Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models

This paper studies the nonlinear adjustment between industrial production and carbon prices – coined as ‘the carbon-macroeconomy relationship’ – in the EU 27. We model carbon price returns and industrial production as nonlinear and state-dependent, with dynamics depending on the sign and magnitude of past realization of returns and the growth of industrial production. Our findings show that (i) macroeconomic activity is likely to affect carbon prices with a lag, due to the specific institutional constraints of this environmental market; (ii) the joint dynamics of industrial production and carbon prices seem adequately captured by two-regime threshold vector error-correction and two-regime Markov-switching VAR models compared to linear models as main competitors. The regime-switching models proposed are profoundly checked for their economic content and statistical congruency, and are found to provide a sound statistical framework for a comprehensive analysis of the carbon-macroeconomy relationship.

[1]  Clive W. J. Granger,et al.  Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates , 1998 .

[2]  Julien Chevallier,et al.  On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting , 2009 .

[3]  Ben Jacobsen,et al.  Striking Oil: Another Puzzle? , 2003 .

[4]  Charles M. Jones,et al.  OIL AND THE STOCK MARKETS , 1996 .

[5]  Cal B. Muckley,et al.  An Emerging Equilibrium in the EU Emissions Trading Scheme , 2010 .

[6]  Kerk L. Phillips.  A two-country model of stochastic output with changes in regime , 1991 .

[7]  Michael T. Owyang,et al.  Business Cycle Phases in U.S. States , 2003 .

[8]  A Markov-Switching Approach to Measuring Exchange Market Pressure , 2007 .

[9]  K. Chan,et al.  Percentage Points of Likelihood Ratio Tests for Threshold Autoregression , 1991 .

[10]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[11]  Thomas H. McCurdy,et al.  Identifying Bull and Bear Markets in Stock Returns , 2000 .

[12]  V. Daly,et al.  The twin deficits in OECD countries: cointegration analysis with regime shifts , 2009 .

[13]  D. Andrews.  Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[14]  D. Andrews.  Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[15]  Jun Cai.  A Markov Model of Switching-Regime ARCH , 1994 .

[16]  Philip Hans Franses,et al.  Nonlinear Time Series Models in Empirical Finance: Frontmatter , 2000 .

[17]  Katrin Assenmacher-Wesche.  Estimating Central Banks' preferences from a time-varying empirical reaction function , 2006 .

[18]  D. M. Keenan,et al.  A Tukey nonadditivity-type test for time series nonlinearity , 1985 .

[19]  H. Geman.  Commodities and Commodity Derivatives: Modelling and Pricing for Agriculturals, Metals and Energy , 2005 .

[20]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[21]  Daniel R. Smith.  Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates , 2002 .

[22]  H. Tong,et al.  On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations , 1985, Advances in Applied Probability.

[23]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .

[24]  Christian Conrad,et al.  Modeling and Explaining the Dynamics of European Union Allowance Prices at High-Frequency , 2010 .

[25]  R. Davies.  Hypothesis testing when a nuisance parameter is present only under the alternative , 1977 .

[26]  James D. Hamilton.  Specification testing in Markov-switching time-series models , 1996 .

[27]  James D. Hamilton.  What is an Oil Shock? , 2000 .

[28]  A. Denny Ellerman,et al.  Over-Allocation or Abatement? A Preliminary Analysis of the EU Ets Based on the 2005 Emissions Data , 2006 .

[29]  J. Stock,et al.  Evidence on Structural Instability in Macroeconomic Time Series Relations , 1994 .

[30]  The Propagation of Regional Recessions , 2012, Review of Economics and Statistics.

[31]  James D. Hamilton,et al.  NONLINEARITIES AND THE MACROECONOMIC EFFECTS OF OIL PRICES , 2010, Macroeconomic Dynamics.

[32]  James D. Hamilton,et al.  New directions in business cycle research and financial analysis , 2002 .

[33]  H. Krolzig.  Markov-Switching Vector Autoregressions: Modelling, Statistical Inference, and Application to Business Cycle Analysis , 1997 .

