Time Series Analysis of Blaisdell Company Data --------------------------------------------------------------------------------------------- log: D:\s209\m14blais.log log type: text opened on: 24 Apr 2006, 12:02:33 . do "C:\DOCUME~1\nielsen\LOCALS~1\Temp\STD04000000.tmp" . use "Z:\mydocs\s209\blaisco.dta", clear . * y is company sales, x is industry sales (mil $) . * do regular regression . regress y x Source | SS df MS Number of obs = 20 -------------+------------------------------ F( 1, 18) =14888.15 Model | 110.256901 1 110.256901 Prob > F = 0.0000 Residual | .133302302 18 .007405683 R-squared = 0.9988 -------------+------------------------------ Adj R-squared = 0.9987 Total | 110.390204 19 5.81001072 Root MSE = .08606 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | .1762828 .0014447 122.02 0.000 .1732475 .1793181 _cons | -1.454753 .2141461 -6.79 0.000 -1.904657 -1.004849 ------------------------------------------------------------------------------ . * next tsset data set to make it time series . * qtr is quarter . generate qtr=_n . tsset qtr time variable: qtr, 1 to 20 . * next regression with DW test . regress y x Source | SS df MS Number of obs = 20 -------------+------------------------------ F( 1, 18) =14888.15 Model | 110.256901 1 110.256901 Prob > F = 0.0000 Residual | .133302302 18 .007405683 R-squared = 0.9988 -------------+------------------------------ Adj R-squared = 0.9987 Total | 110.390204 19 5.81001072 Root MSE = .08606 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | .1762828 .0014447 122.02 0.000 .1732475 .1793181 _cons | -1.454753 .2141461 -6.79 0.000 -1.904657 -1.004849 ------------------------------------------------------------------------------ . estat dwatson Durbin-Watson d-statistic( 2, 20) = .7347276 . * next do Wald-Wolfowitz runs test (first with . * threshold = median, then with threshold=0) . predict e, resid . graph twoway line e qtr, yline(0) . runtest e N(e <= -.0004533920437098) = 10 N(e > -.0004533920437098) = 10 obs = 20 N(runs) = 5 z = -2.76 Prob>|z| = .01 . runtest e, threshold(0) N(e <= 0) = 10 N(e > 0) = 10 obs = 20 N(runs) = 5 z = -2.76 Prob>|z| = .01 . * makes no diff here . * next do Cochrane-Orcutt regression (no iteration) . prais y x, corc twostep Iteration 0: rho = 0.0000 Iteration 1: rho = 0.6312 Cochrane-Orcutt AR(1) regression -- twostep estimates Source | SS df MS Number of obs = 19 -------------+------------------------------ F( 1, 17) = 3453.63 Model | 15.5749186 1 15.5749186 Prob > F = 0.0000 Residual | .076665287 17 .004509723 R-squared = 0.9951 -------------+------------------------------ Adj R-squared = 0.9948 Total | 15.6515839 18 .869532438 Root MSE = .06715 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | .1737583 .0029567 58.77 0.000 .1675202 .1799964 _cons | -1.068526 .4533976 -2.36 0.031 -2.025112 -.1119411 -------------+---------------------------------------------------------------- rho | .6311623 ------------------------------------------------------------------------------ Durbin-Watson statistic (original) 0.734728 Durbin-Watson statistic (transformed) 1.650247 . prais y x, rhotype(tscorr) twostep Iteration 0: rho = 0.0000 Iteration 1: rho = 0.6260 Prais-Winsten AR(1) regression -- twostep estimates Source | SS df MS Number of obs = 20 -------------+------------------------------ F( 1, 18) =13684.91 Model | 60.2240453 1 60.2240453 Prob > F = 0.0000 Residual | .07921376 18 .004400764 R-squared = 0.9987 -------------+------------------------------ Adj R-squared = 0.9986 Total | 60.3032591 19 3.17385574 Root MSE = .06634 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | .1751424 .0022827 76.72 0.000 .1703465 .1799382 _cons | -1.290318 .3395938 -3.80 0.001 -2.003778 -.5768581 -------------+---------------------------------------------------------------- rho | .6260036 ------------------------------------------------------------------------------ Durbin-Watson statistic (original) 0.734728 Durbin-Watson statistic (transformed) 1.675555 . * next, what I