Unit Root Test Statistics Research Articles

The Causality between Economic Growth, Public Debt and Government Spending of Lao PDR

This paper aims to test the causality between economic growth, public debt and government spending. This study used the time series data from 1995-2021 and implied with a VAR model and Granger causality test. In addition, the unit root, cointegration, Lagrange multiplier and Jarque-Bera test statistics was used. The empirical analysis by using VAR model found that public debt and economic growth have no effect on public spending. But government spending affects public debt in the same direction with a statistical significance level of 0.1 meaning that only government spending affects public debt, while public debt does not affect government spending. While government spending and public debt affect economic growth in the same direction with a statistical significance level of 0.01. For the Granger Causality Test, there is a unidirectional relationship means that only government spending and public debt affect economic growth, economic growth does not affect government spending and public debt.

Power of Unit Root Tests Against Nonlinear and Noncausal Alternatives with an Application to the Brent Crude Oil Price

Abstract The increasing sophistication of economic and financial time series modelling creates a need for a test of the time dependence structure of the series which does not require a proper specification of the alternative. Indeed, the latter is unknown beforehand. Yet, the stationarity has to be established before proceeding to the estimation and testing of causal/noncausal or linear/nonlinear models as their econometric theory has been developed under the maintained assumption of stationarity. In this paper, we propose a new unit root test statistics which is both asymptotically consistent against all stationary alternatives and still keeps good power properties in finite sample. A large simulation study is performed to assess the power of our test compared to existing unit root tests built specifically for various kinds of stationary alternatives, when the true DGP is either causal or noncausal, linear or nonlinear stationary. Based on various sample sizes and degrees of persistence, it turns out that our new test performs very well in terms of power in finite sample, no matter the alternative under consideration. The proposed approach is illustrated using recent Brent crude oil price data.

On the validity of the residual-based bootstrap for the unit root test statistic with long memory observations

Consider the AR(1) model, where is a sequence of long memory processes with possibly infinite variance. In this paper, we propose to use a residual-based m-out-of-n bootstrap procedure to approximate the distribution of a least-squares estimator for the autoregressive parameter when this parameter is equal to unity, and its asymptotic validity is also proved.

Development and Degradation: The Nexus between GDP, FDI, and Pollution in India

The nexus between development and environment has been a debatable topic for years, more so when foreign direct investment (FDI is used to accelerate the economy. Since environmental Kuznets curve may not be achievable by all economies and many studies have not been able to establish a consistent relationship between FDI and environment, this study determines the liaison between FDI, GDP, and pollution in India with time series data from 1990 to 2015. While per capita GDP plotted against per capita carbon dioxide (CO2) emission indicates an alarming positive relation, the co-integration between FDI, GDP, and CO2 tested using unit root test statistics (augmented Dickey–Fuller test) for stationarity and then by Johansen and Juselius’s multivariate co-integration technique show a long-run co-integration. Since the existence of a relationship between variables does not prove causality, the variables are phrased in a vector error correction (VEC) form and vector error correction mechanism (VECM) Granger causality/block exogeneity Wald test which reveals that FDI has a positive and significant impact on pollution and GDP attracts FDI. This transitive relation suggests that FDI in pollution-controlling technology would be a feasible solution to sustainable development.

