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Auto CORRELATION

Auto CORRELATION. KULIAH 13 TIME SERIES. Usman B ustaman , S.Si , M.Sc. What’s autocorrelation?. Nature of Problem: correlation between members of series of observations ordered in time [as in time series data] or space [as in cross-sectional data ]

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Auto CORRELATION

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  1. Auto CORRELATION KULIAH 13 TIME SERIES UsmanBustaman, S.Si, M.Sc.

  2. What’s autocorrelation? • Nature of Problem: • correlation between members of series of observations ordered in time [as in time series data] or space [as in cross-sectional data] • Ex: hubunganantara Output danNaker (data kuartalan) • Obskuartal 1 berpengaruhipadaobskuartalberikutnya • Ex: hubunganantaraPendptndanKonsumsiRuta (data cross section) • ObsRuta 1 berpengaruhipadaobsRutaberikutnya • “rumputtetanggaselalulebihhijau”

  3. Pattern upward siklus No systematic pattern downward linier & kuadratik

  4. Penyebab • Inertia / siklus • Seringterjadipada data time series: PDB, indeksharga, pengangguran, produksi, dll • Resesi, recovery  • Specification Bias: Excluded Variables Case. • Variabelygtdkmasukkedlm model, ikutsertadalam “error” • Y=permintaaandagingsapi, X2=hargadagingsapi, X3=income, X4=hargadagingayam • Persamaan: • Dimodelkan:

  5. penyebab • Specification Bias: Incorrect Functional Form. “True” Model Modeled with: vi = where: Other functional form: Cobweb function: Lag function

  6. penyebab • 4. “Manipulasi” Data • Data triwulanan = rata-2 data 3 bln • Inter/extra-polasi data, ex: mengestimasi data antara 1990-2000 dari data sensusth 1990 & 2000 5. Transformasi Data 6. Data Nonstasioner

  7. Autokorelasi (+) , (--)

  8. Apakabarblue? • Perhatikan , jikaterjadiautokorelasi • , error utmisalkanmengikutifungsi • disebutsbgkoefisienautokorelasi • utdisebutsebagaifungsiautoregresiorde 1 (AR1) • t mengikutiasumsi OLS  • Dengandmk Homoskedastic

  9. Apakabarblue? • Jikar = 0.6,  = 0.8, • atau • Var OLS underestimate ! • no longer BLUE  it’s LU

  10. konsekuensi • Karenavar OLS underestimate  estimate parameter mjd non-sig meskikemungkinan (sebenarnya) sig. •  Varians residual, , underestimate thd •  uji t danuji F tidaklagi valid  misleading

  11. Diagnosa • 1. Metodegrafis -- Time sequence plot Positive correlation

  12. diagnosa • 2. Runs Test Asumsi N1, N2 > 10  R ~ normal dgn: N1 = 19, N2 = 21, R = 3 Jika R ada di luar CI  residual berautokorelasi 95% CI   Residual berautokorelasi

  13. diagnosa • 3. Durbin-Watson Test • Durbin–Watson d statistic: • Asumsi: • Model RL mengandungintercept • X non stochastic • utmerupakanfungsiAR1: • ut ~ Normal • Model RL tdkmengandung lag Y padavariabelbebasnya • Tidakadamissing data  karena -1 ≤  ≤ 1  0 ≤ d ≤ 4  Jikatdkadaautokorelasi ( =0), ddisekitarnilai 2

  14. Durbin-watson test

  15. diagnosa • 4. The Breusch–Godfrey (BG) Test / LM Test • Step: • Estimate RL, hitungresidualnya, • Regresikanthd X dan lag residualnya Laluhitung R2-nya • Jika n besar • Tolak Ho jika >

  16. remedial • 1. Metode Generalized Least Square (GLS) Misalkan: Jika rho diketahui: dimana Jika rho tidakdiketahui: 1. Metode first difference  jikad < R2 • Valid jika = 1  ujimenggunakan g statistik: •  kepuusantolak H0 = d statistik

  17. remedial Jika rho tidakdiketahui 2. Estimasi rho menggunakanstatistikd  3. Estimasi rho menggunakan residual  4. Estimasi rho menggunakanmetodeiterasi 2,3,4 LaluestimasiGLS menggunakan

  18. remedial • 2. MetodeNewey-West: HAC (heteroscedasticity- and autocorrelation-consistent) standard errors • . . . . . . • 3. Menambahkanvariabelbebas lain yang penting/mempengaruhivariabeltakbebas ….

  19. Normality test • Histogram • Normal probability plot • Anderson-Darling Normality Test • Jarque–Bera (JB) Test of Normality.

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