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Journal articles on the topic 'Dickey-Fuller test'

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Published: 4 June 2021

Last updated: 4 February 2022

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1

Islam, Masudul, Afroza Akhtar, Sirajum Munira, Md Salauddin Khan, and Md Monzur Murshed. "Optimized Dickey-Fuller Test Refines Sign and Boundary Problems Compare to Traditional Dickey-Fuller Test." International Journal of Statistics and Probability 7, no. 5 (August 3, 2018): 19. http://dx.doi.org/10.5539/ijsp.v7n5p19.

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Impede nonstationarity is vigorous to study performance of time series data and removes long-term components to expose any regular short-term regularity. So, we find miscellaneous unit root tests for instance Dickey-Fuller test, Augmented Dickey-Fuller plus DF-GLS Tests and identify that almost all unit root tests with the estimated model suffer from sign and boundary problems of the parameters to smooth the progress of the non-stationarity problem. In this paper, we usage Dickey-Fuller test and impose some limits on the parameter. Our proposed optimized DF test based on error sum of square (ESS). Monto Carlo simulation method is used to generate simulated critical values for different sample size. Our proposed optimized DF test gives better result than the ordinary DF test with effectiveness, uniformity and power properties. Also, optimized DF improves the sign and boundary problems through imposing some limit on error sum of squares and capture more nonstationarity of time related data.

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2

Fotopoulos, Stergios B., and Sung K. Ahn. "Rank Based Dickey-Fuller Test Statistics." Journal of Time Series Analysis 24, no. 6 (November 2003): 647–62. http://dx.doi.org/10.1111/j.1467-9892.2003.00327.x.

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3

Cheolyong Park, 이희수, Sun Young Hwang, 하정철, and Kim Tae Yoon. "Dickey-Fuller Test for an Extended MA Model." Quantitative Bio-Science 38, no. 1 (May 2019): 1–21. http://dx.doi.org/10.22283/qbs.2019.38.1.1.

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4

Krämer, Walter. "Fractional integration and the augmented Dickey–Fuller Test." Economics Letters 61, no. 3 (December 1998): 269–72. http://dx.doi.org/10.1016/s0165-1765(98)00194-3.

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5

Dolado, Juan J., Jesus Gonzalo, and Laura Mayoral. "A Fractional Dickey-Fuller Test for Unit Roots." Econometrica 70, no. 5 (September 2002): 1963–2006. http://dx.doi.org/10.1111/1468-0262.00359.

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6

Bodhgire, Nandkumar Baburao. "Augmented Dickey - Fuller Unit Root Test for Household Saving." Asian Journal of Research in Banking and Finance 5, no. 8 (2015): 64. http://dx.doi.org/10.5958/2249-7323.2015.00101.7.

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7

Demetrescu, Matei. "On the Dickey–Fuller test with White standard errors." Statistical Papers 51, no. 1 (January 5, 2008): 11–25. http://dx.doi.org/10.1007/s00362-007-0112-1.

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8

Sephton, Peter S. "Critical values of the augmented fractional Dickey–Fuller test." Empirical Economics 35, no. 3 (January 23, 2008): 437–50. http://dx.doi.org/10.1007/s00181-007-0171-0.

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9

Cook, Steven. "Unit root testing in the presence of innovation variance breaks: a simple solution with increased power." Journal of Applied Mathematics 2, no. 5 (2002): 233–40. http://dx.doi.org/10.1155/s1110757x02107029.

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The Dickey-Fuller unit root test is known to suffer severe oversizing in the presence of innovation variance breaks. In this paper, forward and reverse Dickey-Fuller regressions are proposed as a means of correcting this size distortion. The results of Monte Carlo experimentation show such an approach to result in both satisfactory size properties and increased power relative to previously suggested solutions.

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10

Deng, Lu. "Augmented Dickey-Fuller Test and the Lag Length Selection Problem." Applied Mechanics and Materials 130-134 (October 2011): 3019–22. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.3019.

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Many studies indicated that ADF test is very sensitive to different leg length selection models. Based on Hall, and Ng, Perron’s works, this article simulates a more general ARIMA(0,1,q) process and compares the influence of different selection methods to the size and power of the ADF test. Finally, it is proved that the Modified Information Criteria always shows a more proper size and the General to Special Criteria has more robust ADF test properties.