think is equivalent to Hildreth-Lu method of searching for regression estima > tes . * and value of rho that jointly minimize SSE . prais y x, ssesearch Iteration 1: rho = 0.8944 , criterion = -.08340677 Iteration 2: rho = 0.6525 , criterion = -.07905246 Iteration 3: rho = 0.6525 , criterion = -.07905246 Iteration 4: rho = 0.6525 , criterion = -.07905246 Iteration 5: rho = 0.6708 , criterion = -.07902978 Iteration 6: rho = 0.6677 , criterion = -.07902861 Iteration 7: rho = 0.6677 , criterion = -.07902861 Iteration 8: rho = 0.6677 , criterion = -.07902861 Iteration 9: rho = 0.6677 , criterion = -.07902861 Iteration 10: rho = 0.6677 , criterion = -.07902861 Iteration 11: rho = 0.6677 , criterion = -.07902861 Iteration 12: rho = 0.6677 , criterion = -.07902861 Iteration 13: rho = 0.6677 , criterion = -.07902861 Iteration 14: rho = 0.6677 , criterion = -.07902861 Iteration 15: rho = 0.6677 , criterion = -.07902861 Prais-Winsten AR(1) regression -- SSE search estimates Source | SS df MS Number of obs = 20 -------------+------------------------------ F( 1, 18) =13899.09 Model | 61.0236379 1 61.0236379 Prob > F = 0.0000 Residual | .079028607 18 .004390478 R-squared = 0.9987 -------------+------------------------------ Adj R-squared = 0.9986 Total | 61.1026665 19 3.21592981 Root MSE = .06626 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | .1748963 .0024432 71.58 0.000 .1697633 .1800293 _cons | -1.254568 .3637293 -3.45 0.003 -2.018735 -.4904015 -------------+---------------------------------------------------------------- rho | .6677295 ------------------------------------------------------------------------------ Durbin-Watson statistic (original) 0.734728 Durbin-Watson statistic (transformed) 1.728405 . * these results are different from ALSM4e and 5e . * try default prais . prais y x Iteration 0: rho = 0.0000 Iteration 1: rho = 0.6312 Iteration 2: rho = 0.6500 Iteration 3: rho = 0.6528 Iteration 4: rho = 0.6532 Iteration 5: rho = 0.6533 Iteration 6: rho = 0.6533 Iteration 7: rho = 0.6533 Iteration 8: rho = 0.6533 Prais-Winsten AR(1) regression -- iterated estimates Source | SS df MS Number of obs = 20 -------------+------------------------------ F( 1, 18) =13848.94 Model | 60.8198448 1 60.8198448 Prob > F = 0.0000 Residual | .079049867 18 .004391659 R-squared = 0.9987 -------------+------------------------------ Adj R-squared = 0.9986 Total | 60.8988947 19 3.20520498 Root MSE = .06627 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | .1749874 .0023848 73.38 0.000 .1699773 .1799976 _cons | -1.267818 .3549307 -3.57 0.002 -2.0135 -.5221362 -------------+---------------------------------------------------------------- rho | .6532947 ------------------------------------------------------------------------------ Durbin-Watson statistic (original) 0.734728 Durbin-Watson statistic (transformed) 1.711080 . * prais y x, corc not run because of non-convergence . * note prais y x, corc gives results closest to ALSM4e and 5e . * for Hildreth-Lu method, with rho=.9580877, b1=.1605672 . * next do first-differences regression . * note D operator, no constant regression . regress D.y D.x, nocon Source | SS df MS Number of obs = 19 -------------+------------------------------ F( 1, 18) = 1093.14 Model | 5.2637264 1 5.2637264 Prob > F = 0.0000 Residual | .086674155 18 .004815231 R-squared = 0.9838 -------------+------------------------------ Adj R-squared = 0.9829 Total | 5.35040055 19 .281600029 Root MSE = .06939 ------------------------------------------------------------------------------ D.y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | D1. | .1684878 .005096 33.06 0.000 .1577814 .1791941 ------------------------------------------------------------------------------ . * results identical with AMSM4e and 5e for first-differences . end of do-file . log close log: D:\s209\m14blais.log log type: text closed on: 24 Apr 2006, 12:03:47 --------------------------------------------------------------------------------------------- Last modified 24 Apr 2006