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1Academic Journal
المؤلفون: Morvai, Gusztáv, Weiss, Benjamin
مصطلحات موضوعية: keyword:nonparametric estimation, keyword:stationary processes, msc:60G10, msc:60G25, msc:62G05
وصف الملف: application/pdf
Relation: mr:MR4332885; zbl:Zbl 07478632; reference:[1] Algoet, P.: The strong law of large numbers for sequential decisions under uncertainty.IEEE Trans. Inform. Theory 40 (1994), 609-633.; reference:[2] Algoet, P.: Universal schemes for learning the best nonlinear predictor given the infinite past and side information.IEEE Trans. Inform. Theory 45 (1999), 1165-1185. Zbl 0959.62078; reference:[3] Bailey, D. H.: Sequential Schemes for Classifying and Predicting Ergodic Processes.Ph.D. Thesis, Stanford University, 1976.; reference:[4] Csiszár, I., Talata, Zs.: Context tree estimation for not necessarily finite memory processes via BIC and MDL.IEEE Trans. Inform. Theory 52 (2006), 3, 1007-1016.; reference:[5] Györfi, L., Morvai, G., Yakowitz, S.: Limits to consistent on-line forecasting for ergodic time series.IEEE Trans. Inform. Theory 44 (1998), 886-892. Zbl 0899.62122, MR 1607704; reference:[6] Hoeffding, W.: Probability inequalities for sums of bounded random variables.J. Amer. Statist. Assoc. 58 (1963), 13-30. 10.1080/01621459.1963.10500830; reference:[7] Kalikow, S., Katznelson, Y., Weiss, B.: Finitarily deterministic generators for zero entropy systems.Israel J. Math. 79 (1992), 33-45.; reference:[8] Maker, Ph. T.: The ergodic theorem for a sequence of functions.Duke Math. J. 6 (1940), 27-30.; reference:[9] Morvai, G.: Guessing the output of a stationary binary time series.In: Foundations of Statistical Inference (Y. Haitovsky, H. R.Lerche, and Y. Ritov, eds.), Physika-Verlag, pp. 207-215, 2003.; reference:[10] Morvai, G., Yakowitz, S., Algoet, P.: Weakly convergent nonparametric forecasting of stationary time series.IEEE Trans. Inform. Theory 43 (1997), 483-498.; reference:[11] Morvai, G., Weiss, B.: Forecasting for stationary binary time series.Acta Appl. Math. 79 (2003), 25-34.; reference:[12] Morvai, G., Weiss, B.: Intermittent estimation of stationary time series.Test 13 (2004), 525-542.; reference:[13] Morvai, G., Weiss, B.: Inferring the conditional mean.Theory Stochast. Process. 11 (2005), 1-2, 112-120. Zbl 1164.62382; reference:[14] Morvai, G., Weiss, B.: Prediction for discrete time series.Probab. Theory Related Fields 132 (2005), 1-12.; reference:[15] Morvai, G., Weiss, B.: Limitations on intermittent forecasting.Statist. Probab. Lett. 72 (2005), 285-290.; reference:[16] Morvai, G., Weiss, B.: On classifying processes.Bernoulli 11 (2005), 523-532.; reference:[17] Morvai, G., Weiss, B.: Order estimation of Markov chains.IEEE Trans. Inform. Theory 51 (2005), 1496-1497.; reference:[18] Morvai, G., Weiss, B.: Forward estimation for ergodic time series.Ann. I. H. Poincaré Probab. Statist. 41 (2005), 859-870.; reference:[19] Morvai, G., Weiss, B.: On estimating the memory for finitarily Markovian processes.Ann. I. H. Poincaré PR 43 (2007), 15-30.; reference:[20] Morvai, G., Weiss, B.: On sequential estimation and prediction for discrete time series.Stoch. Dyn. 7 (2007), 4, 417-437. Zbl 1255.62228; reference:[21] Morvai, G., Weiss, B.: Estimating the lengths of memory words.IEEE Trans. Inform. Theory 54 (2008), 8, 3804-3807. Zbl 1329.60095; reference:[22] Morvai, G., Weiss, B.: On universal estimates for binary renewal processes.Annals Appl. Probab. 