, Month Forecast, vol.267, pp.12-1388, 2012.

N. Abuaf, J. , and P. , Purchasing power parity in the long run, Journal of Finance, vol.45, pp.157-174, 1990.

P. S. Addison, Wavelet transforms and ecg: a review, Physiological Measurement, vol.26, pp.155-199, 2005.

P. M. Addo, M. Billio, and D. Guégan, A test for a new modelling : The univariate mt-star model
URL : https://hal.archives-ouvertes.fr/halshs-00659158

. Panthéon-sorbonne, , p.11083, 2011.

P. M. Addo, M. Billio, and D. Guégan, Alternative methodology for turning-point detection in business cycle: A wavelet approach. Centre d'Economie de la Sorbonne, p.12023, 2012.
URL : https://hal.archives-ouvertes.fr/halshs-00694420

P. M. Addo, M. Billio, and D. Guégan, Understanding exchange rate dynamics, Proceedings of the 20th International Conference on Computational Statistics, pp.1-14, 2012.

P. M. Addo, M. Billio, and D. Guégan, Nonlinear dynamics and recurrence plots for detecting financial crisis, The North American Journal of Economics and Finance, 2013.
URL : https://hal.archives-ouvertes.fr/halshs-00803450

P. M. Addo, M. Billio, and D. Guégan, Turning point chronology for the eurozone: A distance plot approach, Journal of Business Cycle Measurement & Analysis (forthcoming, 2013.
URL : https://hal.archives-ouvertes.fr/halshs-00803457

P. M. Addo, M. Billio, and D. Guégan, The univariate mt-star model and a new linearity and unit root test procedure, Computational Statistics & Data Analysis, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01310518

J. Aizenman and I. Noy, Overview of the special issue on international finance in the aftermath of the 2008 global crisis, The North American Journal of Economics and Finance, vol.23, pp.265-268, 2012.

J. Anas, M. Billio, L. Ferrara, M. L. Duca, G. ;-g-l-mazzi et al., A turning point chronology for the euro-zone, pp.261-274, 2007.

J. Anas, M. Billio, L. Ferrara, and G. L. Mazzi, A system for dating and detecting turning points in the euro area, The Manchester Schools, vol.76, pp.549-577, 2008.

J. Anas and L. Ferrara, Detecting cyclical turning points: the abcd approach and two probabilitic indicators, Journal of Business Cycle Measurement and Analysis, vol.1, issue.2, pp.1-36, 2006.

M. Arnold and R. Gunther, Adaptive parameter estimation in multivariate self-exciting threshold autoregressive models, Communications in Statistics: Simulation and Computation, vol.30, pp.257-275, 2001.

M. J. Artis, M. Marcellino, and T. Proietti, Dating the euro area business cycle. CEPR Discussion Papers No 3696 and EUI Working Paper, 2002.

M. J. Artis, M. Marcellino, and T. Proietti, Characterising the business cycle for accession countries, 2003.

M. J. Artis, M. Marcellino, and T. Proietti, Dating the euro area business cycle, CEPR Discussion Papers, p.3696, 2003.

R. A. Ashley and D. M. Patterson, Linear versus nonlinear macroeconomics: A statistical test, International Economic Review, vol.30, pp.685-704, 1936.

N. Balke, Credit and economic activity: Credit regimes and nonlinear propagation of shocks, Review of Economics and Statistics, p.82, 2000.

N. S. Balke and T. B. Fomby, Threshold cointegration. International Economics Reviews, vol.38, pp.627-647, 1997.

J. Belaire-franch, Testing for non linearity in an artificial financial market: a recurrence quantification approach, Journal of Economic Behavior and Organization, vol.54, pp.483-494, 2004.

P. Bengoechea and G. Perez-quiros, A useful tool to identify recessions in the euro-area, Economic Papers, p.215, 2004.

M. Billio and R. Casarin, Identifying business cycle turning points with sequential monte carlo methods: An online and real-time application to the euro area, Journal of Forecasting, vol.29, pp.145-167, 2010.

