Optical Orthogonal Codes With Unequal Auto-correlation and Cross-correlation Constraints
Auto CORRELATION
description
Transcript of Auto CORRELATION
![Page 1: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/1.jpg)
AUTO C
ORRELATI
ON
KU
L I AH
13
TI M
E S
ER
I ES
Usm
an
Bu
st a
ma
n,
S. S
i , M
. Sc .
1
![Page 2: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/2.jpg)
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: hubungan antara Output dan Naker (data kuartalan) Obs kuartal 1 berpengaruhi pada obs kuartal
berikutnya
Ex: hubungan antara Pendptn dan Konsumsi Ruta (data cross section) Obs Ruta 1 berpengaruhi pada obs Ruta berikutnya
“rumput tetangga selalu lebih hijau”2
![Page 3: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/3.jpg)
PATTERN
siklus
upward
downward linier & kuadratik
No systematic pattern
3
![Page 4: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/4.jpg)
PENYEBAB1. Inertia / siklus
Sering terjadi pada data time series: PDB, indeks harga, pengangguran, produksi, dll
Resesi , recovery 2. Specification Bias: Excluded Variables
Case. Variabel yg tdk masuk ke dlm model, ikut
serta dalam “error” Y=permintaaan daging sapi, X2=harga daging sapi,
X3=income, X4=harga daging ayam
Persamaan: Dimodelkan:
4
![Page 5: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/5.jpg)
PENYEBAB3. Specification Bias: Incorrect Functional
Form. “True” Model
Modeled with:
vi = where:
Other functional form:Cobweb function:
Lag function
5
![Page 6: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/6.jpg)
PENYEBAB4. “Manipulasi” Data
Data triwulanan = rata-2 data 3 blnInter/extra-polasi data, ex: mengestimasi data antara 1990-2000 dari data sensus th 1990 & 2000
5. Transformasi Data
6. Data Nonstasioner
6
![Page 7: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/7.jpg)
AUTOKORELASI (+) , (--)
7
![Page 8: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/8.jpg)
APA KABAR BLUE?Perhatikan , jika terjadi
autokorelasi
, error ut misalkan mengikuti fungsi
disebut sbg koefisien autokorelasi
ut disebut sebagai fungsi autoregresi orde 1 (AR1)
t mengikuti asumsi OLS
Dengan dmk
Homoskedastic
8
![Page 9: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/9.jpg)
APA KABAR BLUE?
Jika r = 0.6, = 0.8, atau
Var OLS underestimate !
no longer BLUE it’s LU
9
![Page 10: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/10.jpg)
KONSEKUENSI1. Karena var OLS underestimate estimate
parameter mjd non-sig meski kemungkinan (sebenarnya) sig.
2. Varians residual, , underestimate thd
3. uji t dan uji F tidak lagi valid misleading
10
![Page 11: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/11.jpg)
DIAGNOSA1. Metode grafis -- Time sequence plot
Positive correlation
11
![Page 12: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/12.jpg)
DIAGNOSA2. Runs Test
Asumsi N1, N2 > 10 R ~ normal dgn:
Jika R ada di luar CI residual berautokorelasi
N1 = 19, N2 = 21, R = 3
95% CI Residual berautokorelasi
12
![Page 13: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/13.jpg)
DIAGNOSA3. Durbin-Watson Test
Durbin–Watson d statistic:Asumsi:
1. Model RL mengandung intercept
2. X non stochastic
3. ut merupakan fungsi AR1:
4. ut ~ Normal
5. Model RL tdk mengandung lag Y pada variabel bebasnya
6. Tidak ada missing data karena -1 ≤ ≤ 1 0 ≤ d ≤ 4 Jika tdk ada autokorelasi ( =0), d disekitar nilai 2
13
![Page 14: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/14.jpg)
DURBIN-WATSON TEST
14
![Page 15: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/15.jpg)
DIAGNOSA4. The Breusch–Godfrey (BG) Test / LM Test
Step:
1. Estimate RL, hitung residualnya,
2. Regresikan thd X dan lag residualnya
Lalu hitung R2-nya
3. Jika n besar
4. Tolak Ho jika >
15
![Page 16: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/16.jpg)
REMEDIAL1. Metode Generalized Least Square (GLS)
Misalkan:
Jika rho diketahui:
dimana
Jika rho tidak diketahui:1. Metode first difference jika d < R2
Valid jika = 1 uji menggunakan g statistik: kepuusan tolak H0 = d statistik
16
![Page 17: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/17.jpg)
REMEDIALJika rho tidak diketahui2. Estimasi rho menggunakan statistik d
3. Estimasi rho menggunakan residual
4. Estimasi rho menggunakan metode iterasi
2,3,4 Lalu estimasi GLS menggunakan
17
![Page 18: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/18.jpg)
REMEDIAL2. Metode Newey-West: HAC
(heteroscedasticity- and autocorrelation-consistent) standard errors
. . . . . .
3. Menambahkan variabel bebas lain yang penting/mempengaruhi variabel tak bebas ….
18
![Page 19: Auto CORRELATION](https://reader035.fdocuments.net/reader035/viewer/2022062322/56814e63550346895dbc011c/html5/thumbnails/19.jpg)
NORMALITY TESTHistogram
Normal probability plot
Anderson-Darling Normality Test
Jarque–Bera (JB) Test of Normality.
19