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A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes

Citations

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Cited by:

  1. Maggie E. C. Jones & Morten Ørregaard Nielsen & Michał Ksawery Popiel, 2014. "A fractionally cointegrated VAR analysis of economic voting and political support," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 47(4), pages 1078-1130, November.
  2. Samet Gunay, 2018. "Fractionally Cointegrated Vector Autoregression Model: Evaluation of High/Low and Close/Open Spreads for Precious Metals," SAGE Open, , vol. 8(4), pages 21582440188, November.
  3. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
  4. Tommaso Proietti, 2016. "Component-wise Representations of Long-memory Models and Volatility Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 668-692.
  5. Hualde, Javier, 2014. "Estimation of long-run parameters in unbalanced cointegration," Journal of Econometrics, Elsevier, vol. 178(2), pages 761-778.
  6. Haldrup, Niels & Nielsen, Frank S. & Nielsen, Morten Ørregaard, 2010. "A vector autoregressive model for electricity prices subject to long memory and regime switching," Energy Economics, Elsevier, vol. 32(5), pages 1044-1058, September.
  7. Yan, Meng & Chen, Jian & Song, Victor & Xu, Ke, 2022. "Trade friction and price discovery in the USD–CAD spot and forward markets," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
  8. Galán-Gutiérrez, Juan Antonio & Martín-García, Rodrigo, 2021. "Cointegration between the structure of copper futures prices and Brexit," Resources Policy, Elsevier, vol. 71(C).
  9. Do, Hung Xuan & Nepal, Rabindra & Jamasb, Tooraj, 2020. "Electricity market integration, decarbonisation and security of supply: Dynamic volatility connectedness in the Irish and Great Britain markets," Energy Economics, Elsevier, vol. 92(C).
  10. Søren Johansen & Morten Ørregaard Nielsen, 2018. "Testing the CVAR in the Fractional CVAR Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 836-849, November.
  11. Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends and cycles in macroeconomic time series," Papers 2005.05266, arXiv.org, revised May 2020.
  12. Gil-Alana, Luis A. & Moreno, Antonio, 2012. "Uncovering the US term premium: An alternative route," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1181-1193.
  13. Quineche Ricardo, 2021. "Consumption, Aggregate Wealth and Expected Stock Returns: An FCVAR Approach," Journal of Time Series Econometrics, De Gruyter, vol. 13(1), pages 21-42, January.
  14. Daniela Osterrieder, 2013. "Interest Rates with Long Memory: A Generalized Affine Term-Structure Model," CREATES Research Papers 2013-17, Department of Economics and Business Economics, Aarhus University.
  15. Gagnon, Marie-Hélène & Power, Gabriel J. & Toupin, Dominique, 2016. "International stock market cointegration under the risk-neutral measure," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 243-255.
  16. Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends in unobserved components models," Papers 2005.03988, arXiv.org, revised May 2020.
  17. Sepideh Dolatabadi & Paresh Kumar Narayan & Morten Ørregaard Nielsen & Ke Xu, 2018. "Economic significance of commodity return forecasts from the fractionally cointegrated VAR model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(2), pages 219-242, February.
  18. Dolatabadi, Sepideh & Nielsen, Morten Ørregaard & Xu, Ke, 2016. "A fractionally cointegrated VAR model with deterministic trends and application to commodity futures markets," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 623-639.
  19. Søren Johansen & Morten Ørregaard Nielsen, 2012. "The role of initial values in nonstationary fractional time series models," CREATES Research Papers 2012-47, Department of Economics and Business Economics, Aarhus University.
  20. S{o}ren Johansen & Morten {O}rregaard Nielsen, 2022. "Weak convergence to derivatives of fractional Brownian motion," Papers 2208.02516, arXiv.org, revised Oct 2022.
  21. Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Working Papers 1230, Banco de España.
  22. Alexander Boca Saravia & Gabriel Rodríguez, 2022. "Presidential approval in Peru: an empirical analysis using a fractionally cointegrated VAR," Economic Change and Restructuring, Springer, vol. 55(3), pages 1973-2010, August.
