCAcomponents/tickdatayear.txt

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+   7.3121800e+05   7.3158300e+05   7.3194800e+05   7.3231500e+05   7.3267900e+05   7.3304400e+05   7.3340900e+05   7.3377500e+05   7.3414200e+05   7.3450600e+05   7.3486700e+05