While there is good reason to expect crude oil production to be non-linear, previous studies that have examined the stochastic properties of crude oil production have assumed that crude oil production follows a linear process. If crude oil production is a non-linear process, conventional unit root tests, which assume linear and systematic adjustment, could interpret departure from linearity as ...

This study aims to examine the environmental dynamics in Union for Mediterranean (UFM) countries by considering education, urbanization, green innovation, and other key factors period 2001–2016. The data are divided based on income level of UFM analyzed with panel quantile regression, unit root tests, co-integration test, ordinary least squares method, fixed effects model evaluate nexus between...

A time series with a unit root or fractional unit root can be miscategorized in stationarity tests if the series has structural breaks. This finding is tested on Finnish and Swedish party popularity series. The composition and nature of popularity series provide reasons to assume fractional dynamics. The years included, 1987-2001, offer several reasons for the existence of structural breaks. Th...

Let p be a prime. We prove that if a modular unit has a pth root that is again a modular unit, then the level of that root is at most p times the level of the original unit.

In this paper, we consider and examine the performance of two-step LM unit root tests with trend-breaks. In the first step, we jointly test for the existence and location of breaks using a maximum F-test. In the second step, we utilize the identified breaks and test for a unit root. A transformation procedure is adopted so that the tests with trend-breaks are invariant to nuisance parameters. W...

A nonparametric, residual-based block bootstrap procedure is proposed in the context of testing for integrated (unit root) time series. The resampling procedure is based on weak assumptions on the dependence structure of the stationary process driving the random walk and successfully generates unit root integrated pseudo-series retaining the important characteristics of the data. It is more gen...

Unit root tests for time series with level shifts are considered. The level shift is assumed to occur at a known time point. In contrast to some other proposals the level shift is modeled as part of the intercept term of the stationary component of the data generation process which is separated from the unit root component. In this framework simple shift functions result in a smooth transition ...

The random walk is used as a model expressing equitableness and the effectiveness of various finance phenomena. Randomwalk is included in unit root process which is a class of nonstationary processes. Due to its nonstationarity, the least squares estimator LSE of random walk does not satisfy asymptotic normality. However, it is well known that the sequence of partial sum processes of random wal...

It is known that unit root test statistics may not have the usual asymptotic properties when the variance of innovations is unstable. In particular, persistent changes in volatility can cause the size of unit root tests to differ from the nominal level. In this paper we propose a class of modified unit root test statistics that are robust to the presence of unstable volatility. The modification...