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Graphs Graphs Shade U.S. recessions as identified by NBER (ShadeUSRecessions.prg) Plotting empirical distribution functions (edfplot.prg) Plotting joint confidence ellipse (joint.prg) Shade U.S. recessions as identified by NBER

The following program uses command line options to customize the look of a graph. It calls a subroutine to add shades for the periods identified as U.S. recessions by the NBER. The NBER U.S. business cycle expansion and contraction definitions may be found at http://www.nber.org/cycles.html. ' shade U.S. recessions identified by NBER ' last revised 3/24/2004 'include subroutine file include sub_ShadeUSRecessions.prg 'change path to program path %path = @runpath cd %path ' create workfile wfcreate tmp1 q 1948:1 1998:4 ' fetch data from database fetch(d=data_svar) rgnp unemp ' plot data group g1 dlog(rgnp) unemp freeze(graph1) g1.line ' set legend text graph1.setelem(1) legend(Real GNP growth) graph1.setelem(2) legend(Unemployment rate) ' dual scaling graph1.setelem(2) axis(right) ' set frame size graph1.options size(8,2) ' draw zero line graph1.draw(dashline, left, rgb(172,172,172)) 0 ' shade recessions call shadeUSRecessions(graph1, 4) show graph1 The subroutine file sub_shadeUSRecessions.prg contains: ' shade recessions identified by NBER ' last revised 3/27/2004 ' ' g1: name of graph object to add shades ' f : scalar for frequency (f=4 for quarterly and f=12 for monthly) subroutine shadeUSRecessions(graph g1, scalar f) if (f = 12) then g1.draw(shade,bottom) 1857:06 1858:12 g1.draw(shade,bottom) 1860:10 1861:06 g1.draw(shade,bottom) 1865:04 1867:12 g1.draw(shade,bottom) 1869:06 1870:12 g1.draw(shade,bottom) 1873:10 1879:03 g1.draw(shade,bottom) 1882:03 1885:05 g1.draw(shade,bottom) 1887:03 1888:04 g1.draw(shade,bottom) 1890:07 1891:05 g1.draw(shade,bottom) 1893:01 1894:06 g1.draw(shade,bottom) 1895:12 1897:06 g1.draw(shade,bottom) 1899:06 1900:12 g1.draw(shade,bottom) 1902:09 1904:08 g1.draw(shade,bottom) 1907:05 1908:06 g1.draw(shade,bottom) 1910:01 1912:01 g1.draw(shade,bottom) 1913:01 1914:12 g1.draw(shade,bottom) 1918:08 1919:03 g1.draw(shade,bottom) 1920:01 1921:07 g1.draw(shade,bottom) 1923:05 1924:07 g1.draw(shade,bottom) 1926:10 1927:11 g1.draw(shade,bottom) 1929:08 1933:03 g1.draw(shade,bottom) 1937:05 1938:06 g1.draw(shade,bottom) 1945:02 1945:10 g1.draw(shade,bottom) 1948:11 1949:10 g1.draw(shade,bottom) 1953:07 1954:05 g1.draw(shade,bottom) 1957:08 1958:04 g1.draw(shade,bottom) 1960:04 1961:02 g1.draw(shade,bottom) 1969:12 1970:11 g1.draw(shade,bottom) 1973:11 1975:03 g1.draw(shade,bottom) 1980:01 1980:07 g1.draw(shade,bottom) 1981:07 1982:11 g1.draw(shade,bottom) 1990:07 1991:03 g1.draw(shade,bottom) 2001:03 2001:11 else if (f = 4) then g1.draw(shade,bottom) 1857:2 1858:4 g1.draw(shade,bottom) 1860:4 1861:2 g1.draw(shade,bottom) 1865:2 1867:4 g1.draw(shade,bottom) 1869:2 1870:4 g1.draw(shade,bottom) 1873:4 1879:1 g1.draw(shade,bottom) 1882:1 1885:2 g1.draw(shade,bottom) 1887:1 1888:2 g1.draw(shade,bottom) 1890:3 1891:2 g1.draw(shade,bottom) 1893:1 1894:2 g1.draw(shade,bottom) 1895:4 1897:2 g1.draw(shade,bottom) 1899:2 1900:4 g1.draw(shade,bottom) 1902:3 1904:3 g1.draw(shade,bottom) 1907:2 1908:2 g1.draw(shade,bottom) 1910:1 1912:1 g1.draw(shade,bottom) 1913:1 1914:4 g1.draw(shade,bottom) 1918:3 1919:1 g1.draw(shade,bottom) 1920:1 1921:3 g1.draw(shade,bottom) 1923:2 1924:3 g1.draw(shade,bottom) 1926:4 1927:4 g1.draw(shade,bottom) 1929:3 1933:1 g1.draw(shade,bottom) 1937:2 1938:2 g1.draw(shade,bottom) 1945:1 1945:4 g1.draw(shade,bottom) 1948:4 1949:4 g1.draw(shade,bottom) 1953:3 1954:2 g1.draw(shade,bottom) 1957:3 1958:2 g1.draw(shade,bottom) 1960:2 1961:1 g1.draw(shade,bottom) 1969:4 1970:4 g1.draw(shade,bottom) 1973:4 1975:1 g1.draw(shade,bottom) 1980:1 1980:3 g1.draw(shade,bottom) 1981:3 1982:4 g1.draw(shade,bottom) 1990:3 1991:1 g1.draw(shade,bottom) 2001:1 2001:4 else statusline currently only monthly or quarterly frequency supported! endif endif endsub ^Top

