Sains Malaysiana 43(10)(2014): 1623–1633


A Unit Root Test Based on the Modified Least Squares Estimator

(Ujian Unit Akar Berdasarkan Penganggar Ubah Suai Kuasa Dua Terkecil)



Department of Mathematics and Statistics, Faculty of Science and Technology

Thammasat University, Phathum Thani, Thailand


Received: 3 January 2013/Accepted: 13 February 2014



A unit root test based on the modified least squares (MLS) estimator for first-order autoregressive process is proposed and compared with unit root tests based on the ordinary least squares (OLS), the weighted symmetric (WS) and the modified weighted symmetric (MWS) estimators. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of type I error and powers of the unit root tests were estimated via Monte Carlo simulation. The simulation results showed that all unit root tests can control the probability of type I error for all situations. The empirical power of the test is higher than the other unit root tests, and Apart from that, the and tests also provide the highest empirical power. As an illustration, the monthly series of U.S. nominal interest rates on three-month treasury bills is analyzed.


Keywords: First-order autoregressive; ordinary least squares estimator; unit root test; weighted symmetric estimator



Suatu ujian unit akar berdasarkan anggaran ubah suai kuasa dua terkecil (MLS) untuk proses autoregrasi peringkat pertama yang dicadang dan dibandingkan dengan penganggaran ujian unit akar yang berasaskan kuasa dua terkecil biasa (OLS), dengan wajaran simetri (WS) dan yang wajaran simetri ubah suai (MWS). Peratusan taburan nol ujian unit akar juga dilaporkan. Kebarangkalian empirikal daripada jenis ralat I dan kuasa ujian unit akar dianggarkan melalui simulasi Monte Carlo. Keputusan simulasi menunjukkan bahawa semua ujian unit akar boleh mengawal kemungkinan jenis ralat I untuk semua keadaan. Kuasa empirikal ujian adalah lebih tinggi daripada lain-lain ujian unit akar seperti dan Selain itu, dalam ujian dan juga memberikan kuasa empirikal yang tertinggi. Sebagai ilustrasi, siri bulanan kadar faedah nominal US pada bil perbendaharaan tiga bulan dianalisis.


Kata kunci: Autoregrasi peringkat pertama; penganggar kuasa dua terkecil biasa; penganggar wajaran simetri; ujian unit akar


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