18 (2008), 5, 1970-1992. Zbl 1158.62053; reference:[23] Morvai, G., Weiss, B.: Estimating the residual waiting time for binary stationary time series.Proc. ITW2009, Volos 2009, pp. 67-70.; reference:[24] Morvai, G., Weiss, B.: A note on prediction for discrete time series.Kybernetika 48 (2012), 4, 809-823.; reference:[25] Morvai, G., Weiss, B.: Universal tests for memory words.IEEE Trans. Inform. Theory 59 (2013), 6873-6879.; reference:[26] Morvai, G., Weiss, B.: Inferring the residual waiting time for binary stationary time series.Kybernetika 50 (2014), 869-882. Zbl 1308.62067; reference:[27] Morvai, G., Weiss, B.: A versatile scheme for predicting renewal times.Kybernetika 52 (2016), 348-358.; reference:[28] Morvai, G., Weiss, B.: Universal rates for estimating the residual waiting time in an intermittent way.Kybernetika 56, (2020), 4, 601-616.; reference:[29] Morvai, G., Weiss, B.: On universal algorithms for classifying and predicting stationary processes.Probab. Surveys 18 (2021), 77-131. 10.1214/20-PS345; reference:[30] Morvai, G., Weiss, B.: Consistency, integrability and asymptotic normality for some intermittent estimators.ALEA, Lat. Am. J. Probab. Math. Stat. 18 (2021), 1643-1667.; reference:[31] Ryabko, B. Ya.: Prediction of random sequences and universal coding.Problems Inform. Trans. 24 (1988), 87-96. Zbl 0666.94009; reference:[32] Ryabko, D.: Asymptotic Nonparametric Statistical Analysis of Stationary Time Series.Springer, Cham 2019.; reference:[33] Shields, P. C.: The Ergodic Theory of Discrete Sample Paths.In: Graduate Studies in Mathematics. American Mathematical Society 13, Providence 1996. Zbl 0879.28031; reference:[34] Suzuki, J.: Universal prediction and universal coding.Systems Computers Japan 34 (2003), 6, 1-11.; reference:[35] Takahashi, H.: Computational limits to nonparametric estimation for ergodic processes.IEEE Trans. Inform. Theory 57 (2011), 6995-6999.
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2Academic Journal
المؤلفون: Morvai, Gusztáv, Weiss, Benjamin
مصطلحات موضوعية: keyword:nonparametric estimation, keyword:continuous time stationary processes, msc:60G10, msc:60G25, msc:62G05
وصف الملف: application/pdf
Relation: mr:MR4131737; zbl:Zbl 07250731; reference:[1] Algoet, P.: Universal schemes for prediction, gambling and portfolio selection.Ann. Probab. 20 (1992), 901-941. MR 1159579, 10.1214/aop/1176989811; reference:[2] Algoet, P.: The strong law of large numbers for sequential decisions under uncertainty.IEEE Trans. Inform. Theory 40 (1994), 609-633. MR 1295308, 10.1109/18.335876; reference:[3] Algoet, P.: Universal schemes for learning the best nonlinear predictor given the infinite past and side information.IEEE Trans. Inform. Theory 45 (1999), 1165-1185. Zbl 0959.62078, MR 1686250, 10.1109/18.761258; reference:[4] Bailey, D.: Sequential Schemes for Classifying and Predicting Ergodic Processes.Ph.D. Thesis, Stanford University 1976. MR 2626644; reference:[5] Breiman, L.: The individual ergodic theorem of information theory,.Ann. Math. Statist. 28 (1957), 809-811. MR 0092710, 10.1214/aoms/1177706899; reference:[6] Cover, T.: Open problems in information theory.In: 1975 IEEE-USSR Joint Workshop on Information Theory 1975, pp. 35-36. MR 0469507; reference:[7] Chow, Y. S., Teicher, H.: Probability Theory: Independence, Interchangeability, Martingales. Second edition.Springer-Verlag, New York 1978. MR 0513230; reference:[8] Doob, J. L.: Stochastic Processes.Wiley, 1990 MR 1038526; reference:[9] Elton, J.: A law of large numbers for identically distributed martingale differences.Ann. Probab. 