Abstract
This paper compares quasi Monte Carlo methods, in particularso-called (t, m, s)-nets, with classical Monte Carlo approaches forsimulating econometric time-series models. Quasi Monte Carlomethods have found successful application in many fields, such asphysics, image processing, and the evaluation of financederivatives. However, they are rarely used in econometrics. Here,we apply both traditional and quasi Monte Carlo simulation methodsto time-series models that typically arise in macroeconometrics.The numerical experiments demonstrate that quasi Monte Carlomethods outperform traditional ones for all models we investigate.
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Acworth, P., Broadie, M. and Glasserman, P. (1998). A comparison of some Monte Carlo and quasi-Monte Carlo methods 1996. In H. Niederreiter, P. Hellekalek, G. Larcher and P. Zinterhof (eds.), Lecture Notes in Statistics, 127, 1-18.
Bierbrauer, J. and Edel, Y. (1999). Some Good Binary (t, m, s)-Nets, preprint.
Bratley, P. and Fox, B.L. (1988). Sobol's quasirandom sequence generator for multivariate quadrature and optimization. ACM TOMS, 14(1), 88-100.
Caflisch, R.E. and Morokoff, W. (1996). Valuation of mortage-backed securities using the quasi-Monte Carlo method. Technical Report. Department of Mathematics UCLA.
Clayman, A.T., Lawrence, K.M., Mullen, G.L., Niederreiter, H. and Sloane, N.J.A. (2000). Updated tables of parameters of (t, m, s)-nets. Journal of Combinatorial Designs, p. forthcoming.
Ericcsson, N.R. and Marquez, J. (1998). A framework for economic forecasting. Econometrics Journal, 1, C228-C266.
Fang, K.-T., Ma, C.-X., and Winker, P. (2000). Centered l2-discrepancy of random sampling and latin hypercube design, and construction of uniform designs. Mathematical Computation, p. forthcoming.
Franz, W., Göggelmann, K., Schellhorn, M. and Winker, P. (2000). Quasi-Monte Carlo methods in stochastic simulations. Empirical Economics 25, 247-259.
Gentle, J.E. (1998). Random Number Generation and Monte Carlo Methods. Springer, New York.
Halton, J.H. (1960). On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik, 2, 84-90.
Hellekalek, P. (1998). On the assessment of random and quasi-random point sets. In P. Hellekalek and G. Larcher (eds.), Random and Quasi-Random Point Sets. Lecture Notes in Statistics, 138, 49-108. Springer, New York.
Hickernell, F.J. (1998). Ageneralized discrepancy and quadrature error bound. Mathematics of Computation, 67, 299-322.
Larcher and Traunfellner (1994). On the numerical integration of walsh series by number-theoretic methods. Math. Comp., 63, 277-291.
L'Ecuyer, P. and Hellekalek, P. (1998). Random number generators: Selection criteria and testing. In P. Hellekalek and G. Larcher (eds.), Random and Quasi-Random Point Sets. Lecture Notes in Statistics, 138, 223-265. Springer, New York.
Li, J. and Mullen, G. (2000). Parallel computing of a quasi-Monte Carlo algorithm for valuting derivatives. Parallel Computing, 26(5), 641-653.
Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia, PE.
Owen, A.B. (1997). Monte Carlo variance of scrambled net quadrature. SIAM Journal of Numerical Analysis, 34, 1884-1910.
Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992). Numerical Recipes in Fortran 77., 2nd edn. Cambridge University Press, New York, NY.
Ripley, B.D. (1987). Stochastic Simulation. Wiley, New York.
Winker, P. (1999). Quasi-Monte Carlo Policy simulations in a macroeconometric disequilibrium model. In Proceedings of the 14th World Congress International Federation of Automatic Control. Elsevier, Oxford, pp. 45-50.
Winker, P. and Fang, K.-T. (1997). Application of threshold accepting to the evaluation of the discrepancy of a set of points. SIAM Journal on Numerical Analysis, 34(5), 2028-2042.
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Li, J.X., Winker, P. Time Series Simulation with Quasi Monte Carlo Methods. Computational Economics 21, 23–43 (2003). https://doi.org/10.1023/A:1022289509702
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DOI: https://doi.org/10.1023/A:1022289509702