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11

Harris, R. I. D. "Testing for unit roots using the augmented Dickey-Fuller test." Economics Letters 38, no. 4 (April 1992): 381–86. http://dx.doi.org/10.1016/0165-1765(92)90022-q.

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12

Kasparis, Ioannis. "DETECTION OF FUNCTIONAL FORM MISSPECIFICATION IN COINTEGRATING RELATIONS." Econometric Theory 24, no. 5 (July 9, 2008): 1373–403. http://dx.doi.org/10.1017/s0266466608080547.

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A simple specification test based on fully modified residuals and the cumulative sum (CUSUM) test for cointegration of Xiao and Phillips (2002, Journal of Econometrics, 108, 43–61) are considered as means of testing for functional form in long-run cointegrating relations. It is shown that both tests are consistent under functional form misspecification and lack of cointegration. A simulation experiment is carried out to assess the properties of the tests in finite samples. The Dickey–Fuller test is also considered. The simulation results reveal that the first two tests perform reasonably well. However, the Dickey–Fuller test performs poorly under functional form misspecification.

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13

Montañés and Sansó. "The Dickey-Fuller Test Family and Changes in the Seasonal Pattern." Annales d'Économie et de Statistique, no. 61 (2001): 73. http://dx.doi.org/10.2307/20076270.

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14

Cheung, Yin-Wong, and Kon S. Lai. "Lag Order and Critical Values of the Augmented Dickey-Fuller Test." Journal of Business & Economic Statistics 13, no. 3 (July 1995): 277. http://dx.doi.org/10.2307/1392187.

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15

Cheung, Yin-Wong, and Kon S. Lai. "Lag Order and Critical Values of the Augmented Dickey–Fuller Test." Journal of Business & Economic Statistics 13, no. 3 (July 1995): 277–80. http://dx.doi.org/10.1080/07350015.1995.10524601.

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16

Bensalma, Ahmed. "Testing the fractional integration parameter revisited: a fractional Dickey-Fuller test." International Journal of Mathematics in Operational Research 12, no. 4 (2018): 471. http://dx.doi.org/10.1504/ijmor.2018.092106.

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17

Bensalma, Ahmed. "Testing the fractional integration parameter revisited: a fractional Dickey-Fuller test." International Journal of Mathematics in Operational Research 12, no. 4 (2018): 471. http://dx.doi.org/10.1504/ijmor.2018.10011879.

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18

Westerlund, Joakim. "On the asymptotic distribution of the Dickey Fuller-GLS test statistic." Statistics 48, no. 6 (October 18, 2013): 1233–53. http://dx.doi.org/10.1080/02331888.2013.835815.

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19

Leybourne, Stephen, Tae-Hwan Kim, and Paul Newbold. "Examination of Some More Powerful Modifications of the Dickey-Fuller Test." Journal of Time Series Analysis 26, no. 3 (May 2005): 355–69. http://dx.doi.org/10.1111/j.1467-9892.2004.00406.x.

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20

Chaudhry, Ali Farhan, Mian Muhammd Hanif, Sameera Hassan, and Muhammad Irfan Chani. "Efficiency of the Black Foreign Exchange Market." International Journal of Economics and Finance 11, no. 2 (January 20, 2019): 165. http://dx.doi.org/10.5539/ijef.v11n2p165.

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This empirical study is first of its nature to examine the weak-form of efficiency for unofficial foreign exchange market of Pakistan proxied by Japanese Yen (JPY/PKR), Swiss Franc (CHF/PKR), British Pound (GBP/PKR), and US Dollar (USD/PKR) exchange rates. For this we have employed Ljung Box Q-test, unit root tests including Dickey-Fuller (Dickey 1979), Augmented Dickey-Fuller (Dickey 1981) tests and Phillips and Perron (1988) test, Durbin Watson test, Runs-test, and Variance ratio test by using unofficial foreign exchange rate time series of Yen/PKR, CHF/PKR, GBP/PKR and USD/PKR from 1994M07 to 2001M06. Empirical results lead to the conclusion that the unofficial foreign exchange market of Pakistan is weak-form efficiency. The implications of this empirical research are of great importance for designing foreign exchange policy i.e. policy makers (be it accounting, export/import or public policy makers) are to consider fluctuations in unofficial foreign exchange rates while designing official foreign exchange rate policy of developing country like Pakistan. Further, policymakers can enhance the efficiency of official foreign exchange market by intervention subject to a widening of unofficial foreign exchange premium beyond a certain limit in developing countries like Pakistan.

