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Abstrakty
The problem of biased time series mathematical model parameter estimates is well known to be insurmountable. When used to predict future values by extrapolation, even a de minimis bias will eventually grow into a large bias, with misleading results. This paper elucidates how combining antithetic time series solves this baffling problem of bias in the fitted and forecast values by dynamic bias cancellation. Instead of growing to infinity, the average error can converge to a constant.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
57--68
Opis fizyczny
Bibliogr. 21 poz., rys.
Twórcy
autor
- SBI, Florida A&M University and Department of Scientific Computing, Florida State University, Tallahassee, Fl., USA
Bibliografia
- [1] CHAITIN G.J., Randomness and mathematical proof, Sci. Amer., 1975, 232, 47.
- [2] CHATFIELD C., PROTHERO D.L., Box–Jenkins seasonal forecasting: problems in a case study, J. Royal Stat. Soc. (A), 1973, 136, 295.
- [3] CLEMEN R.T., Combining forecasts. A review and annotated bibliography, Int. J. Forecastng, 1989, 5, 559.
- [4] COPAS J.B., Monte Carlo results for estimation in a stable Markov time series, J. Royal Stat. Soc. (A), 1966, 129, 110.
- [5] EINSTEIN A., PODOLSKY B., ROSEN N., Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev., 1935, 47, 777.
- [6] FOOTE R., Mathematics and complex systems, Science, 2007, 318, 410.
- [7] FOURCAST, Application program, EMC, Inc., Version 2010.12, http://www.fourcast.net/fourcast. File: CompanyX.zip., 2010,
- [8] GRILICHES Z., A note on serial correlation bias in estimates of distributed lags, Econometrica, 1961, 29, 65.
- [9] HAMMERSLEY J.M., MORTON K.W., A new Monte Carlo technique. Antithetic variates, Math. Proc. Cambridge Philosophical Society, 1956, 52, 449.
- [10] HEISENBERG W., Über den anschaulichen Inhalt der Quanten theoretischen Kinematik und Mechanik, Z. Phys., 1927, 43, 172.
- [11] KENDALL M.G., Note on bias in the estimation of autocorrelation, Biometrika, 1954, 41, 403.
- [12] KLIEJNEN J.P.C., Antithetic variates, common random numbers and optimal computer time allocation in simulation, Manage. Sci., 1975, 21, 1176.
- [13] KOLMOGOROV A.N., Three approaches to the definition of the quantity of information, Problems Inf. Trans., 1965, 1, 1.
- [14] KOUTSOYIANNIS D., A random walk on water, Hydr. Earth Syst. Sci., 2010, 14, 585.
- [15] LI B., NYCHKA D.W., AMMANN C.M., The value of multi-proxy reconstruction of past climate, J. Am. Stat. Assoc., 2010, 105, 883.
- [16] MARRIOTT F.H.C., POPE J.A., Bias in the estimation of autocorrelations, Biometrika, 1954, 41, 390.
- [17] MyPulse Smart Monitors, Inc., Version 2010.12, http://mypulsemonitor.com/downloadsoftware. html., 2010. D.
- [18] NGNEPIEBA P., RIDLEY A.D., General theory of antithetic time series, J. Appl. Math. Phys., 2015, 3 (12), 1726.
- [19] POPPER K., Quantum Theory and the Schism in Physics. Routledge, London 1992, http://www.scirp. org/journal/jamp http://dx.doi.org/10.4236/jamp.2015.312197
- [20] RIDLEY A.D., Optimal antithetic weights for lognormal time series forecasting, Comput. Oper. Res., 1999, 26, 189.
- [21] RIDLEY A.D., NGNEPIEBA P., Antithetic time series analysis and the CompanyX data, J. Royal Stat. Soc. (A), 2014 (1), 177, 83.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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