9 (1981), 405-412. MR 0614626, 10.1214/aop/1176994414; reference:[10] Györfi, L., Kohler, M., Krzyzak, A., Walk, H.: A Distribution-Free Theory of Nonparametric Regression.Springer Series in Statistics, Springer-Verlag, New York 2002. MR 1920390, 10.1007/b97848; reference:[11] Györfi, L., Morvai, G., Yakowitz, S.: Limits to consistent on-line forecasting for ergodic time series.IEEE Trans. Inform. Theory 44 (1998), 886-892. Zbl 0899.62122, MR 1607704, 10.1109/18.661540; reference:[12] Györfi, L., Ottucsák, Gy.: Sequential prediction of unbounded stationary time series.IEEE Trans. Inform. Theory 53 (2007), 1866-1872. MR 2317147, 10.1109/tit.2007.894660; reference:[13] Györfi, L., Ottucsák, Gy., Walk, H.: Machine Learning for Financial Engineering.Imperial College Press, London 2012. 10.1142/p818; reference:[14] Hall, P., Heyde, C. C.: Martingale Limit Theory and Its Application.Academic Prress, 1975. MR 0624435; reference:[15] Maker, Ph. T.: The ergodic theorem for a sequence of functions.Duke Math. J. 6 (1940), 27-30. MR 0002028, 10.1215/s0012-7094-40-00602-0; reference:[16] Morvai, G.: Estimation of Conditional Distribution for Stationary Time Series.Ph.D. Thesis, Technical University of Budapest 1994.; reference:[17] Morvai, G., Yakowitz, S., Györfi, L.: Nonparametric inferences for ergodic, stationary time series.Ann. Statist. 24 (1996), 370-379. MR 1389896, 10.1214/aos/1033066215; reference:[18] Morvai, G., Weiss, B.: Nonparametric sequential prediction for stationary processes.Ann. Prob. 39 (2011), 1137-1160. MR 2789586, 10.1214/10-aop576; reference:[19] Neveu, J.: Mathematical Foundations of the Calculus of Probability.Holden-Day, 1965. MR 0198505; reference:[20] Ornstein, D.: Guessing the next output of a stationary process.Israel J. of Math. 30 (1978), 292-296. MR 0508271, 10.1007/bf02761077; reference:[21] Ryabko, B.: Prediction of random sequences and universal coding.Probl. Inform. Trans. 24 (1988), 87-96. Zbl 0666.94009, MR 0955983; reference:[22] Scarpellini, B.: Predicting the future of functions on flows.Math. Systems Theory 12 (1979), 281-296. MR 0529563, 10.1007/bf01776579; reference:[23] Scarpellini, B.: Entropy and nonlinear prediction.Probab. Theory Related Fields 50 (1079, 2, 165-178. MR 0551610, 10.1007/bf00533638; reference:[24] Scarpellini, B.: Conditional expectations of stationary processes.Z. Wahrsch. Verw. Gebiete 56 (1981), 4, 427-441. MR 0621658, 10.1007/bf00531426; reference:[25] Shields, P. C.: Cutting and stacking: a method for constructing stationary processes.IEEE Trans. Inform. Theory 37 (1991), 1605-1614. MR 1134300, 10.1109/18.104321; reference:[26] Shiryayev, A. N.: Probability.Springer-Verlag, New York 1984. MR 0737192; reference:[27] Weiss, B.: Single Orbit Dynamics.American Mathematical Society, 2000. MR 1727510
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3Academic Journal
المؤلفون: Aliat, Billel, Hamdi, Fayçal
مصطلحات موضوعية: keyword:Markov-switching models, keyword:periodic $GARCH$ models, keyword:periodic stationarity, keyword:higher-order moments, keyword:Markov-switching $PGARCH$ models, keyword:$GMM$ method, msc:60G10, msc:62M10
وصف الملف: application/pdf