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21

Anggraini, Try Beta, and Yefriza Yefriza. "NILAI TUKAR RUPIAH DAN NET EKSPOR INDONESIA 2000 – 2017 (GRANGER CAUSALITY TEST)." Convergence: The Journal of Economic Development 1, no. 1 (March 31, 2020): 9–24. http://dx.doi.org/10.33369/convergence-jep.v1i1.10854.

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The aims of this research is to find out the relationship of rupiah exchange rate and net export Indonesia. This research covers the periode for 2000.Q1-2017.Q4, used secondary data which were analyzed using Granger Causality Test and Augmented Dickey Fuller (ADF) and existing data processed by using computer program of Eviews 9.0. The stationary properties of the time series data are examined by using Augmented Dickey-Fuller (ADF) test. Granger Causality test is applied to find out long-run relationship along with causality among the variables. The result of the data analysis show that there is no causality between rupiah exchange rate and net xport. Granger Causality test showed that there is unidirectional causality between net export to rupiah exchange rate. It is mean that net export effect rupiah exchange rate, but rupiah exchange rate does not effect net export. Keywords: Causality, Net Export, Exchange Rate

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22

Sollis, Robert. "Fixed and Recursive Right-Tailed Dickey–Fuller Tests in the Presence of a Break under the Null." Journal of Time Series Econometrics 8, no. 1 (January 1, 2016): 1–19. http://dx.doi.org/10.1515/jtse-2013-0004.

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AbstractRight-tailed Dickey–Fuller-type unit root tests against the explosive alternative have become popular in economics and finance for detecting asset price bubbles. This paper studies the size properties of fixed sample and recursive right-tailed Dickey–Fuller tests if the relevant series contains a unit root, but a structural break in the drift parameter occurs. It is shown that positive size distortion and therefore spurious rejections of the unit root null hypothesis in favour of the explosive alternative can be a problem for both types of test. Some possible solutions to this problem are briefly discussed.

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23

Oumarou, Issoufou, and Ousseini A. Maiga. "A Causal Relationship Between Trade, Foreign Direct Investment and Economic Growth in Niger." Journal of Social and Economic Statistics 8, no. 2 (December 1, 2019): 24–38. http://dx.doi.org/10.2478/jses-2019-0003.

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Abstract Foreign direct investment and Trade were regarded as an important elements in enhancing economic development. This study used some time series econometric tests including the Augmented Dickey – Fuller (ADF) unit root test developed by Dickey – Fuller, stationary test developed by Kwiatkowski-Philips-Schmidt-Shin (KPSS), Johansen co-integration test and Granger causality test to analyse the connection between foreign direct investment, trade and economic growth in Niger. The tests results showed a bilateral relationship between trade and economic growth and a unidirectional causal relationship between trade and foreign direct investment with direction from trade to foreign direct investment. The long run effect tests revealed that trade has a positive effect on economic growth while foreign direct investment has a negative effect on economic growth in Niger. On average, ceteris paribus, the coefficients are statistically significant at 5% level.

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24

Aziz, Abdul. "Analisis Critical Root Value pada Data Nonstasioner." CAUCHY 2, no. 1 (November 18, 2011): 1. http://dx.doi.org/10.18860/ca.v2i1.1794.

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<div class="standard"><a id="magicparlabel-2325">A stationery process can be done t-test, on the contrary at non stationery process t-test cannot be done again because critical value of this process isn’t t-distribution. At this research, we will do simulation of time series AR(1) data in four non stationery models and doing unit root test to know critical value at ttest of non stationery process. From the research is yielded that distribution of critical point for t-test of non stationery process comes near to normal with restating simulation of random walk process which ever greater. Result of acquirement of this critical point has come near to result of Dickey-Fuller Test. From this research has been obtained critical point for third case which has not available at tables result of Dickey-Fuller Test. </a></div>

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25

Cook, Steven. "Correcting size distortion of the Dickey–Fuller test via recursive mean adjustment." Statistics & Probability Letters 60, no. 1 (November 2002): 75–79. http://dx.doi.org/10.1016/s0167-7152(02)00280-8.

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26

Tam, Pui Sun. "Finite-sample distribution of the augmented Dickey–Fuller test with lag optimization." Applied Economics 45, no. 24 (August 2013): 3495–511. http://dx.doi.org/10.1080/00036846.2012.724159.

