scholarly journals The Impact of the Initial Condition on Covariate Augmented Unit Root Tests

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Chrystalleni Aristidou ◽  
David I. Harvey ◽  
Stephen J. Leybourne
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Initial Condition ◽  
Unit Root Testing ◽  
The Impact ◽  
Univariate Approach

AbstractWe examine the behaviour of OLS-demeaned/detrended and GLS-demeaned/detrended unit root tests that employ stationary covariates, as proposed by Hansen (1995, “Rethinking the Univariate Approach to Unit Root Testing.”

scholarly journals UNIT ROOT TESTING IN PRACTICE: DEALING WITH UNCERTAINTY OVER THE TREND AND INITIAL CONDITION

2009 ◽  
Vol 25 (3) ◽  
pp. 587-636 ◽  
Author(s):  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
A.M. Robert Taylor
Keyword(s):  
Decision Rule ◽  
Unit Root ◽  
Ordinary Least Squares ◽  
Unit Root Tests ◽  
Trend Detection ◽  
Initial Condition ◽  
Finite Sample ◽  
Testing Procedures ◽  
Unit Root Testing ◽  
Deterministic Trend

In this paper we focus on two major issues that surround testing for a unit root in practice, namely, (i) uncertainty as to whether or not a linear deterministic trend is present in the data and (ii) uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. In each case simple testing procedures are proposed with the aim of maintaining good power properties across such uncertainties. For the first issue, if the initial condition is negligible, quasi-differenced (QD) detrended (demeaned) Dickey–Fuller-type unit root tests are near asymptotically efficient when a deterministic trend is (is not) present in the data generating process. Consequently, we compare a variety of strategies that aim to select the detrended variant when a trend is present, and the demeaned variant otherwise. Based on asymptotic and finite-sample evidence, we recommend a simple union of rejections-based decision rule whereby the unit root null hypothesis is rejected whenever either of the detrended or demeaned unit root tests yields a rejection. Our results show that this approach generally outperforms more sophisticated strategies based on auxiliary methods of trend detection. For the second issue, we again recommend a union of rejections decision rule, rejecting the unit root null if either of the QD or ordinary least squares (OLS) detrended/demeaned Dickey–Fuller-type tests rejects. This procedure is also shown to perform well in practice, simultaneously exploiting the superior power of the QD (OLS) detrended/demeaned test for small (large) initial conditions.

scholarly journals A Different Look at Cointegration Relationship between Quarterly Inflation Rates and Growth via Seasonal Integration Tests

2019 ◽  
Author(s):  
Sera Şanlı ◽  
Mehmet Özmen
Keyword(s):  
Economic Growth ◽  
Unit Root ◽  
Unit Root Test ◽  
Unit Root Tests ◽  
Maximum Order ◽  
Unit Root Testing ◽  
Testing Sequence ◽  
Inflation Rates ◽  
Cointegration Relationship ◽  
Integration Analysis

Detecting the direction of inflation-growth relationship has been a controversial issue in terms of the theoretical framework, notedly since the rise of Mundell-Tobin effect which is based upon the assumption of substitutability between money and capital. In this study, it has been aimed to investigate the cointegrating relationship and its direction between inflation and economic growth covering the period 1998Q1:2014Q4 for Turkey as grounded on the testing sequence that is illustrated by Ilmakunnas (1990) in order to handle unit root testing in a seasonal context by testing the appropriate order of differencing and concerns with the case where SI(2,1) (seasonally integrated of order (2,1)) is the maximum order of seasonal integration. It has been also utilized from ADF unit root test and DHF, HEGY & OCSB seasonal unit root tests in seasonal integration analysis. In the study, five cointegration regressions have been considered in the level, seasonally averaged, quarterly differenced, first differenced and twice differenced forms and two series have been found to have the same degree of seasonal integration as SI(1,1). Applying various residual tests have revealed the presence of a cointegrating relationship between two variables. In addition, the inflation-growth relationship in Turkey has been concluded to perform in an opposite direction.

scholarly journals Impact of Exchange Rate and Oil Prices on Inflation in Pakistan

2021 ◽  
Vol 7 (2) ◽  
pp. 177-185
Author(s):  
Tahira Bano Qasim ◽  
Hina Ali ◽  
Alina Baig ◽  
Maria Shams Khakwani
Keyword(s):  
Exchange Rate ◽  
Unit Root ◽  
Inflation Rate ◽  
Oil Prices ◽  
Oil Price ◽  
Integration Testing ◽  
Integration Technique ◽  
Monthly Data ◽  
Unit Root Testing ◽  
The Impact