Plotting empirical distribution functions

EViews 5  includes built-in tests for goodness-of-fit based on empirical distribution functions. The program EDFPLOT.PRG illustrates how to obtain graphical output to assess the goodness-of-fit. In particular, it illustrates how to overlay the kernel density plot with the theoretical density under test. 'plots for goodness-of-fit tests 'last checked 3/27/2004 '-------------------------------------------------------------------------------------- 'subroutines '-------------------------------------------------------------------------------------- 'evaluate weibull density at xt and store in fx subroutine eval_weibull(series xt, series fx, scalar m, scalar s, scalar a) series zt = (xt - m)/s fx = (a/s) * zt^(a-1) * exp( -(zt^a) ) endsub 'evaluate Gaussian density at xt and store in fx subroutine eval_norm(series xt, series fx, scalar m, scalar s) series zt = (xt - m)/s !pi = @acos(-1) fx = (1/@sqrt(2*!pi)/s) * exp( -(0.5*zt^2) ) endsub '-------------------------------------------------------------------------------------- 'main program '-------------------------------------------------------------------------------------- 'overlay theoretical and empirical distribution wfcreate edfplot u 1 500 'set random number generator rndseed(type=mt) 1234567 'simulate data series x = @rchisq(5) 'kernel density estimate !ngrid = 150 'number of points to evaluate do x.kdensity(!ngrid, b=2.3, o=kdxy) 'make sure workfile is large enough if (@obsrange < !ngrid) then expand 1 !ngrid endif 'convert stored estimates into series smpl 1 !ngrid series xt series ft_kdensity group group1 xt ft_kdensity mtos(kdxy, group1) 'evaluate theoretical distribution at xt series ft_dist call eval_norm(xt, ft_dist, @mean(x), @stdev(x)) graph g1.xyline xt ft_dist ft_kdensity g1.option linepat ' need to set linepat g1.setelem(1) legend() g1.setelem(2) legend(normal) g1.setelem(3) legend(kernel density) g1.setelem(1) lcolor(blue) lpat(dash1) g1.setelem(2) lcolor(red) lpat(solid) g1.legend columns(1) -inbox position(2.3,0) 'qq-plot freeze(g2) x.qqplot(n) g2.setelem(1) legend() g2.addtext(0.1,0.1) QQ-plot 'combine two graphs graph graph1.merge g2 g1 graph1.align(2,0,0) show graph1 'display goodness-of-fit tests show x.edftest(type=normal,showopts) ^Top

Plotting joint confidence ellipse

The following program plots the joint confidence region (an ellipse) of two parameters estimated by OLS. The program estimates a multiple linear regression, extracts two parameters into a vector and its covariance matrix into a sym matrix and calls a subroutine to plot an ellipse.  Note: EViews version 5.0 or later contains a built-in confidence ellipse function as a view of an equation object. 

