An I(2) Cointegration Model with Piecewise Linear Trends: Likelihood Analysis and Application
AbstractThis paper presents likelihood analysis of the I(2) cointegrated vector autoregression with piecewise linear deterministic terms. Limiting behavior of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-28.
Date of creation: 06 Jul 2009
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Cointegration; I(2); Piecewise linear trends; Likelihood analysis; US consumption;
Other versions of this item:
- Takamitsu Kurita & Heino Bohn Nielsen & Anders Rahbek, 2009. "An I(2) Cointegration Model With Piecewise Linear Trends: Likelihood Analysis And Application," Discussion Papers, University of Copenhagen. Department of Economics 09-13, University of Copenhagen. Department of Economics.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-07-11 (All new papers)
- NEP-ECM-2009-07-11 (Econometrics)
- NEP-ETS-2009-07-11 (Econometric Time Series)
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- Juselius, Katarina, 1998. "A Structured VAR for Denmark under Changing Monetary Regimes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 16(4), pages 400-411, October.
- Doornik, Jurgen A, 1998.
" Approximations to the Asymptotic Distributions of Cointegration Tests,"
Journal of Economic Surveys, Wiley Blackwell,
Wiley Blackwell, vol. 12(5), pages 573-93, December.
- Jurgen A. Doornik, 1998. "Approximations To The Asymptotic Distributions Of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 12(5), pages 573-593, December.
- Perron, Pierre, 1989.
"The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,"
Econometrica, Econometric Society,
Econometric Society, vol. 57(6), pages 1361-1401, November.
- Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers, Princeton, Department of Economics - Econometric Research Program 338, Princeton, Department of Economics - Econometric Research Program.
- Luca Fanelli & Emanuele Bacchiocchi, 2005. "Testing the purchasing power parity through I(2) cointegration techniques," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 20(6), pages 749-770.
- Palumbo, Michael & Rudd, Jeremy & Whelan, Karl, 2006.
"On the Relationships Between Real Consumption, Income, and Wealth,"
Journal of Business & Economic Statistics, American Statistical Association,
American Statistical Association, vol. 24, pages 1-11, January.
- Michael Palumbo & Jeremy Rudd & Karl Whelan, 2002. "On the relationships between real consumption, income and wealth," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2002-38, Board of Governors of the Federal Reserve System (U.S.).
- Kongsted, Hans Christian, 2005. "Testing the nominal-to-real transformation," Journal of Econometrics, Elsevier, Elsevier, vol. 124(2), pages 205-225, February.
- Heino Nielsen & Christopher Bowdler, 2006.
"Inflation adjustment in the open economy: an I(2) analysis of UK prices,"
Empirical Economics, Springer,
Springer, vol. 31(3), pages 569-586, September.
- Heino Bohn Nielsen & Christopher Bowdler, 2003. "Inflation Adjustment in the Open Economy: An I(2) Analysis of UK Prices," Economics Papers, Economics Group, Nuffield College, University of Oxford 2003-W05, Economics Group, Nuffield College, University of Oxford.
- Diamandis, Panayiotis F. & Georgoutsos, Dimitris A. & Kouretas, Georgios P., 2000. "The monetary model in the presence of I(2) components: long-run relationships, short-run dynamics and forecasting of the Greek drachma," Journal of International Money and Finance, Elsevier, Elsevier, vol. 19(6), pages 917-941, December.
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