The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Determining the existence of unit roots based on detrended data

추세 제거된 시계열을 이용한 단위근 식별

  • Na, Okyoung (Department of Applied Statistics, Kyonggi University)
  • 나옥경 (경기대학교 응용통계학과)
  • Received : 2021.02.17
  • Accepted : 2021.02.25
  • Published : 2021.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study a method to determine the existence of unit roots by using the adaptive lasso. The previously proposed method that applied the adaptive lasso to the original time series has low power when there is an unknown trend. Therefore, we propose a modified version that fits the ADF regression model without deterministic component using the adaptive lasso to the detrended series instead of the original series. Our Monte Carlo simulation experiments show that the modified method improves the power over the original method and works well in large samples.

본 논문에서는 adaptive lasso 방법을 이용하여 단위근의 존재 여부를 판단하는 방법에 대해 연구하였다. 최근 원 시계열에 상수항과 선형 추세가 포함된 ADF-회귀모형식을 adaptive lasso로 추정하여 단위근을 식별하는 방법이 제안되었으나, 미지의 선형 추세가 존재할 때 검정력이 떨어지는 것으로 나타났다. 이 문제를 해결하기 위해 본 논문에서는 ADF-회귀모형식을 적합시킬 때 원 시계열 대신 선형 추세가 제거된 시계열을 사용하는 수정안을 제안하였다. 그리고 수정안에서는 일차적으로 선형 추세를 제거한 후 모형식을 적합시키기 때문에 ADF-회귀모형식 중 상수항과 선형 추세를 모두 포함하지 않는 모형식을 사용하였다. 기존의 방법보다 수정안을 사용할 때 단위근의 존재를 판단하는 검정력이 향상되는지 모의실험을 통해 검토하였으며, ADF 검정과 DF-GLS 검정과의 비교 실험도 진행하였다. 모의실험 결과 adaptive lasso를 이용하여 단위근의 존재를 판단할 때 원 시계열보다 추세가 제거된 시계열을 사용하는 경우가 높은 정확도를 가지며, 자료의 개수가 충분히 많을 때 단위근을 잘 판단함을 확인할 수 있었다.

Keywords

References

  1. Akaike, H. (1974). A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19, 716-723. https://doi.org/10.1109/TAC.1974.1100705
  2. Dickey, D. and Fuller, W. (1979). Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association, 74, 427-431. https://doi.org/10.2307/2286348
  3. Elliott, G., Rothenberg, T., and Stock, J. (1996). Efficient tests for an autoregressive Unit Root, Econometrica, 64, 813-836. https://doi.org/10.2307/2171846
  4. Enders, W. (2010). Applied econometric time series, third edition, John Wiley & Sons.
  5. Hannan, E. and Quinn, B. (1979). The determination of the order of an autoregression, Journal of the Royal Statistical Society, Series B, 41, 190--195.
  6. Kwiatkowski, D., Phillips, P. C., Schmidt, P., and Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root, Journal of Econometrics, 54, 159-178. https://doi.org/10.1016/0304-4076(92)90104-Y
  7. Na, O. (2019). Model selection for unstable AR process via the adaptive LASSO, The Korean Journal of Applied Statistics, 32, 909-922. https://doi.org/10.5351/KJAS.2019.32.6.909
  8. Na, O. (2020). Discrimination between trend and difference stationary processes based on adaptive lasso, The Korean Journal of Applied Statistics, 33, 723-738. https://doi.org/10.5351/KJAS.2020.33.6.723
  9. Ng, S. and Perron, P. (2001). Lag length selection and the construction of unit root tests with good size and power, Econometrica, 69, 1519-1554. https://doi.org/10.1111/1468-0262.00256
  10. Nelson, C. R. and Plosser, C. I. (1982). Trends and random walks in macroeconomic time series, Journal of Monetary Economics, 10, 139-162. https://doi.org/10.1016/0304-3932(82)90012-5
  11. Phillips, P. C. and Perron, P. (1988). Testing for a unit root in time series regression, Biometrika, 75, 335-346. https://doi.org/10.1093/biomet/75.2.335
  12. Said, S. E. and Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order, Biometrika, 71, 599-607. https://doi.org/10.1093/biomet/71.3.599
  13. Schwarz, G. (1978). Estimating the dimension of a model, Annals of Statistics, 6, 461--464. https://doi.org/10.1214/aos/1176344136
  14. Schwert, G. W. (1989). Tests for unit roots: A Monte Carlo investigation, Journal of Business and Economic Statistics, 7, 147-160. https://doi.org/10.2307/1391432
  15. Vougas, D. (2007). GLS detrending and unit root testing, Economics Letters, 97, 222-229. https://doi.org/10.1016/j.econlet.2007.03.016
  16. Zou, H. (2006). The adaptive lasso and its oracle properties, Journal of the American Statistical Association, 101, 1418-1429. https://doi.org/10.1198/016214506000000735