Money Market Instruments and Financial Deepening in the Nigeria Emerging Economy

The study examined money market instruments and financial deepening in the context of an emerging economy like Nigeria. The study used money market instruments like Treasury bills (TBs), Bankers’ acceptances (BAs), Certificate of deposits (CDs) and Commercial papers (CPs). The ratio of money supply to gross domestic product was a proxy for financial deepening. Time series data was generated from Central Bank of Nigeria Statistical Bulletins in the period 1981 to 2016 for the study. Preliminary tests including Augmented Dickey Fuller (ADF), unit root test and descriptive statistics were carried out before the main econometric procedures were employed to analyze the data. The econometric procedures carried out include granger causality test, the ordinary least square multivariate regression method; the Johansen co-integration and the error correction mechanism methods (ECM). The study found strong effect of money market instruments on financial deepening in Nigeria in the long run. Granger causality test result revealed no directional causality relationship between Treasury bills and financial deepening, while bi-directional causality exists between Certificate of deposits and financial deepening; unidirectional causality exists between Bankers’ acceptances, Commercial papers and financial deepening. The study recommends that policies that promote trading in international money market instruments like Bankers’ acceptances should be strengthened by the Federal government of Nigeria to deepen the financial market as well as enhance the competitiveness of the Nigerian money market in the global market. This should consequently translate to financial deepening in Nigeria and improvement of the economy at large. Keywords: Financial Deepening, Treasury Bills, Bankers’ Acceptances, Certificate of Deposits and Commercial Papers. JEL CLASSIFICATION: M10 DOI : 10.7176/RJFA/10-16-07 Publication date : August 31 st 2019

THE TWIN DEFICITS IN MALAYSIA: EMPIRICAL EVIDENCE

This study examines the twin deficits in Malaysia. The Dickey and Fuller (DF) and Phillips and Perron (PP) unit root test statistics show that all variables examined are non-stationary. The Johansen cointegration test statistics show that there is long-run relationship between external balances and its determinants includes budget balances. Moreover, increases in budget balances will lead to increases in external balances and increase in investment will lead to decreases in external balances. The results of the fully modified ordinary least squares (FMOLS) estimator demonstrate about the same conclusion of the relationship between external balances and budget balances as the conclusion of the Johansen cointegration method. Consolidated budgets will lead to healthy external balances, which are important for achieving sustainable economic growth.

BOOTSTRAP-ASSISTED UNIT ROOT TESTING WITH PIECEWISE LOCALLY STATIONARY ERRORS

In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the limiting null distributions of the conventional unit root test statistics are derived and shown to contain a number of unknown parameters. To circumvent the difficulty of direct consistent estimation, we propose to use the dependent wild bootstrap to approximate the nonpivotal limiting null distributions and provide a rigorous theoretical justification for bootstrap consistency. The proposed method is compared through finite sample simulations with the recolored wild bootstrap procedure, which was developed for errors that follow a heteroscedastic linear process. Furthermore, a combination of autoregressive sieve recoloring with the dependent wild bootstrap is shown to perform well. The validity of the dependent wild bootstrap in a nonstationary setting is demonstrated for the first time, showing the possibility of extensions to other inference problems associated with locally stationary processes.

The dynamic relationship between energy consumption and economic growth in China

ABSTRACTEconomic growth of is mainly associated with technical changes as well as energy consumption of a nation. The causality between energy consumption and economic growth has created much more attention in the literature. With advanced technology and automated comfort life, the requirement of energy demand has been increasing rapidly. The goal of this study is to examine the causal relationship between energy consumption and economic growth in China over the period of 1980 – 2013. As a first step, stationary properties of the selected variables were tested using unit root test statistics. Next, the Johansen co-integration with Vector error correction model (VECM) was applied to examine the dynamic links between among the variables.The result confirmed a long run bidirectional causal relation running between energy consumption and economic growth. Furthermore, results make a significant contribution to policy makers to open up a new direction to the development of energy sector in China.

Unit Root Testing with Unstable Volatility

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 to differ from the nominal level. We propose a class of modified unit root test statistics that are robust to the presence of unstable volatility. The modification is achieved by purging heteroskedasticity from the data using a kernel estimate of volatility before the application of standard tests. In the absence of deterministic trend components, this approach delivers test statistics that achieve standard asymptotics under the null hypothesis of a unit root. When the data are homoskedastic, the local power of unit root tests is unchanged by our modification. We use Monte Carlo simulations to compare the finite sample performance of our modified tests with that of existing methods of correcting for unstable volatility.