[34]  Maria Soledad Martinez Peria.  A regime-switching approach to the study of speculative attacks: A focus on EMS crises , 2002 .

[35]  Eric Ghysels,et al.  On the Periodic Structure of the Business Cycle , 1992 .

[36]  Henrik Madsen,et al.  Adaptive modelling and forecasting of offshore wind power fluctuations with Markov‐switching autoregressive models , 2012 .

[37]  Eric Ghysels,et al.  Série Scientifique Scientific Series the Midas Touch: Mixed Data Sampling Regression Models the Midas Touch: Mixed Data Sampling Regression Models* , 2022 .

[38]  Haldun Sarlan,et al.  Cyclical aspects of business cycle turning points , 2001 .

[39]  Valérie Mignon,et al.  Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance , 2002 .

[40]  H. Tong.  On a threshold model , 1978 .

[41]  Juergen Kaehler,et al.  Markov-Switching Models for Exchange-Rate Dynamics and the Pricing of Foreign-Currency Options , 1994 .

[42]  E. Ghysels,et al.  Série Scientifique Scientific Series Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies , 2022 .

[43]  W. Enders,et al.  Threshold cointegration and purchasing power parity in the pacific nations , 2004 .

[44]  Andrew V. Carter,et al.  Testing for Regime Switching: A Comment , 2012 .

[45]  Julien Chevallier,et al.  Price drivers and structural breaks in European carbon prices 2005–2007 , 2008 .

[46]  Corrado Di Maria,et al.  Abatement and Allocation in the Pilot Phase of the EU ETS , 2009 .

[47]  Wei Xiong,et al.  Index Investment and the Financialization of Commodities , 2010 .

[48]  Marine Carrasco,et al.  Tests for Unit-Root versus Threshold Specification With an Application to the Purchasing Power Parity Relationship , 2004 .

[49]  Hany A. Shawky,et al.  Stock market volatility and the business cycle , 1997 .

[50]  P. Collin‐Dufresne,et al.  The Determinants of Credit Spread Changes , 2001 .

[51]  Robert F. Whitelaw.  Stock Market Risk and Return: An Equilibrium Approach , 1997 .

[52]  Lucio Sarno,et al.  Deviations from purchasing power parity under different exchange rate regimes: Do they revert and, if so, how? , 2006 .

[53]  P. Perron,et al.  Further Evidence on Breaking Trend Functions in Macroeconomic Variables. , 1997 .

[54]  Derek W. Bunn,et al.  Structural interactions of European carbon trading and energy prices , 2009 .

[55]  Raphael N. Markellos,et al.  Modeling CO2 Emission Allowance Prices and Derivatives: Evidence from the European Trading Scheme , 2008 .

[56]  James D. Hamilton.  Causes and Consequences of the Oil Shock of 2007–08 , 2009 .

[57]  Carol Alexander,et al.  Regime dependent determinants of credit default swap spreads , 2008 .

[58]  James D. Hamilton,et al.  Long Swings in the Dollar: Are They in the Data and Do Markets Know It? The American Economic Review , 1990 .

[59]  N. Million.  Central Bank's interventions and the Fisher hypothesis: a threshold cointegration investigation , 2004 .

[60]  M. Seo,et al.  Bootstrap testing for the null of no cointegration in a threshold vector error correction model , 2006 .

[61]  Julien Chevallier,et al.  Risk Aversion and Institutional Information Disclosure on the European Carbon Market: A Case-Study of the 2006 Compliance Event , 2008 .

[62]  Andrew J. Filardo.  Business-Cycle Phases and Their Transitional Dynamics , 1994 .

[63]  P. Sephton.  Spatial Market Arbitrage and Threshold Cointegration , 2003 .

[64]  Ton Vorst,et al.  A Threshold Error Correction Model for Intraday Futures and Index Returns , 1998 .

[65]  B. Hansen,et al.  Testing for two-regime threshold cointegration in vector error-correction models , 2002 .

[66]  Matteo Manera,et al.  The Asymmetric Effects of Oil Shocks on Output Growth: A Markov-Switching Analysis for the G-7 Countries , 2006 .