Relation: mr:MR4077137; zbl:Zbl 07217219; reference:[1] A., Aknouche,, M., Bentarzi,: On the existence of higher-order moments for periodic $GARCH$ models.Statist. Probab. Lett. 78 (2008), 3262-3268. MR 2479488, 10.1016/j.spl.2008.06.010; reference:[2] A., Aknouche,, A., Bibi,: Quasi-maximum likelihood estimation of periodic $GARCH$ and periodic $ARMA$-$GARCH$ processes.J. Time Series Anal. 28 (2009), 19-46. MR 2488634, 10.1016/j.spl.2008.06.010; reference:[3] A., Aknouche,, H., Guerbyenne,: Periodic stationarity of random coefficient periodic autoregressions.Statist. Probab. Lett. 79 (2009), 990-996. MR 2509491, 10.1016/j.spl.2008.12.012; reference:[4] B., Aliat,, F., Hamdi,: On markov-switching periodic $ARMA$ models.Comm. Statist. Theory Methods 47 (2018), 344-364. MR 3765077, 10.1080/03610926.2017.1303734; reference:[5] M., Augustyniak,: Maximum likelihood estimation of the Markov-switching $GARCH$ model.Comput. Statist. Data Anal. 76 (2014), 61-75. MR 3209427, 10.1016/j.csda.2013.01.026; reference:[6] M., Augustyniak,, M., Boudreault,, M., Morales,: Maximum likelihood estimation of the Markov-switching GARCH model based on a general collapsing procedure.Methodol. Comput. Appl. Probab. 20 (2018), 165-188. MR 3760343, 10.1007/s11009-016-9541-4; reference:[7] L., Bauwens,, A., Preminger,, K., Rombouts, J. V.: Theory and inference for Markov switching $GARCH$ model.Econometr. J. 13 (2010), 218-244. MR 2722883, 10.1111/j.1368-423x.2009.00307.x; reference:[8] M., Bentarzi,, F., Hamdi,: Mixture periodic autoregressive conditional heteroskedastic models.Comput. Statist. Data Anal. 53 (2008), 1-16. MR 2528588, 10.1016/j.csda.2008.06.019; reference:[9] M., Bentarzi,, F., Hamdi,: Mixture periodic autoregression with aeriodic $ARCH$ errors.Adv. Appl. Statist. 8 (2008), 219-46. MR 2445517; reference:[10] A., Bibi,, A., Aknouche,: On periodic $GARCH$ processes: Stationarity Statist. 17 (2008), 305-316. MR 2483459, 10.3103/s1066530708040029; reference:[11] A., Bibi,, I., Lescheb,: Strong consistency and asymptotic normality of least squares estimators for $PGARCH$ and $PARMA$-$PGARCH$ models.Statist. Probab. Lett. 80 (2010), 1532-1542. MR 2669757, 10.1016/j.spl.2010.06.007; reference:[12] A., Bibi,, I., Lescheb,: A conditional least squares approach to $PGARCH$ and $PARMA$-$PGARCH$ time series estimation.Comptes Rendus Math. 348 (2010), 1211-1216. MR 2738929, 10.1016/j.crma.2010.10.019; reference:[13] A., Bibi,, I., Lescheb,: Estimation and asymptotic properties in periodic $GARCH(1,1)$ models.Comm. Statist. Theory Methods 42 (2013), 3497-3513. MR 3170947, 10.1080/03610926.2011.633201; reference:[14] M., Billio,, R., Casarin,, A., Osuntuyi,: Efficient Gibbs sampling for Markov switching $GARCH$ models.Comput. Statist. Data Anal. 100 (2016), 37-57. MR 3505789, 10.1016/j.csda.2014.04.011; reference:[15] T., Bollerslev,: Generalized autoregressive conditional heteroskedasticity.J. Econometr. 31 (1986), 307-327. MR 0853051, 10.1016/0304-4076(86)90063-1; reference:[16] T., Bollerslev,, E., Ghysels,: Periodic autoregressive conditional heteroskedasticity.J. Business Econom. Statist. 14 (1996), 139-152. 10.2307/1392425; reference:[17] P., Bougerol,, N., Picard,: Strict stationarity of generalized autoregressive processes.Ann. Probab. 20 (1992), 1714-1730. MR 1188039, 10.1214/aop/1176989526; reference:[18] J., Cai,: A Markov model of Switching-regime $ARCH$.J. Business Econom. Statist. 12 (1994), 309-316. 10.2307/1392087; reference:[19] C., Francq,, M., Roussignol,, M., Zako\"ıan, J.: Conditional heteroskedasticity driven by hidden Markov chains.J. Time Ser. Anal. 22 (2001), 197-220. MR 1820776, 10.1111/1467-9892.00219; reference:[20] C., Francq,, M., Zako\"ıan, J.: The $L^{2}$-structures of standard and switching-regime $GARCH$ models.Stoch. Process. Appl. 115 (2005), 1557-1582. MR 2158020; reference:[21] C., Francq,, M., Zako\"ıan, J.: Deriving the autocovariances of powers of Markov-switching $GARCH$ models with applications to statistical inference.Computat. Statist. Data Anal. 52 (2008), 3027-3046. MR 2424774, 10.1016/j.csda.2007.08.003; reference:[22] H., Franses, P., R., Paap,: Modeling changing day-of-the-week seasonality in stock returns and volatility.Appl. Financ. Econom. 