Unit root quantile autoregression testing with smooth structural changes

By incorporating the flexible Fourier form into quantile autoregression model, this paper proposes three new unit root test statistics, which are robust to both non-Gaussian condition and structural changes. Since their limiting distributions are non-standard, a bootstrap procedure is developed to calculate their critical values. Monte Carlo simulation results show that, while Koenker and Xiao (2004) tests are quite conservative under various kinds of error distributions and structural changes, the newly proposed tests have good size performance except for a little size distortion occasionally. Moreover, our tests have much higher performance especially when the sample size is small.

Testing for Unit Roots in Dynamic Panels with Smooth Breaks and Cross-Sectionally Dependent Errors

We develop the extended unit root testing procedure for dynamic panels characterised by slowly moving trends (SMT) and cross-section dependence (CSD). We allow SMT to follow the smooth logistic transition function and the components error terms to contain the unobserved common factors. We propose the two panel unit root test statistics, one derived by the extended common correlated effects (CCE) estimator and the other based on the Sieve bootstrap. We have conducted extensive simulation exercises and document that the failure to take into account SMT and CSD may lead to misleading inference. On the other hand, we find that both bootstrap and CCE-based tests maintain good power properties in small samples in the presence SMT and CSD. We apply our proposed tests to real interest rates for 17 OECD countries and find overwhelming evidence in favour of the Fisher hypothesis.

REAL EXCHANGE RATE RETURNS AND REAL STOCK PRICE RETURNS IN THE STOCK MARKET OF MALAYSIA

This study examines the relationships between real exchange rate returns and real stock price returns in the stock market of Malaysia. The Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and Dickey and Fuller (DF) unit root test statistics show that all the variables examined are found to be stationary in the first differences. The constant conditional correlation (CCC)-multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model shows that real exchange rate return of Malaysian ringgit against the United States dollar (RM/USD) and real stock price return of Kuala Lumpur Composite Index (KLCI) are found to be negative and significantly correlated. However, there is insignificant correlation between real exchange rate return of Malaysian ringgit against Japanese Yen (RM/¥) and real stock price return of KLCI. Moreover, the CCC-MGARCH models show that real exchange rate returns and real stock price returns of some stocks are found to be significantly correlated. The KPSS unit root test statistics show that the time invariant conditional variances of real exchange rate returns and real stock price returns are mostly found to be stationary in the levels. There is no evidence of Granger causality between the time invariant conditional variances of real exchange rate returns and real stock price return of KLCI but some evidence of Granger causality between the time invariant conditional variances of real exchange rate returns and real stock price returns. There is a link between the exchange rate market and the stock market in Malaysia but not every real stock price return is significantly linked with real exchange rate return.

Physical Capital Investment and Growth: Panel Data Evidence from European Regions

This article empirically assesses the validity of alternative growth models at regional level. This is done by comparing the stochastic properties of physical capital investment and growth using a panel unit root test statistic that is robust to cross-sectional dependence of a spatial nature. Our results for European NUTS 2 regions provide evidence more favorable to the predictions of AK-type endogenous growth models.

Asymptotic properties of the bootstrap unit root test statistic under possibly infinite variance

ABSTRACTIn this article, the unit root test for the AR(1) model is discussed, under the condition that the innovations of the model are in the domain of attraction of the normal law with possibly infinite variances. By using residual bootstrap with sample size m < n (n being the size of the original sample), we bootstrap the least-squares estimator of the autoregressive parameter. Under some mild assumptions, we prove that the null distribution of the unit root test statistic based on the least-square estimator of the autoregressive parameter can be approximated by using residual bootstrap.

Bounds, Breaks and Unit Root Tests

The paper addresses the unit root testing when the range of the time series is limited and considering the presence of multiple structural breaks. The structural breaks can affect the level and/or the boundaries of the time series. The paper proposes five unit root test statistics, whose limiting distribution is shown to depend on the number and position of the structural breaks. The performance of the statistics is investigated by means of Monte Carlo simulations.