[67]  Andrew Ang,et al.  Regime Switches in Interest Rates , 1998 .

[68]  D. Andrews,et al.  Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative , 1992 .

[69]  Julien Chevallier.  Macroeconomics, finance, commodities: Interactions with carbon markets in a data-rich model , 2011 .

[70]  Huimin Chung,et al.  The dynamic relationship between the prices of ADRs and their underlying stocks: Evidence from the threshold vector error correction model , 2005 .

[71]  Zacharias Psaradakis,et al.  On Markov error‐correction models, with an application to stock prices and dividends , 2004 .

[72]  P. Perron,et al.  Computation and Analysis of Multiple Structural-Change Models , 1998 .

[73]  Min Wei,et al.  What Does the Yield Curve Tell Us About GDP Growth? , 2003 .

[74]  Amir H. Alizadeh,et al.  A Markov regime switching approach for hedging energy commodities , 2008 .

[75]  James G. MacKinnon,et al.  Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration , 1996 .

[76]  G. Dionne,et al.  A Reduced Form Model of Default Spreads with Markov-Switching Macroeconomic Factors , 2010 .

[77]  Alain Guay,et al.  Adaptive consistent unit-root tests based on autoregressive threshold model , 2008 .

[78]  S. Chib,et al.  Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts , 1993 .

[79]  Juri Marcucci.  Forecasting Stock Market Volatility with Regime-Switching GARCH Models , 2005 .

[80]  D. Shepherd,et al.  The structure of the Australian growth process: A Bayesian model selection view of Markov switching , 2005 .

[81]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[82]  Patrick Lam,et al.  The Hamilton model with a general autoregressive component , 1990 .

[83]  James Morley,et al.  The Asymmetric Business Cycle , 2012, Review of Economics and Statistics.

[84]  A. Abdulai.  Using threshold cointegration to estimate asymmetric price transmission in the Swiss pork market , 2002 .

[85]  Mark P. Taylor,et al.  Covered Interest Rate Arbitrage in the Interwar Period and the Keynes-Einzig Conjecture , 2002 .

[86]  B. LeBaron,et al.  A test for independence based on the correlation dimension , 1996 .

[87]  Geert Bekaert,et al.  The Determinants of Stock and Bond Return Comovements , 2007 .

[88]  Eric Ghysels,et al.  Regression Models with Mixed Sampling Frequencies , 2010 .

[89]  George Kapetanios,et al.  Unit Root Tests in Three-Regime Setar Models , 2002 .

[90]  D. Bunn,et al.  Policy interactions, risk and price formation in carbon markets , 2009 .

[91]  Chang-Jin Kim,et al.  Nonlinearity and the permanent effects of recessions , 2002 .

[92]  Fatih Onur Hocaoglu,et al.  Examining the link between carbon dioxide emissions and the share of industry in GDP: Modeling and testing for the G-7 countries , 2011 .

[93]  P. Perron,et al.  Critical Values for Multiple Structural Change Tests , 2003 .

[94]  Eric Ghysels,et al.  A Component Model for Dynamic Correlations , 2009 .

[95]  Timo Teräsvirta,et al.  A simple nonlinear time series model with misleading linear properties , 1999 .

[96]  Julien Chevallier,et al.  Carbon Price Drivers: An Updated Literature Review , 2011, Int. J. Appl. Logist..

[97]  Adrian Pagan,et al.  A comparison of two business cycle dating methods , 2003 .

[98]  Zacharias Psaradakis,et al.  Testing the unbiased forward exchange rate hypothesis using a Markov switching model and instrumental variables , 2003 .

[99]  Lutz Kilian,et al.  Exogenous Oil Supply Shocks: How Big Are They and How Much Do They Matter for the U.S. Economy? , 2005, The Review of Economics and Statistics.

[100]  Stephen Gray.  Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process , 1996 .

[101]  Colin P. Hargreaves,et al.  Non-Stationary Time Series Analysis and Cointegration , 1994 .

