Relevant bibliographies by topics / Markov Switching

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Markov Switching'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 March 2023

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Journal articles on the topic "Markov Switching"

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Guérin, Pierre, and Massimiliano Marcellino. "Markov-Switching MIDAS Models." Journal of Business & Economic Statistics 31, no. 1 (January 2013): 45–56. http://dx.doi.org/10.1080/07350015.2012.727721.

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Huang, Yu-Lieh. "Testing Markov switching models." Applied Economics 46, no. 17 (March 3, 2014): 2047–51. http://dx.doi.org/10.1080/00036846.2014.892201.

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Liu, Xiaochun. "Markov switching quantile autoregression." Statistica Neerlandica 70, no. 4 (October 12, 2016): 356–95. http://dx.doi.org/10.1111/stan.12091.

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Liu, Ji-Chun. "INTEGRATED MARKOV-SWITCHING GARCH PROCESS." Econometric Theory 25, no. 5 (October 2009): 1277–88. http://dx.doi.org/10.1017/s0266466608090506.

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This paper investigates stationarity of the so-called integrated Markov-switching generalized autoregressive conditionally heteroskedastic (GARCH) process, which is an important subclass of the Markov-switching GARCH process introduced by Francq, Roussignol, and Zakoïan (2001, Journal of Time Series Analysis 22,197–220) and a Markov-switching version of the integrated GARCH (IGARCH) process. We show that, like the classical IGARCH process, a stationary solution with infinite variance for the integrated Markov-switching GARCH process may exist. To this purpose, an alternative condition for the existence of a strictly stationary solution of the Markov-switching GARCH process is presented, and some results obtained in Hennion (1997, Annals of Probability 25, 1545–1587) are employed. In addition, we also discuss conditions for the existence of a strictly stationary solution of the Markov-switching GARCH process with finite variance, which is a modification of Theorem 2 in Francq et al. (2001).
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Nunian, Mohd Azizi Amin, Siti Meriam Zahari, and S. Sarifah Radiah Shariff. "Modelling foreign exchange rates: a comparison between markov-switching and markov-switching GARCH." Indonesian Journal of Electrical Engineering and Computer Science 20, no. 2 (November 1, 2020): 917. http://dx.doi.org/10.11591/ijeecs.v20.i2.pp917-923.

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Foreign exchange rate is important as it determines a country's economic condition. It is used to carry out transfers of purchasing power between two or more countries. Volatility in exchange rates may result in difficulty in decision making especially, in financial sectors as high volatility could increase the risk in exchange rates. Thus, Markov switching model is employed in this study as it is believed to be efficient in handling not only volatilility but also nonlinearity characteristics in exchange rates. The aims of this study are to model the foreign exchange rates using two models; Markov Switching (M-S) models and Markov Switching Generalized Autoregressive Conditional Heteroscedasticity (M-S GARCH) and to compare these two models based on log-likelihood, AIC and BIC criteria. This study used the quarterly data of foreign exchange rates for Singapore Dollar (SGD), Korean Won (KRW), China Yuan Renminbi (CNY), Japanese Yen (JPY) and the US Dollar (USD) against Malaysia Ringgit (MYR) which were collected from Quarter 4, 2006 to Quarter 1, 2018. The findings indicate that Markov Switching is the best model since it has the highest log-likelihood value, and the lowest AIC and BIC values. The results show that JPY and SGD have highly persistent trends on regime 1 with probability values 0.96 and 0.84, respectively as compared to CNY, KRW and USD, while the latter have high persistent trends on regime 2 with probability values, 0.99, 0.95, 0.82, respectively.
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Hou, Zhenting, Hailing Dong, and Peng Shi. "Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching." ANZIAM Journal 49, no. 2 (October 2007): 231–41. http://dx.doi.org/10.1017/s1446181100012803.