, Bibliography 119

M. Billio, R. Casarin, F. Ravazzolo, and H. K. Van-dijk, Combination schemes for turning point predictions, Quarterly Review of Economics and Finance, vol.52, pp.402-412, 2012.

W. Brock, B. Lebaron, and D. Hsieh, Chaos, and Instability: Statistical Theory and Economic Evidence, 1991.

W. A. Brock and C. L. Sayers, Is the business cycle characterised by deterministic chaos, Journal of Monetary Economics, vol.22, pp.71-90, 1988.

L. Bruce, C. Koger, L. , and J. , Dimentionality reduction of hyperspectral data using discrete wavelet transform feature extraction, IEEE Transactions on Geoscience and Remote Sensing, vol.40, pp.2331-2338, 2002.

G. Bry and C. Boschan, Cyclical Analysis of Time Series: Selected Procedures and Computer Programs, 1971.

D. Buncic, Understanding forecast failure of estar models of real exchange rates, Economics and Econometrics Research Institute (EERI), p.18, 2009.

A. F. Burns and W. C. Mitchell, Measuring business cycles. NBER, 1946.

Z. Cai and E. Masry, Nonparametric estimation of additive nonlinear arx time series: Local linear fitting and projections, Econometric Theory, vol.16, pp.465-501, 2000.

M. Caner and B. E. Hansen, Instrumental variable estimation of a threshold model, Econometric Theory, vol.20, pp.813-843, 2004.

M. Carrasco, F. Bec, and M. B. Salem, Detecting mean reversion in real exchange rates from a multiple regime star model. Annales d'Économie et de Statistique, vol.99, p.100, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00685810

K. S. Chan, Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model, Annals of Statistics, vol.21, pp.521-533, 1993.

K. S. Chan and H. Tong, On the use of the deterministic lyapounov function for the ergodicity of stochastic difference equations, Advances in Applied Probability, vol.17, pp.666-678, 1985.

K. S. Chan and H. Tong, On estimating thresholds in autoregressive models, Journal of Time Series Analysis, vol.7, pp.197-190, 1986.

, Bibliography 120

R. Chen and R. Tsay, Nonlinear additive arx models, Journal of the American Statistical Association, vol.88, pp.955-967, 1993.

R. Chen and R. S. Tsay, Functional-coefficient autoregressive models, Journal of the American Statistical Association, vol.88, pp.298-308, 1993.

F. C. Dias, Nonlinearities over the business cycle: An application of the smooth transition autoregressive model to characterize gdp dynamics for the euro-area and portugal. Bank of Portugal, 2003.

D. A. Dickey and W. A. Fuller, Distribution of the estimators for autoregressive time series, Journal of the American Statistical Association, vol.74, pp.427-431, 1979.

T. Dieu-hang and T. Kompas, A modification of the estar model and testing for a unit root in a nonlinear framework. Discussion Paper, Crowford school of Economics and Government, 2010.

S. Donauer, F. Heinen, and P. Sibbertsen, Identification problems in estar models and a new model. Discussion Paper No. dp-444, 2010.

S. N. Durlauf and P. C. Phillips, Trends versus random walks in time series analvsis, Econometrica, vol.56, pp.1333-1354, 1988.

J. P. Eckmann, S. O. Kamphorst, R. , and D. , Recurrence plots of dynamical systems, Europhys Lett, vol.5, pp.973-977, 1987.

C. Engel, Long-run ppp may not hold after all, Journal of International Economics, vol.57, pp.243-73, 2000.

G. Fagan, J. Henry, and R. Mestre, An area-wide model for the euro area, p.42, 2001.

J. Fan and Q. Yao, Nonlinear time series: nonparametric and parametric methods, 2003.

P. H. Franses and D. Van-dijk, Non-linear time series models in empirical finance, 2000.

M. Gallegati, Wavelet analysis of stock returns and aggregate economic activity, Computational Statistics and Data Analysis, vol.52, pp.3061-3074, 2008.