[102]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[103]  H. Tong,et al.  ON ESTIMATING THRESHOLDS IN AUTOREGRESSIVE MODELS , 1986 .

[104]  K. Lai,et al.  A threshold cointegration analysis of asymmetric price transmission from crude oil to gasoline prices , 2005 .

[105]  Michael P. Clements,et al.  Forecasting US output growth using leading indicators: an appraisal using MIDAS models , 2009 .

[106]  E. Moolman.  A Markov switching regime model of the South African business cycle , 2003 .

[107]  James G. MacKinnon,et al.  Numerical Distribution Functions for Unit Root and Cointegration Tests , 1996 .

[108]  Myung-Jig Kim,et al.  New index of coincident indicators: A multivariate Markov switching factor model approach , 1995 .

[109]  L. Kilian.  The Economic Effects of Energy Price Shocks , 2007 .

[110]  Keith H. Black.  International Asset Allocation with Regime Shifts , 2003 .

[111]  Julien Chevallier,et al.  Detecting instability in the volatility of carbon prices , 2011 .

[112]  Julien Chevallier,et al.  The EU emissions trading scheme: The effects of industrial production and CO2 emissions on carbon prices , 2008 .

[113]  Ulrich Oberndorfer,et al.  EU Emission Allowances and the Stock Market: Evidence from the Electricity Industry , 2008 .

[114]  Allan Timmermann,et al.  Firm Size and Cyclical Variations in Stock Returns , 2000 .

[115]  James D. Hamilton,et al.  Autoregressive conditional heteroskedasticity and changes in regime , 1994 .

[116]  Marc S. Paolella,et al.  An econometric analysis of emission allowance prices , 2008 .

[117]  M. Watson,et al.  Systematic Monetary Policy and the Effects of Oil Price Shocks , 1997 .

[118]  Julien Chevallier,et al.  Jump-robust estimation of realized volatility in the EU emissions trading scheme , 2010 .

[119]  L. Kilian.  Not All Oil Price Shocks are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market , 2006 .

[120]  Hans-Martin Krolzig,et al.  Business Cycle Measurement in the Presence of Structural Change: International Evidence , 2001 .

[121]  Conditional Markov chain and its application in economic time series analysis , 2011 .

[122]  F. Ravazzolo,et al.  Oil and US GDP: A Real-Time Out-of-Sample Examination , 2010 .

[123]  W. Fuller,et al.  LIKELIHOOD RATIO STATISTICS FOR AUTOREGRESSIVE TIME SERIES WITH A UNIT ROOT , 1981 .

[124]  Georgi N. Boshnakov.  Time Series Analysis With Applications in R Series: Springer Texts in Statistics, 2nd Edition , 2009 .

[125]  Massimiliano Marcellino,et al.  A Markov–switching vector equilibrium correction model of the UK labour market , 2002 .

[126]  Raul Susmel,et al.  Interest-Rate Volatility in Emerging Markets , 2003, Review of Economics and Statistics.

[127]  David F. Hendry,et al.  Computer Automation of General-to-Specific Model Selection Procedures , 2001 .

[128]  Shiu‐Sheng Chen,et al.  Do higher oil prices push the stock market into bear territory , 2010 .

[129]  R. Tsay.  Testing and modeling multivariate threshold models , 1998 .

[130]  Michael D. Boldin,et al.  Dating Turning Points in the Business Cycle , 1994 .

[131]  Anna Creti,et al.  Les Cahiers de la Chaire Economie du Climat Carbon Price Drivers : Phase I versus Phase II Equilibrium ? , 2011 .

[132]  Wai Mun Fong,et al.  A Markov switching model of the conditional volatility of crude oil futures prices , 2002 .

[133]  René Garcia,et al.  Série Scientifique Scientific Series Nº 95s-7 Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models , 2022 .

[134]  Allan P. Layton,et al.  Dating and predicting phase changes in the U.S. business cycle , 1996 .

[135]  B. LeBaron,et al.  Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence , 1991 .

[136]  Michael P. Clements,et al.  Can oil shocks explain asymmetries in the US Business Cycle? , 2002 .

