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Publications de l'Institut Mathematique 2010, vol. 88, br. 102, str. 87-98
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AR(1) time series with approximated Beta marginal
(naslov ne postoji na srpskom)
Sažetak(ne postoji na srpskom) We consider the AR(1) time series model Xt - βXt-1 = ξt, β-p ∈ N \ {1}, when Xt has Beta distribution B(p, q), p ∈ (0, 1], q > 1. Special attention is given to the case p = 1 when the marginal distribution is approximated by the power law distribution closely connected with the Kumaraswamy distribution Kum(p, q), p ∈ (0, 1], q > 1. Using the Laplace transform technique, we prove that for p = 1 the distribution of the innovation process is uniform discrete. For p ∈ (0, 1), the innovation process has a continuous distribution. We also consider estimation issues of the model.
Ključne rečiBeta distribution; Kumaraswamy distribution; approximated Beta distribution; Kummer function of the first kind; first order autoregressive model
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Reference
|
|
 
|
Bell, C.B., Smith, E.P. (1986) Infrence for non-negative autoregressive schemes. Communications in Statistics - Theory and Methods, 15(8): 2267-2293
|
|
|
Billingsley, P. (1961) The Lindeberg-Levy theorem for martingales. Proc. Amer. Math. Soc., 12, 788-792
|
|
6
|
Chernick, M.R. (1981) A limit theorem for the maximum of autoregressive processes with uniform marginal distributions. Annals of Probability, 9, 1, 145-149
|
|
|
Demidovich, B.P., Maron, I.A. (1976) Computational mathematics. Moscow: Mir
|
|
10
|
Development Core Team (2009) A language and environment for statistical computing. Vienna: Foundation for Statistical Computing
|
|
|
Đorić, D., Jevremović, V., Mališić, J., Nikolić-Đorić, E. (2007) Atlas of Distributions. Beograd: Građevinski fakultet
|
|
|
Fletcher, S., Ponnambalam, K. (1996) Estimation of reservoir yield and storage distribution using moments analysis. Journal of Hydrology, 182(1-4): 259-275
|
|
1
|
Gaver, D.P., Lewis, P.A.W. (1980) First-order autoregressive gamma sequences and point processes. Adv. in Appl Probab, 12, 727-745
|
|
8
|
Hamilton, J.D. (1994) Time series analysis. Princeton, NJ: Princeton University Press
|
|
|
Humbert, P. (1945) Nouvelles correspondances symboliques. Bull. Sci. Math., 69,: 121
|
|
2
|
Jevremović, V. (1990) Two examples of nonlinear processes with a mixed exponential marginal distribution. Statistics and Probability Letters, 10, 3, 221-224
|
|
|
Jones, M. (2009) Kumaraswamy's distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6(1): 70-81
|
|
|
Kumaraswamy, P. (1980) A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46(1-2): 79-88
|
|
|
Lawrence, A.J., Lewis, P.A.W. (1980) A new autoregressive time series model in exponential variables (NEAR(1)). Adv. Appl. Probab, 13, 826-845
|
|
|
Lawrence, A.J. (1980) The mixed exponential solution to the first-order autoregressive model. J Appl. Probab., 17(2): 546
|
|
|
Mališić, J. (1986) On exponential autoregressive time series models. u: Bauer P. (ur.) Mathematical Statistics and Probability Theory, Dordrecht: Reidel, str. 147-153, vol. B
|
|
1
|
Mckenzie, E. (1985) An autoregressive process for beta random variables. Management Science, 31, 988-997
|
|
|
Mikusinski, J. (1959) On the function whose Laplace transform is exp(−sα), 0 < α < 1. Studia Math, 18 (1959), str. 191-198
|
|
|
Nadarajah, S. (2007) Probability models for unit hydrograph derivation. Journal of Hydrology, 344(3-4): 185-189
|
|
|
Nadarajah, S. (2008) On the distribution of Kumaraswamy. Journal of Hydrology, 348(3-4): 568-569
|
|
|
Novković, M. (1997) Autoregressive time series models with gamma and laplace distribution. Belgrade: Faculty of Mathematics, MSci Thesis
|
|
|
Pollard, H. (1946) The representation of exp(−xλ) as a Laplace integral. Bull. Am. Math. Soc, 52, 908-910
|
|
|
Popović, B.V. (2009) Time series models with marginal distribution from pearson system of distributions. Belgrade: Faculty of Mathematics, MSci Thesis
|
|
1
|
Pourahmadi, M. (1986) On stationarity of the solution of a doubly stochastic model. J Time Ser. Anal., 7, 2, 123-131
|
|
|
Pourahmadi, M. (1988) Stationarity of the solution of Xt = AtXt−1 + ξt and analysis of nongaussian dependent random variables. J Time Ser. Anal., 9(3): 225
|
|
|
Ridout, M.S. (2009) Generating random numbers from a distribution specified by its Laplace transform. Statistics and Computing, 19(4): 439-450
|
|
|
Ristić, M.M., Popović, B.C. (2002) The uniform autoregressive process of the second order (UAR(2)). Statistics & probability letters, vol. 57, br. 2, str. 113-119
|
|
2
|
Sim, C.H. (1986) Simulation of Weibull and Gamma autoregressive stationary process. Commun. Stat. -Simul. Computat, 15, 1141-1146
|
|
|
Stanković, B. (1970) On the function of E.M. Wright. Publ. Inst. Math., Nouv. Sér., 10(24) , 113-124
|
|
|
|
|