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abstractIn this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system. Existing results for Markovian switching systems may then be applied to analyze phase semi-Markovian switching systems. In the following, we obtain asymptotic stability for the distribution of nonlinear stochastic systems with semi-Markovian switching. The results can also be extended to general semi-Markovian switching systems. Finally, an example is given to illustrate the feasibility and effectiveness of the theoretical results obtained.
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Fuh, Cheng-Der, Kwok Wah Remus Ho, Inchi Hu, and Ren-Her Wang. "Option Pricing with Markov Switching." Journal of Data Science 10, no. 3 (March 21, 2021): 483–509. http://dx.doi.org/10.6339/jds.201207_10(3).0008.

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Petričková, Anna. "Moments of Markov-Switching Models." Tatra Mountains Mathematical Publications 61, no. 1 (December 1, 2014): 131–40. http://dx.doi.org/10.2478/tmmp-2014-0032.

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Abstract In this paper we have focused on the class of regime-switching time series models with regimes determined by unobservable variables, concretely Markov-switching models. We have derived 2nd central moment of the MSW models for two cases-state-independent and state-dependent model
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Chiappa, Silvia. "Explicit-Duration Markov Switching Models." Foundations and Trends® in Machine Learning 7, no. 6 (2014): 803–86. http://dx.doi.org/10.1561/2200000054.

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Malyutov, M. B. "Offline fitting Markov switching model." Model Assisted Statistics and Applications 14, no. 3 (July 18, 2019): 193–213. http://dx.doi.org/10.3233/mas-190461.

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Dissertations / Theses on the topic "Markov Switching"

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Blagov, Boris [Verfasser], and Michael [Akademischer Betreuer] Funke. "Four Essays on Markov-Switching DSGE and Markov-Switching VAR Models / Boris Blagov. Betreuer: Michael Funke." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2016. http://d-nb.info/1103233408/34.

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Mazali, Rogério. "Improving mutual fund market timing measures: a markov switching approach." reponame:Repositório Institucional do FGV, 2001. http://hdl.handle.net/10438/55.

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Made available in DSpace on 2008-05-13T13:16:08Z (GMT). No. of bitstreams: 1 1429.pdf: 435505 bytes, checksum: 014d927923de455f14c28a151a16c5e1 (MD5) Previous issue date: 2001-07-31
Market timing performance of mutual funds is usually evaluated with linear models with dummy variables which allow for the beta coefficient of CAPM to vary across two regimes: bullish and bearish market excess returns. Managers, however, use their predictions of the state of nature to deÞne whether to carry low or high beta portfolios instead of the observed ones. Our approach here is to take this into account and model market timing as a switching regime in a way similar to Hamilton s Markov-switching GNP model. We then build a measure of market timing success and apply it to simulated and real world data.
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Koh, You Beng, and 辜有明. "Bayesian analysis in Markov regime-switching models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48521644.

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van Norden and Schaller (1996) develop a standard regime-switching model to study stock market crashes. In their seminal paper, they use the maximum likelihood estimation to estimate the model parameters and show that a two-regime speculative bubble model has significant explanatory power for stock market returns in some observed periods. However, it is well known that the maximum likelihood estimation can lead to bias if the model contains multiple local maximum points or the estimation starts with poor initial values. Therefore, a better approach to estimate the parameters in the regime-switching models is to be found. One possible way is the Bayesian Gibbs-sampling approach, where its advantages are well discussed in Albert and Chib (1993). In this thesis, the Bayesian Gibbs-sampling estimation is examined by using two U.S. stock datasets: CRSP monthly value-weighted index from Jan 1926 to Dec 2010 and S&P 500 index from Jan 1871 to Dec 2010. It is found that the Gibbs-sampling estimation explains the U.S. data better than the maximum likelihood estimation. Moreover, the existing standard regime-switching speculative behaviour model is extended by considering the time-varying transition probabilities which are governed by the first-order Markov chain. It is shown that the time-varying first-order transition probabilities of Markov regime-switching speculative rational bubbles can lead stock market returns to have a second-order Markov regime. In addition, a Bayesian Gibbs-sampling algorithm is developed to estimate the parameters in the second-order two-state Markov regime-switching model.
published_or_final_version
Statistics and Actuarial Science
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Doctor of Philosophy
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Santos, João Ramiro Rodrigues Simões dos. "Credit cycle identification: A Markov-switching application." Master's thesis, NSBE - UNL, 2014. http://hdl.handle.net/10362/11723.