[137]  F. Diebold,et al.  Regime Switching with Time-Varying Transition Probabilities , 2020, Business Cycles.

[138]  Zacharias Psaradakis,et al.  Markov Switching Causality and the Money-Output Relationship , 2003 .

[139]  Stefan Trück,et al.  Modeling the Price Dynamics of Co2 Emission Allowances , 2009 .

[140]  Giampiero M. Gallo,et al.  Volatility spillovers, interdependence and comovements: A Markov Switching approach , 2008, Comput. Stat. Data Anal..

[141]  Eric Zivot,et al.  THRESHOLD COINTEGRATION AND NONLINEAR ADJUSTMENT TO THE LAW OF ONE PRICE , 2001, Macroeconomic Dynamics.

[142]  William D'haeseleer,et al.  Impact of the economic recession on the European power sector's CO2 emissions , 2011 .

[143]  Q. Xiao.  What drives Hong Kong's residential property market—A Markov switching present value model☆ , 2007 .

[144]  Julien Chevallier,et al.  European Carbon Prices and Banking Restrictions: Evidence from Phase I (2005-2007) , 2009 .

[145]  Julien Chevallier,et al.  Emissions Compliances and Carbon Prices under the EU ETS: A Country Specific Analysis of Industrial Sectors , 2009 .

[146]  Julien Chevallier,et al.  Carbon futures and macroeconomic risk factors : a view from the EU ETS , 2009 .

[147]  Clive W. J. Granger,et al.  Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models , 1989 .

[148]  A. Kanas.  Modeling regime transition in stock index futures markets and forecasting implications , 2008 .

[149]  Angel Pardo,et al.  Rolling over stock index futures contracts , 2009 .

[150]  D. Baur,et al.  Institute for International Integration Studies Is Gold a Safe Haven? International Evidence Is Gold a Safe Haven? International Evidence Is Gold a Safe Haven? International Evidence , 2022 .

[151]  Zacharias Psaradakis,et al.  ON THE DETERMINATION OF THE NUMBER OF REGIMES IN MARKOV‐SWITCHING AUTOREGRESSIVE MODELS , 2002 .

[152]  C. Perthuis,et al.  Pricing Carbon: The European Union Emissions Trading Scheme , 2010 .

[153]  Julien Chevallier,et al.  Nonparametric modeling of carbon prices , 2011 .

[154]  Volatility in stock returns for new EU member states: Markov regime switching model , 2007 .

[155]  Jin-Li Hu,et al.  Disaggregated energy consumption and GDP in Taiwan : A threshold co-integration analysis , 2008 .

[156]  Ó. Henry,et al.  Regime switching in the relationship between equity returns and short-term interest rates in the UK , 2009 .

[157]  Gary Koop,et al.  Do recessions permanently change output , 1993 .

[158]  J. Kaehler,et al.  Econometric Analysis of Financial Markets , 2012 .

[159]  Philippe Quirion,et al.  European Emission Trading Scheme and competitiveness: A case study on the iron and steel industry , 2008 .

[160]  Bruce E. Hansen,et al.  Residual-based tests for cointegration in models with regime shifts , 1996 .

[161]  C. Granger,et al.  Modelling Nonlinear Economic Relationships , 1995 .

[162]  Walter Krämer,et al.  The CUSUM test for OLS residuals , 1992 .

[163]  Andreas Löschel,et al.  EU climate policy up to 2020: An economic impact assessment , 2009 .

[164]  Mark J. Holmes.  Threshold cointegration and the short-run dynamics of twin deficit behaviour , 2011 .

[165]  Thomas H. Goodwin.  Business-Cycle Analysis with a Markov-Switching Model , 1993 .

[166]  Peter M. Summers,et al.  How well do Markov switching models describe actual business cycles? The case of synchronization , 2005 .

[167]  Stephen Gray,et al.  Asset market linkages: Evidence from financial, commodity and real estate assets , 2011 .

[168]  B. Hintermann.  Allowance Price Drivers in the First Phase of the EU ETS , 2010 .

