options double crt nodate; name bjnam 'ARIMA(0,0, 1,1, 1,1) - Airline model on 3 Pankratz series'; ? Exact ML estimation ? Follows Newbold, Agiakloglou, and Miller, "Adventures with ARIMA ? Software", International Journal of Forecasting 10, 1994, pp.573-581 ? (abbreviated NAM below) ? The data series are from Pankratz, A. "Forecasting with Dynamic ? Regression Models", 1991, series 12, 23 and 24. Found on the web at ? http://lummi.stanford.edu/class/stat207/WWW/ ? data_page/pankratzdat/pankratz.html (1/98) ? Notes: ? 1. NAM used default convergence criteria, so we would not expect ? the ML1 and ML2 results to agree with TSP to more than 1-3 digits. ? They might well agree to 6 digits if the convergence criteria ? was made especially strict, like it is for TSP here. ? 2. The LogL for the NAM ML1 and ML2 results was computed by TSP, ? using those results to the printed 3 digits. ? 3. For some reason, NAM do not use 12 of the observations for ? each series (for A, they use 168 instead of the full 180, etc.). ? Although they did not say exactly which 12 observations were ? dropped, it appears to be the final 12 months for each series. ? On all 3 series, TSP coefficients match the ML1 and ML2 results ? best when the final 12 months are dropped (versus the first ? 12 months, or zero months). Perhaps these observations were ? to be used for a forecasting performance test. ? 4. The BFGS standard errors computed by TSP do not match the ML1 ? and ML2 standard errors very closely, although these are ? difficult to compute for the second 2 series, when there is ? an MA unit root. ? by Clint Cummins 1/98 ? revised 12/04 - double precision data, numeric second derivatives for SEs ? load; smpl 70:1,84:12; lkwh = log(kwh); ? NAM series A - Pankratz series 12, log of kilowatt hours ? apparently over the sample 70:1,83:12 (skip final 12 months). ? NAM ML1 NAM ML2 TSP ? theta .693 .694 .695934 ? (s.e.) (.057) (.056) (.068610) ? THETA .803 .804 .803243 ? (s.e.) (.076) (.075) (.091994) ? LogL 233.855 233.856 233.856 smpl 70:1,83:12; bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml, nocumpl,noplot,tol=1e-7,grad=c4) lkwh; ? Compute LogL for NAM estimates ?mmake @start .693 .803; ?bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml,nocumpl,noplot,maxit=0) lkwh; ?mmake @start .694 .804; ?bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml,nocumpl,noplot,maxit=0) lkwh; ? NAM series B - Pankratz series 23, Housing Starts ? apparently over the sample 65:1,74:12 (skip final 12 months). ? NAM ML1 NAM ML2 TSP ? theta .270 .269 .271454 ? (s.e.) (.087) (.085) (.083235) ? THETA .967 1.000 1.000000 ? (s.e.) (.601) (153.6) (0) ? LogL -360.755 -360.751 -360.750 smpl 65:1,74:12; bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml, nocumpl,noplot,tol=1e-7,grad=c4) hst23; ? Compute LogL for NAM estimates ?mmake @start .270 .967; ?bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml,nocumpl,noplot,maxit=0) hst23; ?mmake @start .269 1.0; ?bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml,nocumpl,noplot,maxit=0) hst23; ? NAM series C - Pankratz series 