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A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics
This project aims to study credit dynamics and to identify phases of credit cycles at the country level. We applied a Markov-switching (MS) autoregressive framework and a MS with regime-invariant macroeconomic variables to a broad concept of credit, domestic credit. We used a sample of 10 developed countries. MS identification power is assessed using smooth probabilities of low growth states, collected as a by-product of models estimation, against historical databases of crisis events. Conclusions support that MS is accurate in identifying credit cycle phases, and that domestic credit is a good variable for such identification. Additionally, Credit Gap, excess growth over GDP and Broad Money contribute positively to the MS predictions.
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Karadag, Mehmet Ali. "Analysis Of Turkish Stock Market With Markov Regime Switching Volatility Models." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609787/index.pdf.

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In this study, both uni-regime GARCH and Markov Regime Switching GARCH (SW-GARCH) models are examined to analyze Turkish Stock Market volatility. We investigate various models to find out whether SW-GARCH models are an improvement on the uni-regime GARCH models in terms of modelling and forecasting Turkish Stock Market volatility. As well as using seven statistical loss functions, we apply Superior Predictive Ability (SPA) test of Hansen (2005) and Reality Check test (RC) of White (2000) to compare forecast performance of various models.
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Hrabovska, Yevheniia <1994&gt. "A Markov-Switching Model for Bubble Detection in the Stock Market." Master's Degree Thesis, Università Ca' Foscari Venezia, 2017. http://hdl.handle.net/10579/10797.

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In this study I propose a model for the behaviour of the real stock market prices which allows for the existence of speculative bubbles. The bubble is assumed to follow a Markov-switching process with explosive and collapsing regimes. Inference on the model is performed by using observations on the deviations of the log prices from fundamentals. The fundamental prices are assumed to be a function of the discounted future dividends. Data used for estimation includes major stock market indices: SP 500, NASDAQ, Euro Stoxx 50 and major US companies.
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Humala, Acuña Alberto. "Markov switching modelling of interest rate pass-through." Thesis, University of Warwick, 2005. http://wrap.warwick.ac.uk/34676/.

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The first paper, "Interest rate pass-through and financial crises: do switching regimes matter? The case of Argentina", analyses the dynamic relationship between a money market (interbank) rate and different short-term lending rates by measuring their passthrough. Neither linear single-equation modelling nor linear multi-equation systems capture efficiently this relationship. Several financial crises alter the speed and degree of response to interbank rate shocks. Hence, a Markov switching VAR model shows the pass-through increases considerably for all market interest rates in a high-volatility scenario. The model identifies correctly the periods in which regime shifts occur, and associates them to financial crises. The second paper, "Modelling interest rate pass-through with endogenous switching regimes in Argentina", extends the scope of the Markov switching modelling by including time-varying transition probabilities. Interest rate spreads are used as leading indicators. The model allows devaluation expectations and country risks, (measured by rate spreads) to signal regime switching. Estimation results suggest that the passthrough tends to overshoot with financial instability, but to decrease if that condition is sufficiently large and long-lived. Likewise, results show a quite heterogeneous credit market, with a highly efficient transmission mechanism in the corporate segment, but considerably less in the consumer segment. The final paper, "Regime switching in interest rate pass-through and dynamic bank modelling with risks", builds a theoretical model of dynamic bank optimisation, which provides rationale to a regime-switching behaviour in the interest rate pass-through. It is shown that a regime-switching interbank rate induces a nonlinear behaviour in lending and deposit rates and (by further introducing interbank-alike regime-switching risk premiums) in the pass-through. Thus, the pass-through process is consistent with a nonlinear behaviour even if there are no asymmetric adjustment costs in the response to interbank rate shocks. An empirical application to France and Germany provide results that support these conclusions.
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Cheng, Jie. "An Extended Class of Markov Switching Autoregressive Models." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.508540.