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27

Cheung, Yin-Wong, and Kon S. Lai. "Power of the augmented dickey-fuller test with information-based lag selection." Journal of Statistical Computation and Simulation 60, no. 1 (January 1998): 57–65. http://dx.doi.org/10.1080/00949659808811871.

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28

Mantalos, P., and A. Karagrigoriou. "Bootstrapping the augmented Dickey–Fuller test for unit root using the MDIC." Journal of Statistical Computation and Simulation 82, no. 3 (March 2012): 431–43. http://dx.doi.org/10.1080/00949655.2010.539219.

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29

Faroque, Akhter, and Stanley A. Koren. "Diagnosing Housing Bubbles across Rich Countries." International Journal of Economics and Finance 10, no. 4 (March 19, 2018): 179. http://dx.doi.org/10.5539/ijef.v10n4p179.

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This paper addresses an empirical puzzle in the housing bubble literature: models of market fundamentals perform poorly in explaining investor exuberance in housing even though, individually, many fundamentals have strong ability to predict explosive growth in real house prices. We explore two plausible sources for the poor performance: missing fundamentals and missing bubble dynamics. To shed light on the relative importance of these sources, we conduct a detailed two-step investigation of the housing markets in ten rich countries using models, methodologies and datasets that are similar to those employed in the existing literature. Our findings consistently show that the predictive ability of models of market fundamentals can be dramatically enhanced once missing dynamics of housing bubbles are properly accounted for. GSADF denotes Generalised Sup Augmented Dickey–Fuller test and SADF denotes Sup Augmented Dickey–Fuller test.

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30

فرحان, عقيل حميد. "Using dickey _ fuller expanded test for testing variables of investment function in Iraq." Journal of Economics and Administrative Sciences 25, no. 114 (October 1, 2019): 1–19. http://dx.doi.org/10.33095/jeas.v25i114.1752.

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To ascertain the stability or instability of time series, three versions of the model proposed by Dickie-Voller were used in this paper. The aim of this study is to explain the extent of the impact of some economic variables such as the supply of money, gross domestic product, national income, after reaching the stability of these variables. The results show that the variable money supply, the GDP variable, and the exchange rate variable were all stable at the level of the first difference in the time series. This means that the series is an integrated first-class series. Hence, the gross fixed capital formation variable, the variable national income, and the variable interest rate are stable at the time series level. Which means that the series is a complete zero-grade. In this study, it is found that most of these variables are unstable in time series but stable in the first difference. It is also concluded that the contribution of the independent variable (money supply) in the investment becomes negative.

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31

Carrion i Silvestre, Josep Lluı́s, Andreu Sansó i Rosselló, and Manuel Artı́s Ortuño. "Response surfaces estimates for the Dickey-Fuller unit root test with structural breaks." Economics Letters 63, no. 3 (June 1999): 279–83. http://dx.doi.org/10.1016/s0165-1765(99)00044-0.

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32

Vougas, Dimitrios V. "Application of the Dickey-Fuller test to the Nelson and Plosser (1982) Data." Applied Economics Letters 9, no. 8 (June 2002): 511–14. http://dx.doi.org/10.1080/13504850110105736.

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33

Cheung, Yin-Wong, and Kon S. Lai. "PRACTITIONERS CORNER: Lag Order and Critical Values of a Modified Dickey-Fuller Test." Oxford Bulletin of Economics and Statistics 57, no. 3 (May 1, 2009): 411–19. http://dx.doi.org/10.1111/j.1468-0084.1995.mp57003008.x.

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34

Kulaksizoglu, Tamer. "Lag Order and Critical Values of the Augmented Dickey-Fuller Test: A Replication." Journal of Applied Econometrics 30, no. 6 (April 28, 2015): 1010. http://dx.doi.org/10.1002/jae.2458.

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35

Otero, Jesús, and Christopher F. Baum. "Unit-root Tests Based on Forward and Reverse Dickey–Fuller Regressions." Stata Journal: Promoting communications on statistics and Stata 18, no. 1 (March 2018): 22–28. http://dx.doi.org/10.1177/1536867x1801800103.

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In this article, we present the command adfmaxur, which computes the Leybourne (1995, Oxford Bulletin of Economics and Statistics 57: 559–571) unit-root statistic for different numbers of observations and the number of lags of the dependent variable in the test regressions. The latter can be either specified by the user or endogenously determined. We illustrate the use of adfmaxur with an empirical example.