M. Gallegati and M. Gallegati, Wavelet variance analysis of output in g-7 countries, Studies in Nonlinear Dynamics and Econometrics, vol.11, p.6, 2007.

T. Gautama, D. P. Mandic, and M. M. Hulle, A differential entropy based method for determining the optimal embedding parameters of a signal, Proceedings of ICASSP 2003, pp.29-32, 2003.

T. Gautama, D. P. Mandic, and M. M. Hulle, The delay vector variance method for detecting determinism and nonlinearity in time series, Physica D, vol.190, pp.167-176, 2004.

T. Gautama, D. P. Mandic, and M. M. Hulle, A novel method for determining the nature of time series, IEEE Transactions on Biomedical Engineering, vol.51, pp.728-736, 2004.

C. W. Granger and A. P. Andersen, An Introduction to Bilinear Time Series Models. Gottingen: Vandenhoek and Ruprecht, 1978.

C. W. Granger and T. Terasvirta, Modelling Nonlinear Economic Relationship, 1993.

D. Guégan and T. D. Pham, Power of score tests against bilinear time series analysis, Statistica Sinica, vol.2, pp.157-171, 1992.

B. Guttorp, P. Whitcher, P. , and D. , Wavelet analysis of covariance with application to atmospheric time series, Journal of Geophysical Research, vol.105, pp.14941-14962, 2000.

V. Haggan and T. Ozaki, Modeling nonlinear vibrations using an amplitudedependent autoregressive time series model, Biometrika, vol.68, pp.189-96, 1981.

V. Haggan and T. Ozaki, Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model, Biometrika, vol.68, pp.198-196, 1981.

J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, vol.57, pp.357-384, 1989.

J. D. Hamilton, Time Series Analysis, 1994.

B. E. Hansen, Inference when a nuisance parameter is not identified under the null hypthesis, Econometrica, vol.64, pp.413-430, 1996.

B. E. Hansen, Inference in tar models, Studies in Nonlinear Dynamics and Econometrics, vol.2, pp.1-14, 1997.

B. E. Hansen, Testing for linearity, Journal of Economic Surveys, vol.13, pp.551-576, 1999.

B. E. Hansen, Sample splitting and threshold estimation, Econometrica, vol.68, pp.575-603, 2000.

B. E. Hansen, Threshold autoregression in economics, Statistics and Its Interface, vol.4, pp.123-127, 2011.

D. Harding, Non parametric turning point detection dating rules and the construction of the euro zone chronology, Monographs of Official Statistics: Statistical Methods and Business Cycle Analysis of the Euro Zone, pp.122-146, 2004.

A. C. Harvey and T. Trimbur, General model-based filters for extracting trends and cycles in economic time series, Review of Economics and Statistics, vol.85, pp.244-255, 2003.

T. J. Hastie and R. J. Tibshirani, Generalized Additive Models, 1990.

R. Hegger, H. Kantz, and T. Schreiber, Practical implementation of nonlinear time series methods: The tisean package, Chaos, vol.9, pp.413-435, 1999.

A. Ho, K. Moody, G. Peng, C. Mietus, J. Larson et al., Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics, Circulation, vol.96, pp.842-848, 1997.

R. J. Hodrick and E. C. Prescott, Postwar u.s. business cycles: an empirical investigation, Journal of Money, Credit and Banking, vol.29, pp.1-16, 1997.

J. A. Holyst, M. Zebrowska, and K. Urbanowicz, Observation of deterministic chaos in financial time series by recurrence plots, can one control chaotic economy?, Eur Phys J B, vol.20, pp.531-535, 2001.

K. Hubrich and T. Terasvirta, Thresholds and smooth transitions in vector autoregressive models, CREATES Research Paper, p.18, 2013.

