Unit-root tests for explosive behavior

2021 ◽  
Vol 21 (4) ◽  
pp. 999-1020
Author(s):  
Christopher F. Baum ◽  
Jesús Otero
Keyword(s):  
International Economic ◽  
Unit Root ◽  
American Statistical Association ◽  
Unit Root Tests ◽  
Statistical Association ◽  
International Economic Review ◽  
Augmented Dickey Fuller ◽  
Using Data ◽  
The Right ◽  
Rolling Windows

We present a new command, radf, that tests for explosive behavior in time series. The command computes the right-tail augmented Dickey and Fuller (1979, Journal of the American Statistical Association 74: 427–431) unitroot test and its further developments based on supremum statistics derived from augmented Dickey–Fuller-type regressions estimated using recursive windows (Phillips, Wu, and Yu, 2011, International Economic Review 52: 201–226) and recursive flexible windows (Phillips, Shi, and Yu, 2015, International Economic Review 56: 1043–1078). It allows for the lag length in the test regression and the width of rolling windows to be either specified by the user or determined using data-dependent procedures, and it performs the date-stamping procedures advocated by Phillips, Wu, and Yu (2011) and Phillips, Shi, and Yu (2015) to identify episodes of explosive behavior. It also implements the wild bootstrap proposed by Phillips and Shi (2020, Handbook of Statistics: Financial, Macro and Micro Econometrics Using R, Vol. 42, 61–80) to lessen the potential effects of unconditional heteroskedasticity and account for the multiplicity issue in recursive testing. The use of radf is illustrated with an empirical example.

scholarly journals THE IMPACT OF PERSISTENT CYCLES ON ZERO FREQUENCY UNIT ROOT TESTS

2013 ◽  
Vol 29 (6) ◽  
pp. 1289-1313 ◽  
Author(s):  
Tomás del Barrio Castro ◽  
Paulo M.M. Rodrigues ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Unit Root Test ◽  
American Statistical Association ◽  
Unit Root Tests ◽  
Statistical Association ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Augmented Dickey Fuller ◽  
Frequency Unit ◽  
The Impact

In this paper we investigate the impact of persistent (nonstationary or near nonstationary) cycles on the asymptotic and finite-sample properties of standard unit root tests. Results are presented for the augmented Dickey–Fuller (ADF) normalized bias and t-ratio-based tests (Dickey and Fuller, 1979, Journal of the American Statistical Association 745, 427–431; Said and Dickey, 1984; Biometrika 71, 599–607). the variance ratio unit root test of Breitung (2002, Journal of Econometrics 108, 343–363), and the M class of unit-root tests introduced by Stock (1999, in Engle and White (eds.), A Festschrift in Honour of Clive W.J. Granger) and Perron and Ng (1996, Review of Economic Studies 63, 435–463). We show that although the ADF statistics remain asymptotically pivotal (provided the test regression is properly augmented) in the presence of persistent cycles, this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that the t-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994, Journal of Business & Economic Statistics 17, 461–470; Ng and Perron, 1995, Journal of the American Statistical Association 90, 268–281) used to determine the order of augmentation in the ADF regression remain valid in the presence of persistent cycles.

scholarly journals SIGN-BASED UNIT ROOT TESTS FOR EXPLOSIVE FINANCIAL BUBBLES IN THE PRESENCE OF DETERMINISTICALLY TIME-VARYING VOLATILITY

2019 ◽  
Vol 36 (1) ◽  
pp. 122-169 ◽  
Author(s):  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
Yang Zu
Keyword(s):  
International Economic ◽  
Unit Root ◽  
Financial Data ◽  
Unit Root Tests ◽  
Time Varying ◽  
Wild Bootstrap ◽  
Financial Bubbles ◽  
International Economic Review ◽  
Higher Power ◽  
Empirical Illustration

This article considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a sign-based variant of the Phillips, Shi, and Yu (2015, International Economic Review 56, 1043–1077) test. Unlike the original test, the sign-based test does not require bootstrap-type methods to control size in the presence of time-varying volatility. Under a locally explosive alternative, the sign-based test delivers higher power than the original test for many time-varying volatility and bubble specifications. However, since the original test can still outperform the sign-based one for some specifications, we also propose a union of rejections procedure that combines the original and sign-based tests, employing a wild bootstrap to control size. This is shown to capture most of the power available from the better performing of the two tests. We also show how a sign-based statistic can be used to date the bubble start and end points. An empirical illustration using Bitcoin price data is provided.