This study investigates the impact of Exchange Rate (Rupees Vs US $) and oil prices (Pak. Petroleum) and on the inflation rate in Pakistan by applying the Co-Integration technique to the monthly data for all the three series ranging from January 2004 to January 2019.  Unit root testing results provide strong statistical evidence for each of the series to be non-stationary at the level and stationary at first difference. Co-integration testing results confirm the existence of Cointegration among the selected time series.  Moreover, the empirical results of the regression of inflation on the exchange rate and oil price also lead to conclude that both the series have a strong statistical significant impact on inflation in Pakistan.

scholarly journals Smooth Break Detection and De-Trending in Unit Root Testing

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 371
Author(s):  
Furkan Emirmahmutoglu ◽  
Tolga Omay ◽  
Syed Jawad Hussain Shahzad ◽  
Safwan Mohd Nor
Keyword(s):  
Unit Root ◽  
Structural Breaks ◽  
Structural Break ◽  
Unit Root Tests ◽  
Smooth Transition ◽  
Unit Root Testing ◽  
Augmented Dickey Fuller ◽  
Power Comparisons ◽  
Fourier Function ◽  
Unexpected Outcomes

This study explores the methods to de-trend the smooth structural break processes while conducting the unit root tests. The two most commonly applied approaches for modelling smooth structural breaks namely the smooth transition and the Fourier functions are considered. We perform a sequence of power comparisons among alternative unit root tests that accommodate smooth or sharp structural breaks. The power experiments demonstrate that the unit root tests utilizing the Fourier function lead to unexpected results. Furthermore, through simulation studies, we investigate the source of such unexpected outcomes. Moreover, we provide the asymptotic distribution of two recently proposed unit root tests, namely Fourier-Augmented Dickey–Fuller (FADF) and Fourier-Kapetanios, Shin and Shell (FKSS), which are not given in the original studies. Lastly, we find that the selection of de-trending function is pivotal for unit root testing with structural breaks.

A family of nonparametric unit root tests for processes driven by infinite variance innovations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kemal Caglar Gogebakan
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Tuning Parameter ◽  
Infinite Variance ◽  
Finite Sample ◽  
Power Performance ◽  
Finite Sample Size ◽  
Heavy Tailed ◽  
The Impact ◽  
Adf Test

Abstract This paper presents extensions to the family of nonparametric fractional variance ratio (FVR) unit root tests of Nielsen (2009. “A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic.” Econometric Theory 25: 1515–44) under heavy tailed (infinite variance) innovations. In this regard, we first develop the asymptotic theory for these FVR tests under this setup. We show that the limiting distributions of the tests are free of serial correlation nuisance parameters, but depend on the tail index of the infinite variance process. Then, we compare the finite sample size and power performance of our FVR unit root tests with the well-known parametric ADF test under the impact of the heavy tailed shocks. Simulations demonstrate that under heavy tailed innovations, the nonparametric FVR tests have desirable size and power properties.

Point Optimal Tests for Testing the Order of Differencing in ARIMA Models

1993 ◽  
Vol 9 (3) ◽  
pp. 343-362 ◽  
Author(s):  
Pentti Saikkonen ◽  
Ritva Luukkonen
Keyword(s):  
Unit Root ◽  
Null Hypothesis ◽  
Moving Average ◽  
Multivariate Time Series ◽  
Unit Root Tests ◽  
Test Procedures ◽  
Original Series ◽  
Cointegrating Vector ◽  
Unit Root Testing ◽  
Average Unit

Deciding the order of differencing is an important part in the specification of an autoregressive integrated moving average (ARIMA) mode. In most, though not all, cases this means deciding whether to use the original observations or their first differences. Common test procedures used in this context are some variants of autoregressive unit root tests. In these tests, one tests the null hypothesis that the order of differencing is one against the alternative that it is zero. The null hypothesis thus states that the original series is nonstationary and integrated of order one, whereas the alternative assumes that it is stationary. In this paper the situation is reversed so that our null hypothesis states that the original series is stationary, whereas the alternative states that it is integrated of order one. In our approach the use of a differenced series thus means overdifferencing and, consequently, a model with a moving average unit root. Testing for this moving average unit root is the topic of this paper. As discussed by Saikkonen and Luukkonen [26] and Tanaka [31], test procedures obtained for this null hypothesis can also be used to test the null hypothesis that a multivariate time series is cointegrated with a given theoretical cointegrating vector. Since the null hypothesis of cointegration is often of interest and cannot be naturally tested by autoregressive unit root tests, this connection provides an important motivation for the test procedures of this paper.

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