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Dutra, Livia Maria. "Exact Bayesian inference for Markov switching Cox processes." Universidade Federal de Minas Gerais, 2015. http://hdl.handle.net/1843/BUBD-9WGFNQ.

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Statistical modelling of point patterns is an important and common problem in several applications. An important point process, and a generalisation of the Poisson process, is the Cox process, where the intensity function is itself stochastic. We focus on Cox processes in which the intensity function is driven by a nite state space continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). We investigate some probabilistic properties of these processes, three new theorems for these processes are derived and we develop a Bayesian methodology to perform exact inference based on MCMC algorithms. Since the likelihood function is tractable, it facilitates the development of an exact methodology. Simulated studies are presented in order to investigate the efficiency of the methodology on the estimation of MSCP's intensity function and the parameters indexing its law. Finally, an analysis with real data is performed.
A modelagem estatística de dados pontuais é um problema importante e comum em diversas aplicações. Um importante processo pontual, e uma generalização do processo de Poisson, é o processo de Cox, em que a sua função intensidade é também estocástica. O presente trabalho se concentra nos processos de Cox em que sua função intensidade é uma cadeia de Markov em tempo contínuo com espaço de estados nito. Estes processos s~ao referidos como processos de Cox com mudanças Markovianas (PCMM). Algumas propriedades probabilísticas desses processos são investigadas, três novos teoremas enunciados e é desenvolvida uma metodologia Bayesiana para realizar inferência exata, baseada em algoritmos MCMC. O desenvolvimento de uma metodologia exata é facilitado, uma vez que a função de verossimilhança é tratável. São apresentados estudos simulados a m de investigar a e ciência da metodologia para estimação da função intensidade dos PCMM's e dos parâmetros relacionados a ela. Ao fim, realiza-se uma análise com dados reais.
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Fan, Qianzhu. "Stochastic heat equations with Markovian switching." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/stochastic-heat-equations-with-markovian-switching(8958d026-671e-4c63-a639-b4a7b120a968).html.

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This thesis consists of three parts. In the first part, we recall some background theory that will be used throughout the thesis. In the second part, we studied the existence and uniqueness of solutions of the stochastic heat equations with Markovian switching. In the third part, we investigate the properties of solutions, such as Feller property, strong Feller property and stability.
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Books on the topic "Markov Switching"

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Krolzig, Hans-Martin. Markov-Switching Vector Autoregressions. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-51684-9.

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Hamilton, James D., and Baldev Raj, eds. Advances in Markov-Switching Models. Heidelberg: Physica-Verlag HD, 2002. http://dx.doi.org/10.1007/978-3-642-51182-0.

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Timmermann, Allan. Moments of Markov switching models. London: London School of Economics, Financial Markets Group, 1999.

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Gable, Jeff. Analytical derivatives for Markov switching models. Ottawa, Ont: Publications Distribution, Bank of Canada, 1995.

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Chang-Jin, Kim. Dynamic linear models with Markov-switching. Toronto, Ont: York University, Dept. of Economics, 1991.

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Chauvet, Marcelle. Markov switching in disaggregate unemployment rates. [New York, N.Y.]: Federal Reserve Bank of New York, 2001.

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Gable, Jeff. Analytical derivatives of Markov switching models. Ottawa, Ont: Bank of Canada, 1995.

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Canada, Bank of. Switching between chartists and fundamentalists: A Markov Regime-Switching approach. Ottawa: Bank of Canada, 1996.

