Unit root tests

Abstract

Unit roots are nonstationary autoregressive (AR) or autoregressive moving average (ARMA) time series processes which may include an intercept and/or a trend. These processes are used often in economics and finance, but can also be found in other scientific fields. Unit root tests address the null hypothesis of a unit root, and an alternative hypothesis of a stationary (or trend stationary) time series. Critical values for unit root tests are typically derived via simulation of limiting distributions expressed as functionals of Brownian motions. The critical values for the Dickey Fuller unit root test with a constant and linear trend are derived via simulation in the R language. Simulation studies are presented showing that linear regressions with unit root processes often produce spurious results. Additional simulation studies are reviewed providing statistical evidence that near-unit roots can often result in spurious cointegration relationships. Various unit root tests are presented, including ones that allow for structural breaks in intercept and/or trend. Threshold unit root tests are introduced. Simulation studies are used to compare the unit root tests under various scenarios. The case where the analyzed time series may have stationary and nonstationary segments is also considered.

The Determinants of Carbon Dioxide Emissions in Malaysia and Singapore

“…For this, the study adopted the Augmented Dickey Fuller This (ADF) unit root test (Dickey 1976;Dickey & Fuller 1979;Diebold & Kilian 2000;Aritova & Fedorova 2016;Herranz 2017). Subsequently the study employed the Akaike Information Criteria (AIC) in order to select the optimum lag-length for the estimation modelling (Akaike 1969;Akaike 1974;Ivanov & Kilian 2005;Gutierrez et al 2009).…”

An Error Correction Model on the Impact of Government Expenditure on Economic Growth in Liberia from 1970 to 2020: Keynesian Economics Visited

“…The unit roots test was conducted on three variables to test for stationarity or non-stationarity in the model amongst the variables. Herranz opined that unit roots are nonstationary autoregressive (AR) or autoregressive moving-average (ARMA) time series processes [5] that has 1 as a valid root of the characteristic polynomial [3]. The results showed that we can reject the null hypothesis that the series has a unit roots on grounds that the Trace-statistic is Greater than the Probability value for all variables in the series at levels.…”

Etki̇n Ücret Teori̇si̇ Çerçevesi̇nde Türki̇ye’de Reel Ücretler İle Üreti̇m Arasindaki̇ İli̇şki̇ni̇n İncelenmesi̇: Sektörler İle Ekonometri̇k Bi̇r Anali̇z

“…Elde edilen test istatistikleri MacKinnon (1996) kritik değerleriyle karşılaştırılmakta, boş hipotez reddedilemediğinde seride birim kök olduğuna karar verilmektedir. Seride birim kök olması, o serinin durağan olmadığını ifade etmektedir (Herranz, 2017).…”