Eviews5 / EViews5 / Example Files / docs / mcapps

Monte Carlo Applications Monte Carlo Applications Small Sample Distribution of ADF test (simadf.prg) Small sample distribution of ADF tests The program simadf.prg follows the analysis in Rudebusch (1993) "The Uncertain Unit Root in Real GNP," American Economic Review, 83, 1, 264-272. The first part of the program fits a trend stationary and difference stationary model to log US GDP. The impulse response functions from the two models are plotted and contrasted. The second part of the program simulates the distribution of the t-statistic for the unit root test under both models. The results are first stored in a matrix object. Then the results are exported to a second workfile where the matrix results are converted to series for further processing. In particular, we plot the kernel density estimates of the simulated distributions of the t-statistic and compute the size and power of the ADF test. ' program to simulate the small sample distribution of ADF test ' checked 3/25/2004 ' ' Rudebusch (1993) "The Uncertain Unit Root in Real GNP," AER, ' 83, 1, 264-272. ' set up workfile wfcreate adftest q 1948:1 1988:4 ' fill GDP series series gdp gdp.fill 1284,1295.69995117,1303.80004883,1316.40002441,1305.30004883,1302,1312.59997559,1301.90002441,1350.90002441,1393.5,1445.19995117,1484.5,1504.09997559,1548.30004883,1585.40002441,1596,1607.69995117,1612.09997559,1621.90002441,1657.80004883,1687.30004883,1695.30004883,1687.90002441,1671.19995117,1660.80004883,1658.40002441,1677.69995117,1698.30004883,1742.5,1758.59997559,1778.19995117,1793.90002441,1787,1798.5,1802.19995117,1826.59997559,1836.40002441,1834.80004883,1851.19995117,1830.5,1790.09997559,1804.40002441,1840.90002441,1880.90002441,1904.90002441,1937.5,1930.80004883,1941.90002441,1976.90002441,1971.69995117,1973.69995117,1961.09997559,1977.40002441,2006,2035.19995117,2076.5,2103.80004883,2125.69995117,2142.60009766,2140.19995117,2170.89990234,2199.5,2237.60009766,2254.5,2311.10009766,2329.89990234,2357.39990234,2364,2410.10009766,2442.80004883,2485.5,2543.80004883,2596.80004883,2601.39990234,2626.10009766,2640.5,2657.19995117,2669,2699.5,2715.10009766,2752.10009766,2796.89990234,2816.80004883,2821.69995117,2864.60009766,2867.80004883,2884.5,2875.10009766,2867.80004883,2859.5,2895,2873.30004883,2939.89990234,2944.19995117,2962.30004883,2977.30004883,3037.30004883,3089.69995117,3125.80004883,3175.5,3253.30004883,3267.60009766,3264.30004883,3289.10009766,3259.39990234,3267.60009766,3239.10009766,3226.39990234,3154,3190.39990234,3249.89990234,3292.5,3356.69995117,3369.19995117,3381,3416.30004883,3466.39990234,3525,3574.39990234,3567.19995117,3591.80004883,3707,3735.60009766,3779.60009766,3780.80004883,3784.30004883,3807.5,3814.60009766,3830.80004883,3732.60009766,3733.5,3808.5,3860.5,3844.39990234,3864.5,3803.10009766,3756.10009766,3771.10009766,3754.39990234,3759.60009766,3783.5,3886.5,3944.39990234,4012.10009766,4089.5,4144,4166.39990234,4194.20019531,4221.79980469,4254.79980469,4309,4333.5,4390.5,4387.70019531,4412.60009766,4427.10009766,4460,4515.29980469,4559.29980469,4625.5,4655.29980469,4704.79980469,4734.5,4779.70019531 ' work with log transformation series ly = log(gdp) ' estimate trend stationary model equation eq_ts.ls ly c @trend+1 ly(-1) ly(-2) ' estimate difference stationary model equation eq_ds.ls d(ly) c d(ly(-1)) ' compute impulse response from each model ' initialize impulse and response series series u = 0 series ly_ts = 0 series ly_ds = 0 ' create the impulse series U smpl 48:3 48:3 series u = 1 smpl 48:3 88:4 ' compute impulse response from trend stationary model ly_ts = eq_ts.