IDEAS home Printed from
   My bibliography  Save this paper

A Consistent Test for Multivariate Conditional Distributions


  • Fuchun Li
  • Greg Tkacz


We propose a new test for a multivariate parametric conditional distribution of a vector of variables yt given a conditional vector xt. The proposed test is shown to have an asymptotic normal distribution under the null hypothesis, while being consistent for all fixed alternatives, and having non-trivial power against a sequence of local alternatives. Monte Carlo simulations show that our test has reasonable size and good power for both univariate and multivariate models, even for highly persistent dependent data with sample sizes often encountered in empirical finance.

Suggested Citation

  • Fuchun Li & Greg Tkacz, 2009. "A Consistent Test for Multivariate Conditional Distributions," Staff Working Papers 09-34, Bank of Canada.
  • Handle: RePEc:bca:bocawp:09-34

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Kozicki, Sharon & Tinsley, P.A., 2005. "Permanent and transitory policy shocks in an empirical macro model with asymmetric information," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1985-2015, November.
    2. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
    3. Thomas Laubach & John C. Williams, 2003. "Measuring the Natural Rate of Interest," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1063-1070, November.
    4. Glenn D. Rudebusch, 2006. "Monetary Policy Inertia: Fact or Fiction?," International Journal of Central Banking, International Journal of Central Banking, vol. 2(4), December.
    5. Neiss, Katharine S. & Nelson, Edward, 2003. "The Real-Interest-Rate Gap As An Inflation Indicator," Macroeconomic Dynamics, Cambridge University Press, vol. 7(02), pages 239-262, April.
    6. Marc-André Gosselin & René Lalonde, 2006. "An Eclectic Approach to Estimating U.S. Potential GDP," Empirical Economics, Springer, vol. 31(4), pages 951-975, November.
    7. Cayen, Jean-Philippe & van Norden, Simon, 2005. "The reliability of Canadian output-gap estimates," The North American Journal of Economics and Finance, Elsevier, vol. 16(3), pages 373-393, December.
    8. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    9. William B. English & William R. Nelson & Brian P. Sack, 2002. "Interpreting the significance of lagged interest rate in estimated monetary policy rules," Finance and Economics Discussion Series 2002-24, Board of Governors of the Federal Reserve System (U.S.).
    10. René Lalonde & Zhenhua Zhu & Frédérick Demers, 2003. "Forecasting and Analyzing World Commodity Prices," Money Affairs, Centro de Estudios Monetarios Latinoamericanos, vol. 0(1), pages 1-30, January-J.
    11. Marc P. Giannoni & Jean Boivin, 2005. "DSGE Models in a Data-Rich Environment," Computing in Economics and Finance 2005 431, Society for Computational Economics.
    12. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    13. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    14. Edge, Rochelle M. & Kiley, Michael T. & Laforte, Jean-Philippe, 2008. "Natural rate measures in an estimated DSGE model of the U.S. economy," Journal of Economic Dynamics and Control, Elsevier, vol. 32(8), pages 2512-2535, August.
    15. Milani, Fabio, 2007. "Expectations, learning and macroeconomic persistence," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2065-2082, October.
    16. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 797-814.
    17. Rochelle M. Edge & Michael T. Kiley & Jean-Philippe Laforte, 2010. "A comparison of forecast performance between Federal Reserve staff forecasts, simple reduced-form models, and a DSGE model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 720-754.
    18. Yongsung Chang & Taeyoung Doh & Frank Schorfheide, 2007. "Non-stationary Hours in a DSGE Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(6), pages 1357-1373, September.
    19. Clark, Todd E. & Kozicki, Sharon, 2005. "Estimating equilibrium real interest rates in real time," The North American Journal of Economics and Finance, Elsevier, vol. 16(3), pages 395-413, December.
    20. Frédérick Demers, 2003. "The Canadian Phillips Curve and Regime Shifting," Staff Working Papers 03-32, Bank of Canada.
    21. Rudebusch, Glenn D., 2002. "Term structure evidence on interest rate smoothing and monetary policy inertia," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1161-1187, September.
    22. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    23. Ali Dib & Mohamed Gammoudi & Kevin Moran, 2008. "Forecasting Canadian time series with the New Keynesian model," Canadian Journal of Economics, Canadian Economics Association, vol. 41(1), pages 138-165, February.
    24. Malin Adolfson & Michael K. Andersson & Jesper Lindé & Mattias Villani & Anders Vredin, 2007. "Modern Forecasting Models in Action: Improving Macroeconomic Analyses at Central Banks," International Journal of Central Banking, International Journal of Central Banking, vol. 3(4), pages 111-144, December.
    25. Paul Fenton & Stephen Murchison, 2006. "ToTEM: The Bank of Canada's New Projection and Policy-Analysis Model," Bank of Canada Review, Bank of Canada, vol. 2006(Autumn), pages 5-18.
    26. Stephen Murchison & Andrew Rennison, 2006. "ToTEM: The Bank of Canada's New Quarterly Projection Model," Technical Reports 97, Bank of Canada.
    27. Roberts John M., 2001. "Estimates of the Productivity Trend Using Time-Varying Parameter Techniques," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(1), pages 1-32, July.
    28. Rochelle M. Edge & Thomas Laubach & John C. Williams, 2003. "The responses of wages and prices to technology shocks," Working Paper Series 2003-21, Federal Reserve Bank of San Francisco.
    29. Russell Barnett, 2007. "Trend Labour Supply in Canada: Implications of Demographic Shifts and the Increasing Labour Force Attachment of Women," Bank of Canada Review, Bank of Canada, vol. 2007(Summer), pages 5-18.
    30. Julio Rotemberg & Michael Woodford, 1997. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy," NBER Chapters,in: NBER Macroeconomics Annual 1997, Volume 12, pages 297-361 National Bureau of Economic Research, Inc.
    31. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Econometric and statistical methods;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bca:bocawp:09-34. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.