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Ekonometrika

Ekonometrika. Program Studi Statistika , semester Ganjil 2012/2013. Aplikasi permasalahan dengan Autokorelasi. Data kuartal dari 1985 kuartal 1 s/d 1994 kuartal 2 LCONS: pengeluaran konsumsi untuk makanan pada ₤ juta , harga tetap tahun 1992

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Ekonometrika

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  1. Ekonometrika Program StudiStatistika, semester Ganjil2012/2013 Dr. Rahma Fitriani, S.Si., M.Sc

  2. AplikasipermasalahandenganAutokorelasi • Data kuartaldari 1985 kuartal 1 s/d 1994 kuartal 2 • LCONS: pengeluarankonsumsiuntukmakananpada₤juta, hargatetaptahun 1992 • LDISP: pendapatan yang siapdibelanjakan (bersihdaripajak) ataudisposable incomedalam₤juta, hargatetaptahun 1992 • LPRICE: indeksrelatifhargamakanan (padathn 1992 = 100) • Ingindibentuk model: Terdapatindikasibahwagalatpadakuartaltertentudipengaruhiolehgalatpadakuartalsebelumnya.

  3. Dilakukanpendugaan model • Diperolehpendugagalat

  4. Model 1: OLS, using observations 1985:1-1994:2 (T = 38) Dependent variable: LCONS coefficient std. error t-ratio p-value ------------------------------------------------------- const 2,48543 0,788349 3,153 0,0033 *** LDISP 0,529285 0,292327 1,811 0,0788 * LPRICE -0,0640289 0,146506 -0,4370 0,6648 Mean dependent var 4,609274 S.D. dependent var 0,051415 Sum squared resid 0,074882 S.E. of regression 0,046255 R-squared 0,234408 Adjusted R-squared 0,190660 F(2, 35) 5,358118 P-value(F) 0,009332 Log-likelihood 64,43946 Akaike criterion -122,8789 Schwarz criterion -117,9662 Hannan-Quinn -121,1310 rho 0,799544 Durbin-Watson 0,370186 Log-likelihood for cons = -110,713 Karenaadaindikasiautokorelasi, hasilpengujiankurang valid, walaupunsecarateorihubungan yang diperolehbenar

  5. Analisisgrafisterhadapgalat: PolaGalatberdasarkanwaktu • Bentuksiklus • Nilai (+) diikutinilai (+) ataunilai (-) diikutinilai (-) • Indikasiadanyaautokorelasi (+)

  6. Analisisgrafisterhadapgalat: Diagram pencarantarautdanut-1 • Korelasi (+) • Pendugaρ = 0.799

  7. Durbin-Watson statistic = 0,370186 p-value = 1,79769e+308 2.612 2.824 1.388 0.37 1.176

  8. Breusch Godfrey LM test Breusch-Godfrey test for first-order autocorrelation OLS, using observations 1985:1-1994:2 (T = 38) Dependent variable: uhat coefficient std. error t-ratio p-value -------------------------------------------------------- const -0,585980 0,505065 -1,160 0,2540 LDISP 0,245740 0,187940 1,308 0,1998 LPRICE -0,116819 0,0940388 -1,242 0,2226 uhat_1 0,828094 0,113241 7,313 1,80e-08 *** Unadjusted R-squared = 0,611316 Test statistic: LMF = 53,474681, with p-value = P(F(1,34) > 53,4747) = 1,8e-008 Alternative statistic: TR^2 = 23,230012, with p-value = P(Chi-square(1) > 23,23) = 1,44e-006 Ljung-Box Q' = 22,388, with p-value = P(Chi-square(1) > 22,388) = 2,23e-006

  9. Untukmengatasiautokorelasi • Denganasumsiρdiketahuibernilai 0.79 • Dilakukantransformasiterhadapsetiappeubah (lihat slide kuliahsebelumnya)

  10. Output BerdasarkanVariabel yang ditransformasi Model 1: OLS, using observations 1985:1-1994:2 (T = 38) Dependent variable: LCONSSTAR coefficient std. error t-ratio p-value ---------------------------------------------------------- Beta1Star 2.07530 0.833071 2.491 0.0176 ** LDISPSTAR 1.19925 0.231332 5.184 9.19e-06 *** LPRICESTAR -0.642158 0.100061 -6.418 2.18e-07 *** Mean dependent var 0.977251 S.D. dependent var 0.302557 Sum squared resid 0.013405 S.E. of regression 0.019571 R-squared 0.999662 Adjusted R-squared 0.999643 F(3, 35) 34520.25 P-value(F) 8.62e-61 Log-likelihood 97.12460 Akaike criterion -188.2492 Schwarz criterion -183.3364 Hannan-Quinn -186.5013 rho 0.521194 Durbin-Watson 0.957430 Masihadaindikasiautokorelasi: kurangtepatnyapendugaρyang digunakan

  11. UntukMengatasiAutokorelasi • Karenatidakmudahmenentukanρyang tepat, digunakanmetode iterative Cohran - Orcutt

  12. Performing iterative calculation of rho... ITER RHO ESS 1 0,79954 0,0133632 2 0,97044 0,00362232 3 0,97087 0,00362232 Model 3: Cochrane-Orcutt, using observations 1985:2-1994:2 (T = 37) Dependent variable: LCONS coefficient std. error t-ratio p-value ---------------------------------------------------------- const 9,76087 1,05182 9,280 7,63e-011 *** LDISP -0,188101 0,215200 -0,8741 0,3882 LPRICE -0,853863 0,0553046 -15,44 6,28e-017 *** Statistics based on the rho-differenced data: Mean dependent var 4,608665 S.D. dependent var 0,051985 Sum squared resid 0,003620 S.E. of regression 0,010319 R-squared 0,963895 Adjusted R-squared 0,961771 F(2, 34) 120,3161 P-value(F) 3,77e-16 rho -0,136188 Durbin-Watson 2,246817

  13. Hasilmenunjukkanbahwamasalahautokorelasisudahterselesaikan • Hasilujimenjadi valid • Hanyahargamakanan (LPRICE) yang mempengaruhikonsumsi (LCONS) secaranegatif • Pendapatansiapdibelanjakan (LDISP) tidakmempengaruhikonsumsi (LCONS)

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