' plot joint confidence region of two OLS parameters ' replicates Greene (1993,p.191) ' for version 4 12/20/2000 ' last revised 3/27/2004 ' include subroutine include drawEllipse.prg ' load workfile %data = @runpath + "greene6_2" load %data ' estimate equation by OLS equation eq1.ls y x1 x2 x3 x4 x5 ' get c(2) and c(3) vector(2) beta beta(1) = eq1.c(2) beta(2) = eq1.c(3) ' get covariance martrix of c(2) & c(3) sym(2,2) binv binv(1,1) = eq1.@cov(2,2) binv(1,2) = eq1.@cov(2,3) binv(2,2) = eq1.@cov(3,3) ' and invert binv = @inverse(binv) ' call the subroutine to plot the joint confidence ellipse !fcv95 = @qfdist(0.95, 2, eq1.@regobs-eq1.@ncoef) call drawEllipse(beta, binv, 2*!fcv95, "gra1") ' 3rd arg is critical value ' edit legend and title to graph gra1.setelem(1) legend(b_2) gra1.setelem(2) legend(b_3) gra1.addtext(t) Joint vs Individual 0.95 Confidence Region ' add individual 0.95 region as shades !b_low = eq1.c(2)-2*eq1.@stderrs(2) !b_upp = eq1.c(2)+2*eq1.@stderrs(2) gra1.draw(shade,bottom) !b_low !b_upp gra1.draw(dashline,bottom) !b_low gra1.draw(dashline,bottom) !b_upp !b_low = eq1.c(3)-2*eq1.@stderrs(3) !b_upp = eq1.c(3)+2*eq1.@stderrs(3) gra1.draw(shade,left) !b_low !b_upp gra1.draw(dashline,left) !b_low gra1.draw(dashline,left) !b_upp show gra1 The subroutine to draw the ellipse is given by: ' subroutine to plot an ellipse represented as a quadratic form ' (x-x0)'B(x-x0) = c ' ' where the inputs are ' ' x0: 2x1 vector ' B: 2x2 symmetric matrix ' c: scalar ' %gname: name for graph object ' ' 1/22/99 h. ' revised 3/27/2004 subroutine drawEllipse(vector x0, sym B, scalar c, string %gname) ' input error check !rows = @rows(B) !cols = @columns(B) if (@rows(x0)<>2 or !rows<>2 or !cols<>2) then statusline input arguments must have dimension 2 return endif ' get eigenvalues/eigenvectors matrix ve = @eigenvectors(B) vector va = @eigenvalues(B) ' construct the rotation matrix !ang = @atan(ve(2,1)/ve(1,1)) ' angle matrix(2,2) rot rot.fill(b=r) @cos(!ang),-@sin(!ang),@sin(!ang),@cos(!ang) ' draw the unrotated ellipse vector(101) theta !pi = @acos(-1) for !i = 1 to 101 theta(!i) = (!i-1)*2*!pi/100 next !a = @sqrt(c/va(1)) ' width of ellipse !b = @sqrt(c/va(2)) matrix(2,101) xy for !i=1 to 101 xy(1,!i) = !a*@cos(theta(!i)) xy(2,!i) = !b*@sin(theta(!i)) next ' rotate matrix rx = rot*xy ' offset matrix ones = @filledmatrix(1,101,1) rx = rx + x0*ones rx = @transpose(rx) ' plot freeze({%gname}) rx.scat ' connect scatter without symbols {%gname}.setelem(1) lpat(solid) symbol(none) endsub ^Top