52 (2000), 3027-3046.; reference:[23] G., Gladyshev, E.: Periodically correlated random sequences.Doklady Akademii Nauk SSSR 137 (1961), 1026-1029. MR 0126873; reference:[24] F., Gray, S.: Modeling the conditional distribution of interest rates as a regime-switching process.J. Financ. Econom. 42 (1996), 27-62. 10.1016/0304-405x(96)00875-6; reference:[25] M., Haas,, S., Paolella, M.: Mixture and regime-switching $GARCH$ models.In: Handbook of Volatility Models and their Applications 2012, pp. 71-102. MR 3307112, 10.1002/9781118272039.ch3; reference:[26] M., Haas,, S., Mittnik,, S., Paolella, M.: A new approach to Markov-switching $GARCH$ models.J. Financ. Econometr. 2 (2004), 493-530. 10.1093/jjfinec/nbh020; reference:[27] F., Hamdi,, S., Souam,: Mixture periodic $GARCH $ models: Applications to exchange rate modeling.In: Modeling, Simulation and Applied Optimization (ICMSAO), 5th International Conference on IEEE, 2013. 10.1109/icmsao.2013.6552570; reference:[28] F., Hamdi,, S., Souam,: Mixture periodic $GARCH$ models: theory and applications.Empir. Econom. 55 (2018), 1925-1956. 10.1007/s00181-017-1348-9; reference:[29] D., Hamilton, J.: A new approach to the economie analysis of nonstationary time series and the business cycle.Econometrica 57 (1989), 357-384. MR 0996941, 10.2307/1912559; reference:[30] D., Hamilton, J., R., Susmel,: Autoregressive condiational heteroskedasticity and changes in regime.J. 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Rev. 28 (1987), 3, 777-787. MR 0912975, 10.2307/2526578; reference:[37] N., Regnard,, M., Zako\"ıan, J.: Structure and estimation of a class of nonstationary yet nonexplosive $GARCH$ models.J. Time Series Anal. 31 (2010), 348-364. MR 2724515, 10.1111/j.1467-9892.2010.00669.x
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4Academic Journal
المؤلفون: Morita, Takehiko
مصطلحات موضوعية: keyword:strictly stationary process, keyword:martingale-coboundary decomposition, msc:28D05, msc:60G10, msc:60G42
وصف الملف: application/pdf
Relation: mr:MR4034441; zbl:Zbl 07144903; reference:[1] Billingsley P.: Ergodic Theory and Information.John Wiley & Sons, New York, 1965. MR 0192027; reference:[2] Hall P., Heyde C. C.: Martingale Limit Theory and Its Application.Probability and Mathematical Statistics, Academic Press, New York, 1980. Zbl 0462.60045, MR 0624435; reference:[3] Samek P., Volný D.: Uniqueness of a martingale-coboundary decomposition of a stationary processes.Comment. Math. Univ. Carolin. 33 (1992), no. 1, 113–119. MR 1173752; reference:[4] Volný D.: Approximating martingales and the central limit theorem for strictly stationary processes.Stochastic Process. Appl. 44 (1993), no. 1, 41–74. MR 1198662, 10.1016/0304-4149(93)90037-5; reference:[5] Walters P.: An Introduction to Ergodic Theory.Graduate Texts in Mathematics, 79, Springer, New York, 1982. Zbl 0958.28011, MR 0648108, 10.1007/978-1-4612-5775-2
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5Academic Journal
المؤلفون: Magiera, Wladyslaw, Libal, Urszula, Wielgus, Agnieszka
مصطلحات موضوعية: keyword:covariance matrix, keyword:higher-order statistics, keyword:adaptive, keyword:nonlinear, msc:15B05, msc:15B51, msc:60G10, msc:60G15, msc:93E24
وصف الملف: application/pdf