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36

FURUOKA, Fumitaka. "MEAN REVERSION IN UNEMPLOYMENT: NEW FINDINGS FROM THE BALTIC TIGERS." Technological and Economic Development of Economy 23, no. 3 (September 18, 2015): 462–82. http://dx.doi.org/10.3846/20294913.2015.1070769.

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The tendency of the unemployment rate to revert to the mean value or the natural rate of unemployment has been one of the most discussed topics in macroeconomics. This study focused on three Baltic countries – Estonia, Latvia and Lithuania – as case studies to investigate unemployment dynamics. Three unit root tests were performed for this purpose: 1) the Augmented DickeyFuller (ADF) test, 2) the Seemingly Unrelated Regressions Augmented Dickey-Fuller (SURADF) test and 3) the Fourier Augmented Dickey-Fuller (FADF) test. The null hypothesis was that unemployment in the Baltic countries is a unit root process. As the findings revealed, the ADF test and the SURADF test failed to reject the null hypothesis of a unit root for all the three Baltic countries. However, the nonlinear FADF test could not reject the null hypothesis for Lithuania. This means that unemployment in Lithuania could be described as a stationary process. As such, it has the tendency to revert to a sustainable level. By contrast, unemployment in Estonia and Latvia would be best characterised as a non-stationary process where the unemployment rate lacks the mean reverting behaviour.

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37

Cernohorska, Libena. "The relationship between M3 and consumer price index in the Czech Republic." New Trends and Issues Proceedings on Humanities and Social Sciences 4, no. 10 (January 12, 2018): 23–32. http://dx.doi.org/10.18844/prosoc.v4i10.3059.

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The aim of this paper is to analyse the influence of monetary aggregate M3 on consumer price index (CPI) in the Czech Republic. Co-integration of this selected indicator M3 is demonstrated in relation to the development of CPI using the Engle – Granger co-integration test. These tests are applied to selected statistical data from 2003 to 2016. First step is to determine the optimum delay using Akaike criteria for all-time series analysed. Then the presence of a unit root is analysed using the Dickey–Fuller test. Based on the test results, time series is excluded, which appears to be stationary. If the conditions are met, testing then continued with the Engle–Granger test to detect cointegration relations, which would determine a longterm relationship between selected variables. Based on these tests, it is found that at a significance level of 0.05 doesn’t exist cointegration relationship between M3 and CPI in the Czech Republic. Conclusions resulting from the verification of the hypotheses are supported with graphical visualisation of data from which it is apparent that these hypotheses can be rejected. Keywords: Akaike crieteria, Dickey–Fuller test, Engle–Granger cointegration test, CPI, M3.

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38

Hansen, Bruce E. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power." Econometric Theory 11, no. 5 (October 1995): 1148–71. http://dx.doi.org/10.1017/s0266466600009993.

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In the context of testing for a unit root in a univariate time series, the convention is to ignore information in related time series. This paper shows that this convention is quite costly, as large power gains can be achieved by including correlated stationary covariates in the regression equation.The paper derives the asymptotic distribution of ordinary least-squares estimates of the largest autoregressive root and its t-statistic. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a convex combination of the Dickey-Fuller distribution and the standard normal, the mixture depending on the correlation between the equation error and the regression covariates. The local asymptotic power functions associated with these test statistics suggest enormous gains over the conventional unit root tests. A simulation study and empirical application illustrate the potential of the new approach.

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39

Pervaiz, Javed, Teng Jian-Zhou, and Junaid Masih. "Long Run Relationship between Selected Macroeconomic Indicators and Banking Sector in Pakistan." International Journal of Economics and Finance 10, no. 2 (January 5, 2018): 67. http://dx.doi.org/10.5539/ijef.v10n2p67.

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The study investigated the long run relationship between selected macroeconomic indicators and banking sector index in Pakistan. The selected macroeconomic indicators are Exports, Industrial Production, CPI, and KIBOR as short-term interest rate, Money Supply (M0), Nominal Exchange Rate between Pakistan and United States of America (USA), Oil Prices and the Interest rate on Pakistan Government bond ten years, as the long-term interest rate. Monthly time series was used from January 2009 to August 2015. The study applied Augmented Dickey-Fuller test to determine the stationarity levels for the selected macroeconomic indicators and banking sector index, Phillips-Perron test to validate the results of Augmented Dickey-Fuller test, a bound testing technique in ARDL model to investigate the long run relationship between selected macroeconomic variables and banking sector index. Results suggested the presence of a long-run relationship between macroeconomic variables exchange rate, inflation, oil price and banking sector index in Pakistan. Results of Granger causality test suggested unidirectional causality running from macroeconomic variables KIBOR and oil prices to banking sector index in Pakistan. Further, unidirectional causality was found running from banking sector index to government bond in Pakistan.