[169]  Michael D. Bradley,et al.  Forecasting with a nonlinear dynamic model of stock returns and industrial production , 2004 .

[170]  Julien Chevallier,et al.  EUA and sCER phase II price drivers: Unveiling the reasons for the existence of the EUA-sCER spread , 2011 .

[171]  Takatoshi Ito,et al.  Meteor Showers or Heat Waves? Heteroskedastic Intra-Daily Volatility in the Foreign Exchange Market , 1988 .

[172]  Hong-Ghi Min,et al.  Nonlinear dynamics in arbitrage of the S&P 500 index and futures: A threshold error-correction model , 2010 .

[173]  Perry Sadorsky.  Oil price shocks and stock market activity , 1999 .

[174]  Allan Timmermann,et al.  Moments of Markov switching models , 2000 .

[175]  James D. Hamilton.  This is what happened to the oil price-macroeconomy relationship , 1996 .

[176]  Fads or Bubbles? , 1997 .

[177]  Lukas Menkhoff,et al.  Markov switching regimes in a monetary exchange rate model , 2005 .

[178]  O. Bajo‐Rubio,et al.  Searching for threshold effects in the evolution of budget deficits: an application to the Spanish case , 2004 .

[179]  Howell Tong,et al.  Threshold autoregression, limit cycles and cyclical data- with discussion , 1980 .

[180]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[181]  W. Enders,et al.  Cointegration and Threshold Adjustment , 1998 .

[182]  Joanna Janczura,et al.  An empirical comparison of alternate regime-switching models or electricity spot prices , 2010 .

[183]  L. Kilian.  A Comparison of the Effects of Exogenous Oil Supply Shocks on Output and Inflation in the G7 Countries , 2008 .

[184]  Massimo Guidolin,et al.  An Econometric Model of Nonlinear Dynamics in the Joint Distribution of Stock and Bond Returns , 2004 .

[185]  James D. Hamilton.  Regime switching models , 2010 .

[186]  Derek W. Bunn,et al.  Coevolution of policy, market and technical price risks in the EU ETS , 2011 .

[187]  Marine Carrasco,et al.  Misspecified Structural Change, Threshold, and Markov-switching models , 2002 .

[188]  Axel Pierru,et al.  Effects of the Uncertainty about Global Economic Recovery on Energy Transition and CO2 Price , 2011 .

[189]  Vicente Esteve,et al.  Threshold cointegration and nonlinear adjustment between goods and services inflation in the United States , 2006 .

[190]  Daniel R. Smith.  Evaluating Specification Tests for Markov-Switching Time Series Models , 2007 .

[191]  Bruce E. Hansen,et al.  Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis , 1996 .

[192]  Georgios P. Kouretas,et al.  Testing for two-regime threshold cointegration in the parallel and official markets for foreign currency in Greece , 2005 .

[193]  Thomas H. McCurdy,et al.  Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth , 1994 .

[194]  E. Ghysels,et al.  MIDAS Regressions: Further Results and New Directions , 2006 .

[195]  A. Beltratti,et al.  The Effects of the Introduction of the Euro on the Volatility of European Stock Markets , 2002 .

[196]  M. Pippenger,et al.  A Note on the Empirical Power of Unit Root Tests under Threshold Processes , 2009 .

[197]  The EU Emissions Trading Scheme: Disentangling the Effects of Industrial Production and CO2 Emissions on Carbon Prices , 2008 .

[198]  H. Tong.  Birth of the threshold time series model , 2007 .

[199]  Timo Teräsvirta,et al.  Smooth transition autoregressive models - A survey of recent developments , 2000 .

[200]  P. Perron,et al.  Estimating and testing linear models with multiple structural changes , 1995 .

[201]  Wai Mun Fong,et al.  Modelling the conditional volatility of commodity index futures as a regime switching process , 2001 .

[202]  Bruce E. Hansen,et al.  THRESHOLD AUTOREGRESSION WITH A UNIT ROOT , 2001 .

[203]  Bruce E. Hansen,et al.  Erratum: The likelihood ratio test under nonstandard conditions: Testing the Markov switching model of GNP , 1996 .