  23. Federico Carlini & Paolo Santucci de Magistris, 2019. "On the Identification of Fractionally Cointegrated VAR Models With the Condition," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 134-146, January.
  24. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
  25. Eduardo Rossi & Paolo Santucci de Magistris, 2013. "A No‐Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(1), pages 77-102, January.
  26. Cameron Cornell & Lewis Mitchell & Matthew Roughan, 2023. "Vector Autoregression in Cryptocurrency Markets: Unraveling Complex Causal Networks," Papers 2308.15769, arXiv.org.
  27. Guglielmo Maria Caporale & Luis Gil‐Alana, 2020. "Prospects for a Monetary Union in the East Africa Community: Some Empirical Evidence," South African Journal of Economics, Economic Society of South Africa, vol. 88(2), pages 174-185, June.
  28. Duan, Kun & Li, Zeming & Urquhart, Andrew & Ye, Jinqiang, 2021. "Dynamic efficiency and arbitrage potential in Bitcoin: A long-memory approach," International Review of Financial Analysis, Elsevier, vol. 75(C).
  29. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
  30. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
  31. Stoupos, Nikolaos & Kiohos, Apostolos, 2022. "Bond markets integration in the EU: New empirical evidence from the Eastern non-euro member-states," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
  32. Sepideh Dolatabadi & Morten Ørregaard Nielsen & Ke Xu, 2015. "A Fractionally Cointegrated VAR Analysis of Price Discovery in Commodity Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(4), pages 339-356, April.
  33. Monge, Manuel & Cristóbal, Enrique, 2021. "Terrorism and the behavior of oil production and prices in OPEC," Resources Policy, Elsevier, vol. 74(C).
  34. Monge, Manuel & Gil-Alana, Luis A., 2021. "Lithium industry and the U.S. crude oil prices. A fractional cointegration VAR and a Continuous Wavelet Transform analysis," Resources Policy, Elsevier, vol. 72(C).
  35. Gil-Alana, Luis A. & Yaya, OlaOluwa S. & Awe, Olushina O., 2017. "Time series analysis of co-movements in the prices of gold and oil: Fractional cointegration approach," Resources Policy, Elsevier, vol. 53(C), pages 117-124.
  36. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.
  37. Stefanos Kechagias & Vladas Pipiras, 2020. "Modeling bivariate long‐range dependence with general phase," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 268-292, March.
  38. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
  39. Massimiliano Caporin & Fulvio Fontini & Paolo Santucci De Magistris, 2017. "Price convergence within and between the Italian electricity day-ahead and dispatching services markets," "Marco Fanno" Working Papers 0215, Dipartimento di Scienze Economiche "Marco Fanno".
  40. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
  41. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers 10-28, University of Copenhagen. Department of Economics.
  42. Leandro Maciel, 2020. "Technical analysis based on high and low stock prices forecasts: evidence for Brazil using a fractionally cointegrated VAR model," Empirical Economics, Springer, vol. 58(4), pages 1513-1540, April.
  43. Pérez-Rodríguez, Jorge V. & Andrada-Félix, Julián & Rachinger, Heiko, 2021. "Testing the forward volatility unbiasedness hypothesis in exchange rates under long-range dependence," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
  44. Luis Gil-Alana & Antonio Moreno, 2012. "Fractional integration and structural breaks in U.S. macro dynamics," Empirical Economics, Springer, vol. 43(1), pages 427-446, August.
  45. Katarzyna Łasak & Johannes Lont, 2020. "Observation Driven Long Run Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 551-575, February.
  46. Baruník, Jozef & Dvořáková, Sylvie, 2015. "An empirical model of fractionally cointegrated daily high and low stock market prices," Economic Modelling, Elsevier, vol. 45(C), pages 193-206.
  47. Yaya, OlaOluwa S. & Ogbonna, Ahamuefula E. & Olubusoye, Olusanya E., 2019. "How persistent and dynamic inter-dependent are pricing of Bitcoin to other cryptocurrencies before and after 2017/18 crash?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
  48. Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2014. "Long- versus medium-run identification in fractionally integrated VAR models," Economics Letters, Elsevier, vol. 122(2), pages 299-302.