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40

Castro, Tomas del Barrio, and Denise R. Osborn. "TESTING FOR SEASONAL UNIT ROOTS IN PERIODIC INTEGRATED AUTOREGRESSIVE PROCESSES." Econometric Theory 24, no. 4 (April 4, 2008): 1093–129. http://dx.doi.org/10.1017/s0266466608080420.

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This paper examines the implications of applying the Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) (HEGY) seasonal root tests to a process that is periodically integrated. As an important special case, the random walk process is also considered, where the zero-frequency unit root t-statistic is shown to converge to the Dickey–Fuller distribution and all seasonal unit root statistics diverge. For periodically integrated processes and a sufficiently high order of augmentation, the HEGY t-statistics for unit roots at the zero and semiannual frequencies both converge to the same Dickey–Fuller distribution. Further, the HEGY joint test statistic for a unit root at the annual frequency and all joint test statistics across frequencies converge to the square of this distribution. Results are also derived for a fixed order of augmentation. Finite-sample Monte Carlo results indicate that, in practice, the zero-frequency HEGY statistic (with augmentation) captures the single unit root of the periodic integrated process, but there may be a high probability of incorrectly concluding that the process is seasonally integrated.

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41

Bisaglia, Luisa, and Isabella Procidano. "On the power of the Augmented Dickey–Fuller test against fractional alternatives using bootstrap." Economics Letters 77, no. 3 (November 2002): 343–47. http://dx.doi.org/10.1016/s0165-1765(02)00146-5.

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42

PAIVA, Denise de Assis, and Thelma SÁFADI. "STUDY OF TESTS FOR TREND IN TIME SERIES." REVISTA BRASILEIRA DE BIOMETRIA 39, no. 2 (June 17, 2021): 311–33. http://dx.doi.org/10.28951/rbb.v39i2.471.

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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.

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43

Malik, Muhammad Shoukat, Raisham Hayee, and Raima Adeel. "Financial Development and Economic Growth: Time Series Analysis of Economy of Pakistan." International Finance and Banking 5, no. 2 (December 21, 2018): 59. http://dx.doi.org/10.5296/ifb.v5i2.14091.

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This study aims in understanding the causal relationship between financial development and economic growth. This research used annual data and applied dickey fuller test and granger causality test in order to understand stationary level and causation in variables. The results of this test give support to first hypothesis that financial development causes economic growth. While no evidence was found on the support of our second hypothesis i.e. economic growth is causing financial development.

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44

Iliyasu, Jamilu, and Ndayezhin D. Saba. "Testing for Single Bubble Episode in the Nigerian Stock Market: An Empirical Investigation." Central Bank of Nigeria Journal of Applied Statistics, Vol. 10 No. 1 (August 27, 2019): 29–49. http://dx.doi.org/10.33429/cjas.10119.2/6.

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This study tested for a single bubble episode in the Nigerian Stock Exchange (NSE) by utilizing monthly data on nominal and real all-share index (ASI) from January 2010 to December 2017. Analysis of data based on Sup Augmented Dickey-Fuller (SADF) test for bubble detection suggested non-existence of a bubble in the NSE between 2010 and 2017. Though there was an indication of one explosive episode in September 2011 at which the Dickey-Fuller statistic lied above the critical values sequence line. However, it was not a bubble but a short deviation from trend. The study also estimated a time-varying long memory parameter, using a fractionally-integrated autoregressive model to check the robustness of the SADF test and it provided further evidence on the absence of a bubble. These findings showed that the behaviour of stock prices was not driven by a bubble in the Nigerian Stock Exchange (NSE). The study, therefore recommended that a time-to-time bubble diagnostic check on the exchange so that symptoms of a bubble can be early detected and managed to avoid losses that may result from the bust.

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Nielsen, Morten Ørregaard. "A POWERFUL TEST OF THE AUTOREGRESSIVE UNIT ROOT HYPOTHESIS BASED ON A TUNING PARAMETER FREE STATISTIC." Econometric Theory 25, no. 6 (December 2009): 1515–44. http://dx.doi.org/10.1017/s0266466609990247.

