THE EFFECT OF AUTOCORRELATION IN ERROR TERMS ON THE POWER OF THE DICKEY FULLER UNIT ROOT TEST: A SIMULATION APPROACH
Abstract
In this study, as the most basic unit root test
Dickey Fuller tests, which effects are considered, have been investigated with
including error term autocorrelation. As known, the Dickey Fuller Unit Root
tests determine the stability of the variable by using the
(tau) statistic of the autoregressive variable
coefficient parameter in the system. However, if the parameter coefficient is
close to one, the test is criticized justly. In this case test suggests
frequently non-stationary rather than stationary. The aim of the study is to
discuss the determination of the stability under the correlation of error
terms. At the study the stationary test is discussed with the simulation
results if there is a case the error terms are correlated. According to the
results determined in the study, the stationary series were being suggested
more often as nonstationary, considering the correlation of error terms.
However, even if autocorrelation is weak, when it is removed from the system,
being stationary has become more clearly suggested if series truly are. As a
result, even if there is autocorrelation that can be accepted as insignificant
in the system, it is decided that to be removing from the system in order to
judge being stationary accurately.
References
- Dickey, David, A., and Pantula, Sastry, G., (1987). “Determining the Order of Differencing in Autoregressive Processes”. Journal of Business & Economic Statistics, 5 (4), 455-461.
- Dickey, David, A., and Fuller, A., Wayne, (1981). “Likelihood Ratio Statistics for Autoregressive Time Series with Unit Root”. The Econometric Society, Econometrica, 49 (4), 1057-1072.
- Dickey, David, A., and Fuller, A., Wayne, (1979). “Distribution of the Estimators for Autoregressive Time Series with a Unit Root”. American Statistical Association, 74 (366), 427-431.
- Elliot, Graham, Rothnberg, Thomas, J., and Stock, James, H., (1996). “Efficient Tests for an Autoregressive Unit Root”. The Econometric Society, Econometrica, 64 (4), 813-836.
- Enders, Walter, (2014). Applied Econometric Time Series. Wiley Series in Probability and Statistics.
- Guilkey, David, K., and Schmidt, Peter, (1989). “Extended Tabulations for Dickey-Fuller Tests”. Economics Letters, 31 (4), 355-357.
- Hazsa, David, P., and Fuller, Wayne, A., (1982). “Testing for Nonstationary Parameter Specifications in Seasonal Time Series Model”. Institute of Mathematical Statistics, The Annals of Statistics, 10 (4), 1209-1216.
- Leybourne, Stephen, J., Mills, Terence, C., and Newbold, Paul, (1998). “Spurious Rejections by Dickey-Fuller Tests in the Presence of a Break Under Null”. Journal of Econometrics, 87 (1), 191-203.
- Nabeya, Seiji, and Tanaka, Katsudo, (1990). “A General Approach to the Limiting Distribution for Estimators in Time Series Regressions with Nonstable Autoregressive Errors”. The Econometric Society, Econometrica, 58 (1), 145-163.
- Perron, Phillips, (1989). “The Great Crash, The Oil Prices Shock, and the Unit Root Hypothesis”. The Econometric Society, Econometrica, 57 (6), 1361-1401.
- Perron, Phillips, (1988a). “Testing for a Unit Root in Time Series Regression”. Oxford University Press, Biometrika, 75 (2), 335-346.
- Perron, Phillips, (1988b). “Trends and Random Walks in Macroeconomic Time Series; Further Evidence from a New Approach”. Journal of Economic Dynamics and Control, 12 (2-3), 297-332.
- Phillips, Peter, C., B., and Oularis, S., (1990). “Asymptotic Properties of Residual Based Tests for Cointegration”. The Econometric Society, Econometrica, 58 (1), 165-193.
- Xiao, Zhijie, and Phillips, Peter, C., B., (1998). “An ADF Coefficient Test for a Unit Root in ARMA Models of Unknown Order with Empirical Applications to the US Economy”. Econometrics Journal, 1, 27-43.