Globalization, International Trade, and CO2 Convergence

2021 ◽  
pp. 53-64
Author(s):  
Furkan Yıldız
Keyword(s):  
International Trade ◽  
Co2 Emissions ◽  
Unit Root ◽  
Unit Root Tests ◽  
Stochastic Convergence ◽  
Group Of Seven ◽  
Augmented Dickey Fuller ◽  
Trade Partner ◽  
Per Capita ◽  
Trade Partners

The goal of this study is to investigate the potential effects of international trade on per-capita CO2 emissions among trade partners. To achieve this purpose, the Group of Seven (G7) countries and each of their developing trade-partner countries with the highest trade volume have been selected as the sample. The stochastic convergence methodology has been employed using Augmented Dickey Fuller (ADF), Phillips-Perron (PP), and Enders-Lee Fourier unit root tests in order to test for convergence or divergence. Various results have been obtained from the unit root tests. These results suggest international trade to have no general or common effects on per capita CO2 emissions.

scholarly journals On the Performance of Wavelet Based Unit Root Tests

2018 ◽  
Vol 11 (3) ◽  
pp. 47 ◽  
Author(s):  
Burak Eroğlu ◽  
Barış Soybilgen
Keyword(s):  
Least Squares ◽  
Unit Root ◽  
Moving Average ◽  
Asymptotic Properties ◽  
Generalized Least Squares ◽  
Unit Root Tests ◽  
Augmented Dickey Fuller ◽  
Wavelet Methods

In this paper, we apply the wavelet methods in the popular Augmented Dickey-Fuller and M types of unit root tests. Moreover, we provide an extensive comparison of the wavelet based unit root tests which also includes the recent contributions in the literature. Moreover, we derive the asymptotic properties of the wavelet based unit root tests under generalized least squares detrending mechanism. We demonstrate that the wavelet based M tests exhibit better size performance even in problematic cases such as the presence of negative moving average innovations. However, the power performances of the wavelet based unit root tests are quite similar to each other.

scholarly journals ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS

2012 ◽  
Vol 28 (5) ◽  
pp. 1121-1143 ◽  
Author(s):  
Tomás del Barrio Castro ◽  
Denise R. Osborn ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Linear Process ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
Martingale Difference ◽  
Linear Processes ◽  
Seasonal Unit Roots ◽  
Null Distributions ◽  
Augmented Dickey Fuller

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.

scholarly journals STUDY OF TESTS FOR TREND IN TIME SERIES

2021 ◽  
Vol 39 (2) ◽  
pp. 311-333
Author(s):  
Denise de Assis PAIVA ◽  
Thelma SÁFADI
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Structural Breaks ◽  
Consumer Price Index ◽  
Unit Root Tests ◽  
Metropolitan Region ◽  
Maximum Temperature ◽  
Pettitt Test ◽  
Using Data ◽  
Time Series Methodology

The time series methodology is an important tool when using data over time. The time series can be composed of the components trend (Tt), seasonality (St) and the random error (at). The aim of this study was to evaluate the tests used to analyze the trend component, which were: Pettitt, Run, Mann-Kendall, Cox-Stuart and the unit root tests (Dickey-Fuller, Dickey-Fuller Augmented and Zivot and Andrews), given that there is a discrepancy between the test results found in the literature. The four series analyzed were the maximum temperature in the Lavras city, MG, Brazil, the unemployment rate in the Metropolitan Region of S~ao Paulo (RMSP), the Broad Consumer Price Index (IPCA) and the nominal Gross Domestic Product (GDP) of Brazil. It was found that the unit root tests showed similar results in relation to the presence of the stochastic trend for all series. Furthermore, the turning point of the Pettitt test diverged from all the structural breaks found through the Zivot and Andrews test, except for the GDP series. Therefore, it was found that the trend tests diverged, obtaining similar results only in relation to the unemployment series.