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Chang-Jin, Kim. Estimation of Markov regime-switching regression models with endogenous switching. [St. Louis, Mo.]: Federal Reserve Bank of St. Louis, 2003.

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Vigfusson, Robert. Switching between chartists and fundamentalists: A Markov regime-switching approach. Ottawa: Bank of Canada, 1996.

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Book chapters on the topic "Markov Switching"

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Mizrach, Bruce, and James Watkins. "A Markov Switching Cookbook." In Dynamic Modeling and Econometrics in Economics and Finance, 33–43. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5129-4_2.

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Cocozza-Thivent, Christiane. "Switching Processes." In Markov Renewal and Piecewise Deterministic Processes, 187–208. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70447-6_10.

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Yushkevich, A. A. "Optimal Switching Problem for Markov Chains." In Markov Processes and Controlled Markov Chains, 255–86. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4613-0265-0_15.

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Chauvet, Marcelle, and Yanpin Su. "Nonstationarities and Markov Switching Models." In Recent Advances in Estimating Nonlinear Models, 123–46. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8060-0_7.

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Fabbrini, Viola, Massimo Guidolin, and Manuela Pedio. "Results from Markov Switching Models." In Transmission Channels of Financial Shocks to Stock, Bond, and Asset-Backed Markets: An Empirical Model, 50–67. London: Palgrave Macmillan UK, 2016. http://dx.doi.org/10.1007/978-1-137-56139-8_5.

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Chauvet, Marcelle, Chinhui Juhn, and Simon Potter. "Markov switching in disaggregate unemployment rates." In Advances in Markov-Switching Models, 61–88. Heidelberg: Physica-Verlag HD, 2002. http://dx.doi.org/10.1007/978-3-642-51182-0_4.

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Yamaka, Woraphon, Paravee Maneejuk, and Songsak Sriboonchitta. "Markov Switching Beta-skewed-t EGARCH." In Lecture Notes in Computer Science, 184–96. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14815-7_16.

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Krolzig, Hans-Martin. "The Markov-Switching Vector Autoregressive Model." In Lecture Notes in Economics and Mathematical Systems, 6–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-51684-9_2.

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Lu, Hsin-Min, Daniel Zeng, and Hsinchun Chen. "Markov Switching Models for Outbreak Detection." In Infectious Disease Informatics and Biosurveillance, 111–44. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-6892-0_6.

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Hamilton, James D., and Baldev Raj. "New directions in business cycle research and financial analysis." In Advances in Markov-Switching Models, 3–16. Heidelberg: Physica-Verlag HD, 2002. http://dx.doi.org/10.1007/978-3-642-51182-0_1.

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Conference papers on the topic "Markov Switching"

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Tang, Xiaobin. "Research on Markov-Switching model." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002578.

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Cuesta-Infante, Alfredo, and Kalyan Veeramachaneni. "Markov Switching Copula Models for Longitudinal Data." In 2016 IEEE 16th International Conference on Data Mining Workshops (ICDMW). IEEE, 2016. http://dx.doi.org/10.1109/icdmw.2016.0159.

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Vardanyan, Yelena, and Mohammad Reza Hesamzadeh. "Modeling regime switching in day-ahead market prices using Markov model." In 2016 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe). IEEE, 2016. http://dx.doi.org/10.1109/isgteurope.2016.7856316.

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Zaky, Ahmed Bayoumy, and Walid Gomaa. "Car following regime taxonomy based on Markov switching." In 2014 IEEE 17th International Conference on Intelligent Transportation Systems (ITSC). IEEE, 2014. http://dx.doi.org/10.1109/itsc.2014.6957871.

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Lemos, J. M., L. M. Rato, and J. S. Marques. "Switching reconfigurable control based on hidden Markov models." In 1999 European Control Conference (ECC). IEEE, 1999. http://dx.doi.org/10.23919/ecc.1999.7099375.

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Wai, Phoong Seuk, Mohd Tahir Ismail, and Sek Siok Kun. "Gold price effect on stock market: A Markov switching vector error correction approach." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882604.