  49. Ke Xu & Yu‐Lun Chen & Bo Liu & Jian Chen, 2024. "Price discovery and long‐memory property: Simulation and empirical evidence from the bitcoin market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(4), pages 605-618, April.
  50. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
  51. Daniela Osterrieder & Daniel Ventosa-Santaulària & J. Eduardo Vera-Valdés, 2015. "Unbalanced Regressions and the Predictive Equation," CREATES Research Papers 2015-09, Department of Economics and Business Economics, Aarhus University.
  52. Zhenxiong Li & Marwan Izzeldin & Xingzhi Yao, 2020. "Return predictability of variance differences: A fractionally cointegrated approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(7), pages 1072-1089, July.
  53. Carlini, Federico & Christensen, Bent Jesper & Datta Gupta, Nabanita & Santucci de Magistris, Paolo, 2023. "Climate, wind energy, and CO2 emissions from energy production in Denmark," Energy Economics, Elsevier, vol. 125(C).
  54. Morten Ørregaard Nielsen & Sergei S. Shibaev, 2015. "Forecasting daily political opinion polls using the fractionally cointegrated VAR model," Working Paper 1340, Economics Department, Queen's University.
  55. Abbritti, Mirko & Carcel, Hector & Gil-Alana, Luis & Moreno, Antonio, 2023. "Term premium in a fractionally cointegrated yield curve," Journal of Banking & Finance, Elsevier, vol. 149(C).
  56. Dimitriou, Dimitrios & Kenourgios, Dimitris & Simos, Theodore, 2020. "Are there any other safe haven assets? Evidence for “exotic” and alternative assets," International Review of Economics & Finance, Elsevier, vol. 69(C), pages 614-628.
  57. Carlos D. Ramirez, 2024. "The effect of economic policy uncertainty under fractional integration," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 23(1), pages 89-110, January.
  58. Lena Dräger & Theoplasti Kolaiti & Philipp Sibbertsen, 2023. "Measuring macroeconomic convergence and divergence within EMU using long memory," Empirical Economics, Springer, vol. 65(5), pages 2333-2356, November.
  59. Afsin Sahin, 2019. "Loom of Symmetric Pass-Through," Economies, MDPI, vol. 7(1), pages 1-25, February.
  60. Luis A. Gil-Alana & Antonio Moreno & Seonghoon Cho, 2012. "The Deaton paradox in a long memory context with structural breaks," Applied Economics, Taylor & Francis Journals, vol. 44(25), pages 3309-3322, September.
  61. Proietti, Tommaso, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," MPRA Paper 57230, University Library of Munich, Germany.
  62. Søren Johansen & Morten Ørregaard Nielsen, 2019. "Nonstationary Cointegration in the Fractionally Cointegrated VAR Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(4), pages 519-543, July.
  63. Simwaka, Kisu, 2012. "Time varying fractional cointegration," MPRA Paper 39505, University Library of Munich, Germany.
  64. Vadim Kufenko & Niels Geiger, 2016. "Business cycles in the economy and in economics: an econometric analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(1), pages 43-69, April.
  65. Monge, Manuel & Gil-Alana, Luis Alberiko, 2021. "Spatial crude oil production divergence and crude oil price behaviour in the United States," Energy, Elsevier, vol. 232(C).
  66. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
  67. Håvard Hungnes, 2016. "Fractionality and co-fractionality between Government Bond yields," Discussion Papers 838, Statistics Norway, Research Department.
  68. Lovcha, Yuliya & Perez-Laborda, Alejandro, 2018. "Monetary policy shocks, inflation persistence, and long memory," Journal of Macroeconomics, Elsevier, vol. 55(C), pages 117-127.
  69. Juan Antonio Galán-Gutiérrez & Rodrigo Martín-García, 2022. "Fundamentals vs. Financialization during Extreme Events: From Backwardation to Contango, a Copper Market Analysis during the COVID-19 Pandemic," Mathematics, MDPI, vol. 10(4), pages 1-23, February.