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This paper presents a family of simple nonparametric unit root tests indexed by one parameter,d, and containing the Breitung (2002,Journal of Econometrics108, 342–363) test as the special cased= 1. It is shown that (a) each member of the family withd> 0 is consistent, (b) the asymptotic distribution depends ondand thus reflects the parameter chosen to implement the test, and (c) because the asymptotic distribution depends ondand the test remains consistent for alld> 0, it is possible to analyze the power of the test for different values ofd. The usual Phillips–Perron and Dickey–Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties.It is shown that members of the family withd< 1 have higher asymptotic local power than the Breitung (2002) test, and whendis small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear time trend. Furthermore, generalized least squares (GLS) detrending is shown to improve power whendis small, which is not the case for the Breitung (2002) test. Simulations demonstrate that when applying a sieve bootstrap procedure, the proposed variance ratio test has very good size properties, with finite-sample power that is higher than that of the Breitung (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented Dickey–Fuller test with lag length chosen by an information criterion.

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Lu, Zhiping, Ming Li, and Wei Zhao. "Stationarity Testing of Accumulated Ethernet Traffic." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/217213.

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We investigate the stationarity property of the accumulated Ethernet traffic series. We applied several widely used stationarity and unit root tests, such as Dickey-Fuller test and its augmented version, Phillips-Perron test, as well as the Kwiatkowski-Phillips-Schmidt-Shin test and some of its generalizations, to the assessment of the stationarity of the traffic traces at the different time scales. The quantitative results in this research provide evidence that when the time scale increases, the accumulated traffic series are more stationary.

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Shaik, Muneer, and S. Maheswaran. "Random Walk in Emerging Asian Stock Markets." International Journal of Economics and Finance 9, no. 1 (December 13, 2016): 20. http://dx.doi.org/10.5539/ijef.v9n1p20.

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<p>The random walk hypothesis is an important area of research in finance and many tools have been proposed to investigate the behaviour of the fluctuations in stock prices. However, a detail study on emerging Asian stock markets which employ the various unit root tests has not been done. In this paper, we employ six different unit root tests such as the Augmented Dickey and Fuller test (1979), Phillips and Perron test (1988), Kwiatkowski-Phillips-Schmidt-Shin test(1992), Dickey-Fuller GLS (ERS) test (1996), Elliot-Rothenberg-Stock Point-Optimal test (1996) and Ng and Perron (2001) unit root tests on 10 emerging Asian stock markets to detect for the presence of a random walk in stock prices. We have conducted the unit root tests during different sub-sample time periods of global financial crisis to check for robustness. To be specific, we have found that during the overall sample period (2001-2015) 8 out of 10 Asian stock markets and during the pre-crisis period (2001-2007) all the 10 Asian stock market prices do follow random walk according to the unit root tests under consideration. However, during the crisis & post-crisis period (2008-2015) we have found only 5 out of 10 Asian markets follow the random walk movement based on unit root tests.</p>

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Paparoditis, Efstathios, and Dimitris N. Politis. "The asymptotic size and power of the augmented Dickey–Fuller test for a unit root." Econometric Reviews 37, no. 9 (July 11, 2016): 955–73. http://dx.doi.org/10.1080/00927872.2016.1178887.

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Cook, Steven. "A finite-sample sensitivity analysis of the Dickey–Fuller test under local-to-unity detrending." Journal of Applied Statistics 33, no. 2 (March 2006): 233–40. http://dx.doi.org/10.1080/02664760500251725.

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50

Dorta, Miguel, and Gustavo Sanchez. "Bootstrap unit-root test for random walk with drift: The bsrwalkdrift command." Stata Journal: Promoting communications on statistics and Stata 21, no. 1 (March 2021): 39–50. http://dx.doi.org/10.1177/1536867x211000003.

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In this article, we introduce the command bsrwalkdrift, which is primarily intended to perform a bootstrap unit-root test under the null hypothesis of random walk with drift. The method implemented in this command is considerably more precise than the corresponding case of the conventional augmented Dickey–Fuller test, which can be inaccurate when the true value of the drift term is small relative to the standard deviation of the innovations. The command also has an option to account for deterministic linear trend and another option to perform bootstrap unit-root tests under the null hypothesis of random walk without drift.

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