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Tan, Kangrong, and Shozo Tokinaga. "Markov Regime Switching Analysis for the Pandemic and the Dynamics of German Market." In 2021 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2021. http://dx.doi.org/10.1109/csci54926.2021.00162.

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Gorynin, Ivan, Emmanuel Monfrini, and Wojciech Pieczynski. "Unsupervised learning of Markov-switching stochastic volatility with an application to market data." In 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP). IEEE, 2016. http://dx.doi.org/10.1109/mlsp.2016.7738821.

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Zheng, Hao, Feng Guo, Jiahui Zhu, and Xiangyu Ge. "Empirical Analysis of China’s Stock Market Volatility Based on Markov Switching GARCH Model." In 2021 5th Annual International Conference on Data Science and Business Analytics (ICDSBA). IEEE, 2021. http://dx.doi.org/10.1109/icdsba53075.2021.00080.

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Devianto, Dodi, Maiyastri, Uqwatul Alma Wisza, Michelin Wara, Putri Permathasari, and Rika Okda Marlina Zen. "Time Series of Rainfall Model with Markov Switching Autoregressive." In 2018 International Conference on Applied Information Technology and Innovation (ICAITI). IEEE, 2018. http://dx.doi.org/10.1109/icaiti.2018.8686745.

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Reports on the topic "Markov Switching"

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Kim, Chang-Jin, Jeremy M. Piger, and Richard Startz. Estimation of Markov Regime-Switching Regression Models with Endogenous Switching. Federal Reserve Bank of St. Louis, 2003. http://dx.doi.org/10.20955/wp.2003.015.

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Farmer, Roger E. A., Tao Zha, and Daniel Waggoner. Understanding Markov-Switching Rational Expectations Models. Cambridge, MA: National Bureau of Economic Research, February 2009. http://dx.doi.org/10.3386/w14710.

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Nelson, Charles R., Jeremy M. Piger, and Eric Zivot. Markov Regime Switching and Unit Root Tests. Federal Reserve Bank of St. Louis, 2001. http://dx.doi.org/10.20955/wp.2001.013.

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Foerster, Andrew, Juan Rubio-Ramírez, Daniel Waggoner, and Tao Zha. Perturbation Methods for Markov-Switching DSGE Models. Cambridge, MA: National Bureau of Economic Research, August 2014. http://dx.doi.org/10.3386/w20390.

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Dueker, Michael J. Markov Switching in GARCH Processes and Mean Reverting Stock Market Volatility. Federal Reserve Bank of St. Louis, 1994. http://dx.doi.org/10.20955/wp.1994.015.

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Engel, Charles. Can the Markov Switching Model Forecast Exchange Rates? Cambridge, MA: National Bureau of Economic Research, November 1992. http://dx.doi.org/10.3386/w4210.

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Lubis, Iman. PENDEKATAN MODEL MARKOV SWITCHING PADA PASAR MODAL INDONESIA. Jurnal Madani: Ilmu Pengetahuan, Teknologi, dan Humaniora, September 2018. http://dx.doi.org/10.33753/madani.v1i2.22.

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Neely, Christopher J., and Michael J. Dueker. Can Markov Switching Models Predict Excess Foreign Exchange Returns? Federal Reserve Bank of St. Louis, 2001. http://dx.doi.org/10.20955/wp.2001.021.

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Owyang, Michael T., Christopher H. Wheeler, Jeremy M. Piger, and Howard J. Wall. The Economic Performance of Cities: A Markov-Switching Approach. Federal Reserve Bank of St. Louis, 2006. http://dx.doi.org/10.20955/wp.2006.056.

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10

Misas A., Martha, and María Teresa Ramírez-Giraldo. Colombian economic growth under Markov switching regimes with endogenous transition probabilities. Bogotá, Colombia: Banco de la República, December 2006. http://dx.doi.org/10.32468/be.425.

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