@coefs(3)*ly_ts(-1) + eq_ts.@coefs(4)*ly_ts(-2) + u ' compute impulse response from difference stationary model ly_ds = ly_ds(-1) + eq_ds.@coefs(2)*d(ly_ds(-1)) + u ' plot the impulse responses smpl 48:3 58:3 graph gh1.line ly_ts ly_ds ' label graph gh1.setelem(1) legend(Trend stationary model) gh1.setelem(2) legend(Difference stationary model) gh1.addtext(t) Impulse Response Functions show gh1 '-------------------------------------------------------------------------- ' simulate ADF t-stats from each model '-------------------------------------------------------------------------- ' initialize simulated series smpl 48:1 48:2 series lyts = ly series lyds = ly ' declare matrix to store simulated ADF t-stats !n = 1000 ' number of replications matrix(!n,2) adft ' declare working equation equation eq_test ' monte carlo loop rndseed 123456789 smpl 48:3 @last for !i = 1 to !n ' trend stationary model ' simulate series lyts = eq_ts.@coefs(1) + eq_ts.@coefs(2)*(@trend+1) + eq_ts.@coefs(3)*lyts(-1) + eq_ts.@coefs(4)*lyts(-2) + eq_ts.@se*nrnd ' run ADF test eq_test.ls d(lyts) lyts(-1) c @trend+1 d(lyts(-1)) ' store t-stat adft(!i,1) = eq_test.@tstat(1) ' difference stationary model ' simulate series lyds = lyds(-1) + eq_ds.@coefs(1) + eq_ds.@coefs(2)*d(lyds(-1)) + eq_ds.@se*nrnd ' run ADF test eq_test.ls d(lyds) lyds(-1) c @trend+1 d(lyds(-1)) ' store t-stat adft(!i,2) = eq_test.@tstat(1) next ' store actual ADF t-stat eq_test.ls d(ly) ly(-1) c @trend+1 d(ly(-1)) !tadf = eq_test.@tstat(1) ' store results to database db db_mcarlo.edb store adft ' close workfile close adftest '-------------------------------------------------------------------------- ' process results as series in new workfile '-------------------------------------------------------------------------- ' create new workfile wfcreate result u 1 !n ' fetch results fetch adft ' declare series series t_ts series t_ds ' convert simulated t-stats to series group gr1 t_ts t_ds mtos(adft,gr1) ' determine knots for kernel density estimates ' to ensure it fits in current workfile !knots = 100 if (!knots>!n) then !knots = !n endif smpl 1 !knots for %mod ts ds ' store kernel density estimates do t_{%mod}.kdensity(!knots, o=kdmat_{%mod}) ' convert density estimates to series series kd{%mod}_x series kd{%mod}_f group g{%mod} kd{%mod}_x kd{%mod}_f mtos(kdmat_{%mod}, g{%mod}) next 'compute empirical size of test ' area of H0 to the left of !tadf smpl @all if t_ds<=!tadf !siz = @obs(t_ds)/!n 'compute empirical power of test ' area of H1 to the left of !tadf smpl @all if t_ts<=!tadf !pow = @obs(t_ts)/!n ' plot the two density estimates in one graph smpl 1 !knots group g3 gts gds freeze(graph1) g3.xyline(b) 'graph1.setelem(1) legend(Alternative (trend stationary)) 'graph1.setelem(2) legend(Null (difference stationary)) graph1.addtext(t) Kernel density estimates of simulated t-distribution graph1.legend -display graph1.addtext(1.2,0.1) H1 (trend stationary) graph1.addtext(1.8,0.8) H0 (difference stationary) ' draw vertical dashline at actual t-stat graph1.draw(dashline, bottom, rgb(156,156,156)) !tadf graph1.addtext(2.8,2.4) size = !siz graph1.addtext(2.8,2.6) power = !pow show graph1 stop ^Top