The Issue of Logistics and Its Correlation to Economic Growth in Turkey

2021 ◽  
Vol 11 (1) ◽  
pp. 66-80
Author(s):  
Berrak Erkumru Can ◽  
Dilek Temiz Dinç ◽  
Aytaç Gökmen
Keyword(s):  
Economic Growth ◽  
Unit Root ◽  
Unit Root Tests ◽  
Short Term ◽  
Turkish Republic ◽  
Goods And Services ◽  
Augmented Dickey Fuller

Logistics is a considerable issue for the development of a state and its economy. Logistics is involved the forward and backward flows of goods and services from the point of production and point of consumption, and it is considerable for the development of the economy of a country. Yet, the aim of this paper is to review the correlation between the logistics sector of the Turkish Republic and its correlation to economic growth by employing Augmented Dickey Fuller-ADF, Phillips-Perron (PP), Kwiatkowski, Phillips, Schmidt, Shin (KPSS), Elliott, Rothenberg and Stock Point Optimal, and Ng-Perron unit root tests. As a result, there is a bidirectional positive causality between logistics sector and economic growth in the long-term, but there is no causality for short term. Moreover, the novelty of this paper is that it is the most up-to-date study to research logistics and its correlation to economics in Turkey.

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.

Investigation of the price linkage between Asian LNG spot and Far East Asian LNG prices and its implications

2018 ◽  
Vol 1 (1) ◽  
pp. 52-65
Author(s):  
Muhammad Anas Pradipta
Keyword(s):  
Natural Gas ◽  
Unit Root ◽  
East Asian ◽  
Far East ◽  
Unit Root Tests ◽  
Spot Prices ◽  
South Korean ◽  
Natural Gas Prices ◽  
Augmented Dickey Fuller

For so many times, Far East Asian liquid natural gas (LNG) buyers have been using price linked to crude oil-indexed, now they need to find another alternative pricing formula for their crucial energy supply as a better price structure that could reflect the market is needed. LNG spot price is expected to be the pillar for the future LNG trading, especially for Far East Asia Market. As less and less long-term contracts are signed in the Far East Asia Market, this creates an additional demand for the LNG in the spot market, while it raises some issues about the presence of different LNG pricing mechanisms. Most of the LNG spot prices in Asia are indexed to the relatively low natural gas prices in Atlantic Basin. Furthermore, the advancement of drilling technology in the US drives down its natural gas prices, resulting in price discrepancies between Asian LNG spot and East Asian LNG prices. This study investigates whether there is a price linkage between Asian LNG spot and East Asian LNG prices. This study comprehends 91 observations collected from January 2010 to July 2017. Johansen co-integration tests were carried out to examine the existence of long-run relationship on the spot, Japanese and South Korean LNG prices. The Augmented Dickey-Fuller (ADF), Phillip-Perron (PP), and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) unit root tests were conducted first before proceeding to the co-integration tests. The results showed that Asian LNG spot prices did not have price linkage for monthly averages of Japanese and South Korean LNG prices. The analyses also indicated that Taiwan LNG markets move together with Asian LNG spot markets. As a conclusion, the results inferred that supply dependency on LNG spot cargoes governed the price linkage among these Asian LNG markets. The use of gas indexed LNG price mechanism did not reflect the economic fundamentals in Asia-Pacific Basin. JEL Classification: Q41Keywords: Price linkage, Johansen co-integration, augmented Dickey-Fuller, Phillip-Perron, and Kwiatkowski-Phillips-Schmidt-Shin, unit root tests, Far East Asian LNG spot prices, LNG spot and short-term cargoes, long-term contracts, spot prices, energy: demand and supply, prices

scholarly journals RIPPLE EFFECT AND REGIONAL HOUSE PRICES DYNAMICS IN CHINA

2016 ◽  
Vol 20 (4) ◽  
pp. 397-408 ◽  
Author(s):  
Chi-Chuan LEE ◽  
Chien-Chiang LEE ◽  
Shu-Hen CHIANG
Keyword(s):  
Unit Root ◽  
House Prices ◽  
Unit Root Test ◽  
Unit Root Tests ◽  
Ripple Effect ◽  
Seemingly Unrelated Regressions ◽  
Long Run ◽  
Equilibrium Relationship ◽  
Augmented Dickey Fuller ◽  
Long Run Equilibrium

This paper examines the stationarity properties, the long-run equilibrium and the leadlag relationship among the regional house prices in China from December 2000 to July 2013. Unlike traditional unit-root tests, the panel seemingly unrelated regressions augmented Dickey-Fuller (SURADF) unit-root test reveals that the regional house prices in China are a mixture of I(0) and I(1) processes. There is concrete evidence in favor of the hypothesis of a long-run equilibrium relationship among all regions, except for Shanghai region, and supporting the price diffusion or ripple effect among these Chinese cities. Finally, we determine that these regional house prices exhibit uni-directional causalities running from Beijing, Chongqing, and Shenzhen to Guangzhou and Tianjin, respectively.

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