J. S. Iwanski and E. Bradley, Recurrence plots of experimental data: To embed or not to embed, Chaos, vol.8, pp.861-871, 1998.

M. Jensen, An approximate wavelet mle of short and long memory parameters, Studies in Nonlinear Dynamics and Econometrics, vol.3, pp.239-253, 1999.

H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, vol.123, 1997.

G. Kapetanios, Y. Shin, and A. Snell, Testing for a unit root in the nonlinear star framework, Journal of Econometrics, vol.112, pp.359-379, 2003.

D. Kaplan, Exceptional events as evidence for determinism, Physica D, vol.73, issue.1, pp.38-48, 1994.

C. J. Keylock, Constrained surrogate time series with preservation of the mean and variance structure, Physical Review E, vol.73, p.36707, 2006.

C. J. Keylock, Improved preservation of autocorrelative structure in surrogate data using an initial wavelet step. Nonlinear Processes in Geophysics, vol.15, pp.435-444, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00303003

J. M. Keynes, The General Theory of Employment, Interest and Money. Macmillan, 1936.

C. J. Kim and C. R. Nelson, State-Space Models with Regime-Switching: Classical and Gibbs-Sampling Approaches with Applicationss, 1999.

Z. G. Kontolemis, Does growth vary over the business cycle? some evidence from the g7 countries, Economica, vol.64, pp.441-460, 1997.

R. Kruse, A new unit root test against estar based on a class of modified statistics. Discussion Paper No. dp-398, 2008.

D. Kugiumtzis, Test your surrogate data before you test for nonlinearity, Physics Review E, vol.60, pp.2808-2816, 1999.

P. R. Kumar and P. Varaiya, Stochastic Systems: Estimation, Identification, and Adaptive Control, 1986.

C. Kyrtsou and C. E. Vorlow, Complex dynamics in macroeconomics: A noval approach, New Trends in Macroeconomics, pp.223-238, 2005.

L. Leistritz, W. Hesse, A. , and M. , Development of interaction measures based on adaptive non-linear time series analysis of biomedical signals, Biomed Tech, vol.51, pp.64-69, 2006.

N. N. Leonenko and L. F. Kozachenko, Sample estimate of the entropy of a random vector, Problems of Information Transmission, vol.23, pp.95-101, 1987.

J. Lothian and M. P. Taylor, Real exchange rate behavior of purchasing power parity under the current float, Journal of Political Economy, vol.104, 1996.

H. Lutkepohl and H. Kratzig, Applied Time Series Econometrics, 2004.

R. Luukkonen, P. Saikkonen, and T. Terasvirta, Testing linearity against smooth transition autoregressive models, Biometrica, vol.75, pp.491-499, 1988.

R. Luukkonen, P. Saikkonen, and T. Terasvirta, Testing linearity against smooth transition autoregressive models, Biometrika, vol.75, pp.491-499, 1988.

N. Marwan, A historical review of recurrence plots, The European Physical Journal -Special Topics, vol.164, pp.3-12, 2008.

N. Marwan and J. Kurths, Nonlinear analysis of bivariate data with cross recurrence plots, Physics Letters A, vol.302, pp.299-307, 2002.

N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, Recurrence plots for the analysis of complex systems, Physics Reports, vol.438, pp.237-329, 2007.

N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, and J. Kurths, Recurrence-plot-based measures of complexity and its application to heart-rate variability, Physics Review E, vol.66, p.26702, 2002.

E. Masry and D. Tjøstheim, Nonparametric estimation and identification of arch nonlinear time series: Strong convergence and asymptotic normality, Econometric Theory, vol.11, pp.258-289, 1995.

E. Masry and D. Tjøstheim, Additive arx time series and projection estimates, Econometric Theory, vol.13, pp.214-252, 1997.