HATA TERİMLERİNDEKİ OTOKORELASYONUN DİCKEY FULLER BİRİM KÖK TESTİNİN GÜCÜ ÜZERİNDEKİ ETKİSİ: SİMÜLASYON MODEL YAKLAŞIMI
Abstract
Bu çalışmada en temel
birim kök testi olarak kabul edilen Dickey Fuller birim kök testlerinin, hata
terimlerinin korelasyonlu olması sonucu etkilenmesi durumu incelenmiştir.
Bilindiği üzere Dickey Fuller birim kök testleri ile sistemdeki otoregresif
değişkenin parametre katsayısının
(tau) istatistiği ile söz konusu değişkenin
durağanlığı belirlenmektedir. Ancak parametre katsayısının bire yakın çıkması
durumunda test eleştirilmektedir. Test bu durumda durağanlık olgusu yerine
durağan dışılığı sıkça önermektedir. Çalışmada belirlenen sonuçlara göre, hata
terimlerinin korelasyonlu olması ve bu durumunun göz ardı edilmesi ile durağan
seriler daha sık bir şekilde durağan dışı olma eğilimindedir. Bununla beraber
otokorelasyonun zayıf olsa da sistemden uzaklaştırılması halinde serinin
durağan çıkma olasılığı daha net bir şekilde önerilmektedir.
References
- Dickey, David, A., and Pantula, Sastry, G., (1987). “Determining the Order of Differencing in Autoregressive Processes”. Journal of Business & Economic Statistics, 5 (4), 455-461.
- Dickey, David, A., and Fuller, A., Wayne, (1981). “Likelihood Ratio Statistics for Autoregressive Time Series with Unit Root”. The Econometric Society, Econometrica, 49 (4), 1057-1072.
- Dickey, David, A., and Fuller, A., Wayne, (1979). “Distribution of the Estimators for Autoregressive Time Series with a Unit Root”. American Statistical Association, 74 (366), 427-431.
- Elliot, Graham, Rothnberg, Thomas, J., and Stock, James, H., (1996). “Efficient Tests for an Autoregressive Unit Root”. The Econometric Society, Econometrica, 64 (4), 813-836.
- Enders, Walter, (2014). Applied Econometric Time Series. Wiley Series in Probability and Statistics.
- Guilkey, David, K., and Schmidt, Peter, (1989). “Extended Tabulations for Dickey-Fuller Tests”. Economics Letters, 31 (4), 355-357.
- Hazsa, David, P., and Fuller, Wayne, A., (1982). “Testing for Nonstationary Parameter Specifications in Seasonal Time Series Model”. Institute of Mathematical Statistics, The Annals of Statistics, 10 (4), 1209-1216.
- Leybourne, Stephen, J., Mills, Terence, C., and Newbold, Paul, (1998). “Spurious Rejections by Dickey-Fuller Tests in the Presence of a Break Under Null”. Journal of Econometrics, 87 (1), 191-203.
- Nabeya, Seiji, and Tanaka, Katsudo, (1990). “A General Approach to the Limiting Distribution for Estimators in Time Series Regressions with Nonstable Autoregressive Errors”. The Econometric Society, Econometrica, 58 (1), 145-163.
- Perron, Phillips, (1989). “The Great Crash, The Oil Prices Shock, and the Unit Root Hypothesis”. The Econometric Society, Econometrica, 57 (6), 1361-1401.
- Perron, Phillips, (1988a). “Testing for a Unit Root in Time Series Regression”. Oxford University Press, Biometrika, 75 (2), 335-346.
- Perron, Phillips, (1988b). “Trends and Random Walks in Macroeconomic Time Series; Further Evidence from a New Approach”. Journal of Economic Dynamics and Control, 12 (2-3), 297-332.
- Phillips, Peter, C., B., and Oularis, S., (1990). “Asymptotic Properties of Residual Based Tests for Cointegration”. The Econometric Society, Econometrica, 58 (1), 165-193.
- Xiao, Zhijie, and Phillips, Peter, C., B., (1998). “An ADF Coefficient Test for a Unit Root in ARMA Models of Unknown Order with Empirical Applications to the US Economy”. Econometrics Journal, 1, 27-43.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | October 12, 2017 |
| Submission Date | October 26, 2017 |
| Published in Issue | Year 2015 Volume: 8 Issue: 1 |
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