Unit root test against ESTAR with deterministic components

This article intends to notify that asymptotic distributions of the nonlinear unit root test statistics must be rigorously treated if deterministic components are included in the estimated regression. The simple inductive argument of replacing the standard Brownian motion by either the demeaned or demeaned and detrended ones usually adopted in the literature is invalid. New results on the asymptotic distributions of the t-ratio to test the null of the unit root against the nonlinear exponential smooth transition autoregressive (ESTAR) with deterministic components are provided.

The Calculation of Some Limiting Distributions Arising in Near‐Integrated Models with GLS Detrending

Many unit root test statistics are based on detrended data, with the method of generalized least squares (GLS) detrending being popular in the setting of a near‐integrated model. This article determines the properties of some associated limiting distributions when the GLS detrending is based on a linear time trend. A fundamental result for the moment generating function of two key functionals of the relevant stochastic process is provided and used to compute probability density functions and cumulative distribution functions, as well as means and variances, of the limiting distributions of some statistics of interest. The exact moments and percentiles of some of these distributions are compared with those obtained by simulations, and it is found that, even with a large number of replications and a large sample size, the errors resulting from the simulation methods are not negligible. Some further applications, including a comparison of limiting power functions of different unit root test statistics and the consideration of a more complicated statistic, are also provided.

Derivative Trading and Spot Market Volatility: Evidence from Indian Market

The present study tries to estimate the effect of introduction of individual stock derivatives on the underlying stock volatility in Indian stock market. To estimate the effect of introduction of derivatives on stock market, GARCH family models which are known for their ability to model volatility. The return series of the ten companies were tested using methods like, unit root test and descriptive statistics to confirm that GARCH models could be used. Using these models, the asymmetric nature of stock returns and the volatility of stock returns on the introduction of derivatives are checked. The results reveal that the introduction of derivatives has decreased the volatility of the underlying stock returns. It was also found that most of the stock returns show asymmetric behaviour.

Testing for Unit Roots Under Multiple Possible Trend Breaks and Non‐Stationary Volatility Using Bootstrap Minimum Dickey–Fuller Statistics

In a recent paper, Harvey et al. (2013) (HLT) propose a new unit root test that allows for the possibility of multiple breaks in trend. Their proposed test is based on the infimum of the sequence (across all candidate break points) of local GLS detrended augmented Dickey–Fuller‐type statistics. HLT show that the power of their unit root test is robust to the magnitude of any trend breaks. In contrast, HLT show that the power of the only alternative available procedure of Carrion‐i‐Silvestre et al. (2009), which employs a pretest‐based approach, can be very low indeed (even zero) for the magnitudes of trend breaks typically observed in practice. Both HLT and Carrion‐i‐Silvestre et al. (2009) base their approaches on the assumption of homoskedastic shocks. In this article, we analyse the impact of non‐stationary volatility (for example, single and multiple abrupt variance breaks, smooth transition variance breaks and trending variances) on the tests proposed in HLT. We show that the limiting null distribution of the HLT unit root test statistic is not pivotal under non‐stationary volatility. A solution to the problem, which does not require the practitioner to specify a parametric model for volatility, is provided using the wild bootstrap and is shown to perform well in practice. A number of different possible implementations of the bootstrap algorithm are discussed.

Detection of Stationary Errors in Multiple Regressions with Integrated Regressors and Cointegration

This article studies the problem of detecting sequentially stationary error terms in a multiple regression model with a difference-stationary multivariate I(1)-regressor. The detection of cointegration is covered as a special case. We provide the asymptotic distribution theory for a monitoring procedure that is related to a well-known nonparametric unit root test statistic calculated from sequentially updated least squares residuals. Functional limit theorems for the corresponding sequential processes and central limit theorems for the detectors used to raise an alarm are established under the no-change null hypothesis as well as under change-point models covering a change to I(0)-errors and a change of the regression coefficients as well. We also discuss extensions to the case that continuous time processes are discretely sampled to obtain the data allowing to apply the procedures to high-frequency data as well. Our results show that we can handle the infill asymptotics assuming that nonstationary continuous-time processes such as semimartingales are discretely observed, by virtue of the general assumptions that we impose. The finite sample properties are investigated by a simulation study.