P. Mcadam and . Us, Comparing business-cycle features, European Central Bank Working Paper, p.283, 2003.

D. L. Mcleish, A maximal inequality and dependent strong laws, The Annals of Probability, vol.5, pp.829-839, 1975.

R. Meese and K. Rogoff, Was it real? the exchange rate-interest differential relation over the modern floating rate period, Journal of Finance, vol.43, pp.933-948, 1988.

W. C. Mitchell, Business cycles. the problem and its setting, National Bureau of Economic Research, 1927.

E. Monch and H. Uhlig, Towards a monthly business cycle chronology for the euro area, Journal of Business Cycle Measurement and Analysis, vol.1, 2005.

P. G. O'connell, The overvaluation of purchasing power parity, Journal of International Economics, vol.44, pp.1-19, 1998.

J. Y. Park and P. C. Phillips, Statistical inference in regressions with integrated processes: Part i, Econometric Theory, vol.4, pp.468-497, 1988.

R. Pascalau, Testing for a unit root in the asymmetric nonlinear smooth transition framework, Finance and Legal Studies, 2007.

G. A. Pfann, P. C. Schotman, and R. Tschernig, Nonlinear interest rate dynamics and implications for the term structure, Journal of Econometrics, vol.74, pp.149-176, 1996.

D. T. Pham, The mixing property of bilinear and generalized random coefficient autoregressive models, Stochastic Processes and Their Applications, vol.23, pp.291-300, 1986.

P. C. Phillips and P. Perron, Testing for a unit root in time series regression, Biometrika, vol.75, pp.335-346, 1988.

J. Pitarakis, A joint test for structural stability and a unit root in autoregressions, Computational Statistics & Data Analysis

, , 2012.

M. B. Priestley, Non-linear and Non-stationary Time Series Analysis, 1988.

L. Qian, On maximum likelihood estimators for a threshold autoregression, Journal of Statistical Planning and Inference, vol.75, pp.21-46, 1998.

J. Ramsey, The contributions of wavelets to the analysis of economic and financial data, Philosophical Transactions of the Royal Society of London A, vol.357, pp.2593-2606, 1999.

J. Ramsey and C. Lampart, The decomposition of economic relationships by time scale using wavelets: Expenditure and income, Studies in Nonlinear Dynamics and Econometrics, vol.3, pp.23-42, 1998.

M. C. Romano, M. Thiel, J. Kurths, I. Z. Kiss, H. et al., Detection of synchronization for non-phase-coherent and non-stationary data, Europhysics Letters, vol.71, pp.466-472, 2005.

P. Rothman, D. Van-dijk, and P. H. Franses, A multivariate star analysis of the relationship between money and output, 1999.

S. E. Said and W. A. Dickey, Testing for a unit root in autoregressive moving average models of unknown order, Biometrika, vol.71, pp.599-607, 1984.

T. Schreiber and A. Schmitz, Improved surrogate data for nonlinearity tests, Physics Review Lett, vol.77, pp.635-638, 1996.

T. Schreiber and A. Schmitz, Surrogate time series, Physica D, vol.142, pp.346-382, 2000.

D. E. Sichel, Business cycle asymmetry: a deeper look, Economic Inquiry XXXI, pp.224-236, 1993.

J. H. Stock and M. W. Watson, Testing for common trends, Journal of the American Statistical Association, vol.83, pp.1097-1107, 1988.

M. W. Stock and J. H. Watson, Forecasting inflation, Journal of Monetary Economics, vol.44, pp.293-335, 1999.

B. Strikholm and T. Terasvirta, A sequential procedure for determining the number of regimes in a threshold autoregressive model, Econometrics Journal, p.9, 2006.

F. Strozzi, E. Gutiérrez, C. Noè, T. Rossi, M. Serati et al., Measuring volatility in the nordic spot electricity market using recurrence quantification analysis, The European Physical Journal-special Topics, vol.164, pp.105-115, 2008.

R. T. Subba and M. M. Gabr, An Introduction to Bispectral Analysis and Bilinear Time Series Models. No. 24 in Lecture Notes in Statistics, 1984.