  70. Mustanen, Dmitri & Maaitah, Ahmad & Mishra, Tapas & Parhi, Mamata, 2022. "The power of investors’ optimism and pessimism in oil market forecasting," Energy Economics, Elsevier, vol. 114(C).
  71. Forte, Santiago & Lovreta, Lidija, 2019. "Volatility discovery: Can the CDS market beat the equity options market?," Finance Research Letters, Elsevier, vol. 28(C), pages 107-111.
  72. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," CREATES Research Papers 2014-15, Department of Economics and Business Economics, Aarhus University.
  73. Johansen, Søren & Nielsen, Morten Ørregaard, 2016. "The Role Of Initial Values In Conditional Sum-Of-Squares Estimation Of Nonstationary Fractional Time Series Models," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1095-1139, October.
  74. Stoupos, Nikolaos & Kiohos, Apostolos, 2021. "Energy commodities and advanced stock markets: A post-crisis approach," Resources Policy, Elsevier, vol. 70(C).
  75. Oloko, Tirimisiyu F. & Ogbonna, Ahamuefula E. & Adedeji, Abdulfatai A. & Lakhani, Noman, 2021. "Oil price shocks and inflation rate persistence: A Fractional Cointegration VAR approach," Economic Analysis and Policy, Elsevier, vol. 70(C), pages 259-275.
  76. Shimotsu, Katsumi, 2012. "Exact local Whittle estimation of fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 169(2), pages 266-278.
  77. Tanin, Tauhidul Islam & Sarker, Ashutosh & Brooks, Robert & Do, Hung Xuan, 2022. "Does oil impact gold during COVID-19 and three other recent crises?," Energy Economics, Elsevier, vol. 108(C).
  78. Clements, A.E. & Hurn, A.S. & Volkov, V.V., 2016. "Common trends in global volatility," Journal of International Money and Finance, Elsevier, vol. 67(C), pages 194-214.
  79. Yao, Xingzhi & Izzeldin, Marwan & Li, Zhenxiong, 2019. "Modelling systems with a mixture of I(d) and I(0) variables using the fractionally co-integrated VAR model," Economics Letters, Elsevier, vol. 181(C), pages 160-163.
  80. Monge, Manuel & Poza, Carlos & Borgia, Sofía, 2022. "A proposal of a suspicion of tax fraud indicator based on Google trends to foresee Spanish tax revenues," International Economics, Elsevier, vol. 169(C), pages 1-12.
  81. Nikolaos Stoupos & Apostolos Kiohos, 2022. "Euro Area: Towards a European Common Bond? – Empirical Evidence from the Sovereign Debt Markets," Journal of Common Market Studies, Wiley Blackwell, vol. 60(4), pages 1019-1046, July.
  82. Federico Carlini & Katarzyna (K.A.) Lasak, 2018. "Likelihood based inference for an Identifiable Fractional Vector Error Correction Model," Tinbergen Institute Discussion Papers 18-085/III, Tinbergen Institute.
  83. Alia Afzal & Philipp Sibbertsen, 2021. "Modeling fractional cointegration between high and low stock prices in Asian countries," Empirical Economics, Springer, vol. 60(2), pages 661-682, February.
  84. Adebola, Solarin Sakiru & Gil-Alana, Luis A. & Madigu, Godfrey, 2019. "Gold prices and the cryptocurrencies: Evidence of convergence and cointegration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1227-1236.
  85. Barros, Carlos Pestana & Gil-Alana, Luis A. & Payne, James E., 2011. "An analysis of oil production by OPEC countries: Persistence, breaks, and outliers," Energy Policy, Elsevier, vol. 39(1), pages 442-453, January.
  86. Dechert, Andreas, 2014. "Fraktionale Kointegrationsbeziehungen zwischen Euribor-Zinssätzen," W.E.P. - Würzburg Economic Papers 93, University of Würzburg, Department of Economics.
  87. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
  88. Marc Gronwald & Sania Wadud, 2024. "“My Name Is Bond. Green Bond.” Informational Efficiency of Climate Finance Markets," CESifo Working Paper Series 11029, CESifo.
