Halkos, George and Kevork, Ilias (2002): Confidence intervals in stationary autocorrelated time series.

PDF
MPRA_paper_31840.pdf Download (295kB)  Preview 
Abstract
In this study we examine in covariance stationary time series the consequences of constructing confidence intervals for the population mean using the classical methodology based on the hypothesis of independence. As criteria we use the actual probability the confidence interval of the classical methodology to include the population mean (actual confidence level), and the ratio of the sampling error of the classical methodology over the corresponding actual one leading to equality between actual and nominal confidence levels. These criteria are computed analytically under different sample sizes, and for different autocorrelation structures. For the AR(1) case, we find significant differentiation in the values taken by the two criteria depending upon the structure and the degree of autocorrelation. In the case of MA(1), and especially for positive autocorrelation, we always find actual confidence levels lower than the corresponding nominal ones, while this differentiation between these two levels is much lower compared to the case of AR(1).
Item Type:  MPRA Paper 

Original Title:  Confidence intervals in stationary autocorrelated time series 
Language:  English 
Keywords:  Covariance stationary time series; Variance of the sample mean; Actual confidence level 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  31840 
Depositing User:  Nickolaos Tzeremes 
Date Deposited:  26 Jun 2011 10:23 
Last Modified:  26 Sep 2019 09:54 
References:  Adam, N.R., 1983. Achieving a confidence interval for parameters estimated by simulation. Management Science, Vol.29, pp. 856866. Conway, R.W., 1963. Some tactical problems in digital simulation. Management Science, Vol. 10, pp. 4761. Crane, M.A., and D.L. Iglehart, 1974a. Simulating stable stochastic systems, I: General multiserver queues. Journal of the Association for Computing Machinery, Vol. 21, pp.103113. Crane, M.A., and D.L. Iglehart, 1974b. Simulating stable stochastic systems, II: Markov chains. Journal of the Association for Computing Machinery, Vol. 21, pp.114123. Crane, M.A., and D.L. Iglehart, 1974c Simulating stable stochastic systems, III: Regenerative processes and discrete event simulations. Operations Research, Vol. 23, pp.3345. Crane, M.A., and D.L. Iglehart, 1975. Simulating stable stochastic systems, IV: Approximation techniques. Management Science, Vol. 21, pp.12151224. Ducket, S.D., and A.A.B. Pritsker, 1978. Examination of simulation output using spectral methods. Mathematical Computing Simulation, Vol. 20, pp. 5360. Efron, B., 1979. Bootstrap methods: Another look at the jackknife. The Annals of Statistics 7, 126 Efron, B. and Tibshirani, R., 1993. An Introduction to the Bootstrap. Chapman & Hall, New York. Fishman, G.S., 1971. Estimating the sample size in computing simulation experiments. Management Science, Vol. 18, pp. 2138. Fishman, G.S., 1973a. Statistical analysis for queuing simulations. Management Science, Vol. 20, pp. 363369. Fishman, G.S., 1973b. Concepts and methods in discrete event digital simulation. John Wiley and Sons, New York. Fishman, G.S., 1977. Achieving specific accuracy in simulation output analysis. Communication of the Association for computing Machinery, Vol. 20, pp. 310315. Fishman, G., 1978. Principles of Discrete Event Simulation. Wiley, New York. Fishman, G., 1999. Monte Carlo: Concepts, Algorithms, and Applications. Springer, New York. Gafarian, A.V., Ancker, C.J., JR, and T. Morisaku, 1978. Evaluation of commonly used rules for detecting steady state in computer simulation. Naval Research Logistics Quarterly, Vol. 25, pp. 511529. Gordon, G., 1969. System simulation. PrenticeHall, Englewood Cliffs N.j. Hall, P., Horowitz, J. and Jing, B.Y., 1995. On blocking rules for the bootstrap with dependent data. Biometrika 82, 561574. Heidelberger, P., and P.D. Welch, 1981a. A spectral method for confidence interval generation and run length control in simulations. Communications of the Association for Computing Machinery, Vol. 24, pp. 