F. Takens, Detecting strange attractors in turbulence, Lecture notes in mathematics, pp.366-387, 1981.

M. P. Taylor, D. A. Peel, and L. Sarno, Nonlinear mean-reversion in real exchange rates: Toward a solution to the purchasing power parity puzzles, International Economic Review, vol.42, pp.1015-1042, 2001.

A. Teolis, Computational signal processing with wavelets, 1998.

T. Terasvirta, Specification, estimation, and evaluation of smooth transition autoregressive models, Journal of the American Statistical Association, vol.89, pp.208-218, 1994.

T. Terasvirta, Specification, estimation and evaluation of smooth transition autoregressive models, Journal of the American Statistical Association, vol.89, pp.208-218, 1994.

T. Terasvirta, A. , and H. M. , Characterizing nonlinearities in business cycles using smooth transition autoregressive models, Journal of Applied Econometrics, vol.7, pp.119-136, 1992.

T. Terasvirta and C. W. Granger, Modelling Nonlinear Dynamic Relationships, 1993.

T. Terasvirta, D. Tjostheim, and C. W. Granger, Aspects of modelling nonlinear time series, Handbook of Econometrics, vol.4, 1994.

J. D. Theiler, J. Eubank, S. Longtin, A. Galdrikian, and B. Farmer, Testing for nonlinearity in time series: the method of surrogate data, Physica A, vol.58, pp.77-94, 1992.

D. Tjøstheim, Estimation in nonlinear time series models, Stochastic Processes and their Applications, vol.21, pp.251-273, 1986.

D. Tjøstheim, Non-linear time series and markov chains, Advances in Applied Probability, vol.22, pp.587-611, 1990.

H. Tong, On a threshold model, Pattern Recognition and Signal Processing, 1978.

H. Tong, Threshold models in non-linear time series analysis, Lecture notes in statistics 21, 1983.

H. Tong and . Non, Linear Time Series. A Dynamical Systems Approach, 1990.

R. Tsay, Testing and modeling multivariate threshold models, Journal of the American Statistical Association, vol.93, pp.1188-1202, 1998.

R. L. Tweedie, Sufficient conditions for ergodicity and recurrence of markov chain on a general state space, Stochastic Processes and Their Applications, vol.3, pp.385-402, 1975.

R. L. Tweedie, Sufficient conditions for ergodicity and recurrence of markov chains on a general state space, Stochastic Processes and Their Applications, vol.3, pp.385-403, 1975.

, Bibliography 128

R. L. Tweedie, Invariant measures for markov chains with no irreducibility assumptions, Journal of Applied Probability, vol.25, pp.275-285, 1988.

D. Van-dijk, T. Terasvirta, and P. H. Franses, Smooth transition autoregressive models -a survey of recent developments, Econometric Reviews, vol.21, pp.1-47, 2002.

D. V. Vougas, On unit root testing with smooth transitions, Computational Statistics & Data Analysis, vol.51, issue.2, pp.797-800, 2006.

D. B. Walden, P. , and A. T. , Wavelet Methods for Time Series Analysis, 2000.

M. C. Weigend and A. S. Casdagli, Exploring the continuum between deterministic and stochastic modelling, in time series prediction: Forecasting the future and understanding the past, pp.347-367, 1994.

H. O. Wold, A study in the analysis of stationary time series, 1938.

S. N. Wood, A. , and N. H. , Gams with integrated model selection using penalized regression splines and applications to environmental modelling, Ecological Modelling, vol.157, pp.157-177, 2002.

J. P. Zbilut, A. Giuliani, and J. C. Webber, Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification, Physics Letters A, vol.246, pp.122-128, 1998.

J. P. Zbilut and J. C. Webber, Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A, vol.171, pp.199-203, 1992.

J. P. Zbilut and J. C. Webber, Dynamical assessment of physiological systems and states using recurrence plot strategies, Journal of Applied Physiology, vol.76, pp.965-973, 1994.