  89. Morten Ø. Nielsen & Michal Ksawery Popiel, 2018. "A Matlab Program And User's Guide For The Fractionally Cointegrated Var Model," Working Paper 1330, Economics Department, Queen's University.
  90. Stoupos, Nikolaos & Kiohos, Apostolos, 2022. "Euro area stock markets integration: Empirical evidence after the end of 2010 debt crisis," Finance Research Letters, Elsevier, vol. 46(PB).
  91. Bent Jesper Christensen & Nabanita Datta Gupta & Paolo Santucci de Magistris, 2021. "Measuring the impact of clean energy production on CO2 abatement in Denmark: Upper bound estimation and forecasting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 118-149, January.
  92. Massimo Franchi & Paolo Paruolo, 2019. "A general inversion theorem for cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1176-1201, November.
  93. Tim Bollerslev & Daniela Osterrieder & Natalia Sizova & George Tauchen, 2011. "Risk and Return: Long-Run Relationships, Fractional Cointegration, and Return Predictability," CREATES Research Papers 2011-51, Department of Economics and Business Economics, Aarhus University.
  94. Bollerslev, Tim & Osterrieder, Daniela & Sizova, Natalia & Tauchen, George, 2013. "Risk and return: Long-run relations, fractional cointegration, and return predictability," Journal of Financial Economics, Elsevier, vol. 108(2), pages 409-424.
  95. Monge, Manuel & Claudio-Quiroga, Gloria & Poza, Carlos, 2024. "Chinese economic behavior in times of covid-19. A new leading economic indicator based on Google trends," International Economics, Elsevier, vol. 177(C).
  96. Eduardo Rossi & Paolo Santucci de Magistris, 2009. "A No Arbitrage Fractional Cointegration Analysis Of The Range Based Volatility," CREATES Research Papers 2009-31, Department of Economics and Business Economics, Aarhus University.
  97. Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2013. "Fractionally Integrated VAR Models with a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-step Estimation," University of Regensburg Working Papers in Business, Economics and Management Information Systems 471, University of Regensburg, Department of Economics.
  98. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
  99. Luis Alberiko Gil-Alaña & Borja Balprad & Guglielmo Maria Caporale & Hector Carcel, 2015. "Exchange Rate Dynamics and Monetary Unions in Africa: A Fractional Integration and Cointegration Analysis," NCID Working Papers 11/2015, Navarra Center for International Development, University of Navarra.
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  119. Xu, Ke & Chen, Yu-Lun & Yang, J. Jimmy, 2023. "Market uncertainty, persistent arbitrage-free violation, and price discovery in RMB market," International Review of Financial Analysis, Elsevier, vol. 90(C).
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  124. Carlos P. Barros & Joao R. Faria & Luis A. Gil-Alana, 2009. "Persistence on airline accidents," Faculty Working Papers 08/09, School of Economics and Business Administration, University of Navarra.
  125. Monge, Manuel & Lazcano, Ana & Parada, José Luis, 2023. "Growth vs value investing: Persistence and time trend before and after COVID-19," Research in International Business and Finance, Elsevier, vol. 65(C).
  126. Tobias Hartl, 2020. "Macroeconomic Forecasting with Fractional Factor Models," Papers 2005.04897, arXiv.org.
  127. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," CREATES Research Papers 2019-02, Department of Economics and Business Economics, Aarhus University.
  128. Marc Gronwald & Sania Wadud & Kingsley Dogah, 2024. "Oil Market Efficiency, Quantity of Information, and Oil Market Turbulence," CESifo Working Paper Series 10995, CESifo.
  129. Jesús Tomás Monge Moreno & Manuel Monge, 2023. "Consumer Sentiment in the United States and the Impact of Mental Disorders on Consumer Behavior—Time Trends and Persistence Analysis," Mathematics, MDPI, vol. 11(13), pages 1-10, July.
  130. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2020. "Modelling Loans to Non-Financial Corporations within the Eurozone: A Long-Memory Approach," CESifo Working Paper Series 8674, CESifo.
  131. Dechert, Andreas, 2012. "Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks," MPRA Paper 41044, University Library of Munich, Germany.
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