233245. Heidelberger, P., and P.D. Welch, 1981b. Adaptive spectral methods for simulation output analysis. IBM Journal of Research and Development, Vol. 25, pp. 860876. Heidelberger, P., and P.D. Welch, 1983. Simulation run length control in the presence of an initial transient. Operations Research, Vol. 31, pp. 11091144. Kevork, I.S, 1990. Confidence Interval Methods for Discrete Event Computer Simulation: Theoretical Properties and Practical Recommendations. Unpublished Ph.D. Thesis, University of London, London Kim, Y., Haddock, J. and Willemain, T., 1993a. The binary bootstrap: Inference with autocorrelated binary data. Communications in Statistics: Simulation and Computation 22, 205216. Kim, Y., Willemain, T., Haddock, J. and Runger, G., 1993b. The threshold bootstrap: A new approach to simulation output analysis. In: Evans, G.W., Mollaghasemi, M., Russell, E.C., Biles, W.E. (Eds.), Proceedings: 1993 Winter Simulation Conference, pp. 498502. Kelton, D.W. and A.M. Law, 1983. A new approach for dealing with the startup problem in discrete event simulation. Naval Research Logistics Quarterly, Vol. 30, pp. 6410658. Künsch, H., 1989. The jackknife and the bootstrap for general stationary observations. The Annals of Statistics 17, 12171241. Lavenberg, S., S., and C. H. Sauer, 1977. Sequential stopping rules for the regenerative method of simulation. IBM Journal of Research and Development, Vol. 21, pp. 545558. Law, A.M., 1983. Statistical analysis of simulation output data. Operations Research, Vol. 31, pp. 9831029. Law, A.M., and J.S. Carson, 1978. A sequential procedure for determining the length of a steady state simulation. Operation Research, Vol. 27, pp. 10111025. Law, A.M., and W.D. Kelton, 1982a. Confidence interval for steady state simulations: II. A survey of sequential procedures. Management Science, Vol. 28, pp. 560562. Law, A.M., and W.D. Kelton, 1982b. Simulation modelling and analysis. McGraw Hill, New York. Law, A.M., and W.D. Kelton, 1984. Confidence intervals for steady state simulations: I. A survey of fixed sample size procedures. Operation Research, Vol. 32, pp. 12211239. Law, A. and Kelton, W., 1991. Simulation Modeling and Analysis, second ed. McGrawHill, New York. Liu, R. and Singh, K., 1992. Moving blocks jackknife and bootstrap capture weak dependence. In: Le Page, R., Billard, L., (Eds.), Exploring the Limits of Bootstrap. Wiley, New York, pp.225248. Mechanic, H., and W. McKay, 1966. Confidence intervals for averages of dependent data in simulation II. Technical report 17202 IBM, Advanced Systems Development Division. Park, D. and Willemain, T., 1999. The threshold bootstrap and threshold jackknife. Computational Statistics and Data Analysis 31, 187202. Park, D.S., Kim, Y.B., Shin, K.I. and Willemain, T.R., 2001. Simulation output Analysis using the threshold bootstrap, European Journal of Operational Research 134, 1728. Quenouille, M., 1949. Approximation tests of correlation in time series. Journal of Royal Statistical Society Series B 11, 6884. Schriber, T.J., 1974. Simulation using GPSS. John Wiley and Sons, New York. Sargent, R.G., Kang, K. and Goldsman, D., 1992. An investigation of finitesample behavior of confidence interval estimators. Operation Research 40, 898913. Schruben, L., 1983. Confidence interval estimation using standardized time series. Operations Research 31, 10901108. Song, W.T., 1996. On the estimation of optimal batch sizes in the analysis of simulation output. European Journal of Operational Research 88, 304319. Song, W.T. and Schmeiser, B.W., 1995. Optimal meansquarederror batch sizes. Management Science 41, 111123. Tukey, J., 1958. Bias and confidence interval in not quite large samples (Abstract). The Annals of Mathematical Statistics 29, 614. Voss, P., Haddock, J. and Willemain, T., 1996. Estimating steady state mean from short transient simulations. In: Charnes, J.M., Morrice, D.M., Brunner, D.T. Welch, P.D., 1987. On the relationship between batch means, overlapping batch means and spectral estimation. Proceedings of the 1987 Winter Simulation Conference, pp. 320323. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/31840 