24, Housing Sales ? apparently over the sample 65:1,74:12 (skip final 12 months). ? NAM ML1 NAM ML2 TSP ? theta .200 .216 .201153 ? (s.e.) (.086) (.083) (.087025) ? THETA .967 1.000 1.000000 ? (s.e.) (.724) (57.3) (.029658) ? LogL -295.760 -295.745 -295.730 smpl 65:1,74:12; bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml, nocumpl,noplot,tol=1e-7,grad=c4) hsl24; ? Compute LogL for NAM estimates ?mmake @start .200 .967; ?bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml,nocumpl,noplot,maxit=0) hsl24; ?mmake @start .216 1.0; ?bjest(ndiff=1,nsdiff=1,nma=1,nsma=1,exactml,nocumpl,noplot,maxit=0) hsl24; end; noprint; freq m; smpl 70:1,84:12; read kwh; 74.5 64.1 64.2 60.6 61.8 73.1 85.0 81.3 70.3 70.1 70.9 78.6 82.6 70.6 72.7 65.0 62.0 84.9 84.9 89.7 82.5 78.4 79.0 85.9 93.1 84.7 80.8 76.1 83.9 90.9 98.5 114.6 88.0 91.4 94.3 103.6 104.9 89.5 91.1 83.7 88.1 100.0 116.5 122.7 99.8 98.4 94.7 97.2 102.0 87.6 90.7 83.3 89.4 93.6 130.3 111.2 93.3 96.9 99.1 105.9 110.7 100.4 100.1 95.3 99.0 110.7 143.6 131.5 102.6 104.5 103.1 117.4 122.7 107.4 110.2 96.7 98.9 119.8 144.1 143.7 118.0 114.5 120.4 140.4 143.6 114.7 111.4 105.3 115.4 124.4 152.5 130.6 119.6 116.4 121.7 137.6 146.4 130.5 123.5 115.8 115.1 133.6 147.0 157.7 148.5 124.9 130.4 144.1 157.7 143.6 133.8 128.8 124.5 130.5 153.6 157.5 135.1 131.3 142.6 149.4 154.0 145.6 142.3 126.6 124.3 139.6 178.3 162.4 144.8 138.6 140.1 154.5 158.9 144.8 138.4 130.8 129.1 145.1 179.5 172.8 150.8 147.1 146.1 161.9 174.7 157.7 149.7 145.2 143.3 144.2 182.8 190.8 158.3 157.5 157.3 170.3 173.2 153.5 162.1 146.9 144.6 166.3 223.1 236.3 181.8 165.7 168.7 199.0 193.8 174.1 182.9 158.8 165.0 186.8 207.3 238.8 175.6 183.0 181.9 194.7 smpl 65:1,75:12; read hst23; 52.149 47.205 82.150 100.931 98.408 97.351 96.489 88.830 80.876 85.750 72.351 61.198 46.561 50.361 83.236 94.343 84.748 79.828 69.068 69.362 59.404 53.530 50.212 37.972 40.157 40.274 66.592 79.839 87.341 87.594 82.344 83.712 78.194 81.704 69.088 47.026 45.234 55.431 79.325 97.983 86.806 81.424 86.398 82.522 80.078 85.560 64.819 53.847 51.300 47.909 71.941 84.982 91.301 82.741 73.523 69.465 71.504 68.039 55.069 42.827 33.363 41.367 61.879 73.835 74.848 83.007 75.461 77.291 75.961 79.393 67.443 69.041 54.856 58.287 91.584 116.013 115.627 116.946 107.747 111.663 102.149 102.882 92.904 80.362 76.185 76.306 111.358 119.840 135.167 131.870 119.078 131.324 120.491 116.990 97.428 73.195 77.105 73.560 105.136 120.453 131.643 114.822 114.746 106.806 84.504 86.004 70.488 46.767 43.292 57.593 76.946 102.237 96.340 99.318 90.715 79.782 73.443 69.460 57.898 41.041 39.791 39.959 62.498 77.777 92.782 90.284 92.782 90.655 84.517 93.826 71.646 55.650 smpl 65:1,75:12; read hsl24; 38 44 53 49 54 57 51 58 48 44 42 37 42 43 53 49 49 40 40 36 29 31 26 23 29 32 41 44 49 47 46 47 43 45 34 31 35 43 46 46 43 41 44 47 41 40 32 32 34 40 43 42 43 44 39 40 33 32 31 28 34 29 36 42 43 44 44 48 45 44 40 37 45 49 62 62 58 59 64 62 50 52 50 44 51 56 60 65 64 63 63 72 61 65 51 47 54 58 66 63 64 60 53 52 44 40 36 28 36 42 53 53 55 48 47 43 39 33 30 23 29 33 44 54 56 51 51 53 45 45 44 38