Relation: mr:MR3893125; zbl:Zbl 07031749; reference:[1] Dewilde, P.: Stochastic modelling with orthogonal filters.In: Outils et modeles mathematiques pour l'automatique, l'analyse de systemes et le traitement du signal, CNRS (ed.), Paris 1982, pp. 331-398. MR 0782526; reference:[2] Lee, D. T. L., Morf, M., Friedlander, B.: Recursive least-squares ladder estimation algorithms.IEEE Trans. Circuit Systems CAS 28 (1981), 467-481. MR 0629997, 10.1109/tcs.1981.1085020; reference:[3] Jurečková, J.: Regression quantiles and trimmed least squares estimator under a general design.Kybernetika 20 (1984), 5, 345-357. Zbl 0561.62027, MR 0776325; reference:[4] Levinson, N.: The Wiener RMS error criterion in filter design and prediction.J. Math. Physics 25 (1947), 261-278. MR 0019257, 10.1002/sapm1946251261; reference:[5] Mandl, P., Duncan, T. E., Pasik-Duncan, B.: On the consistency of a least squares identification procedure.Kybernetika 24 (1988), 5, 340-346. MR 0970211; reference:[6] Mendel, J. M.: Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications.Proc. IEEE 79 (1991), 3, 278-305. 10.1109/5.75086; reference:[7] Pázman, A.: Probability distribution of the multivariate nonlinear least squares estimates.Kybernetika 20 (1984), 3, 209-230. MR 0763647; reference:[8] Pronzato, L., Pázman, A.: Second-order approximation of the entropy in nonlinear least-squares estimation.Kybernetika 30 (1994), 2, 187-198. MR 1283494; reference:[9] Schur, I.: Methods in 0perator Theory and Signal Processing.Operator Theory: Advances and Applications 18, Springer-Verlag 1086. 10.1007/978-3-0348-5483-2; reference:[10] Stellakis, H. M., Manolakos, E. M.: Adaptive computation of higher order moments and its systolic realization.Int. J. Adaptive Control Signal Process. 10 (1996), 283-302. 10.1002/(sici)1099-1115(199603)10:2/33.3.co;2-2; reference:[11] Wiener, N.: Nonlinear Problems in Random Theory.MIT Press, 1958. MR 0100912; reference:[12] Zarzycki, J.: Multidimensional nonlinear Schur parametrization of non-gaussian stochastic signals - Part one: Statement of the problem.MDSSP J. 15 (2004), 3, 217-241. MR 2075150, 10.1023/b:mult.0000028007.05748.48
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6Academic Journal
المؤلفون: Morvai, Gusztáv, Weiss, Benjamin
مصطلحات موضوعية: keyword:nonparametric estimation, keyword:stationary processes, msc:60G10, msc:60G25, msc:62G05
وصف الملف: application/pdf
Relation: mr:MR3532511; zbl:Zbl 06644299; reference:[1] Bahr, B. von, Esseen, C. G.: Inequalities for the $r$th Absolute Moment of a Sum of Random Variables, $1\leq r \leq 2$.Annals Math. Statist. 36 (1965), 299-303. MR 0170407, 10.1214/aoms/1177700291; reference:[2] Csiszár, I., Shields, P.: The consistency of the BIC Markov order estimator.Annals Statist. 28 (2000), 1601-1619. Zbl 1105.62311, MR 1835033, 10.1214/aos/1015957472; reference:[3] Csiszár, I.: Large-scale typicality of Markov sample paths and consistency of MDL order estimators.IEEE Trans. Inform. Theory 48 (2002), 1616-1628. Zbl 1060.62092, MR 1909476, 10.1109/tit.2002.1003842; reference:[4] Feller, W.: An Introduction to Probability Theory and its Applications Vol. I. Third edition.John Wiley and Sons, New York - London - Sydney 1968. MR 0228020; reference:[5] Ghahramani, S.: Fundamentals of Probability with Stochastic Processes. Third edition.Pearson Prentice Hall, Upper Saddle River NJ 2005.; reference:[6] Morvai, G., Weiss, B.: Order estimation of Markov chains.IEEE Trans. Inform. Theory 51 (2005), 1496-1497. MR 2241507, 10.1109/tit.2005.844093; reference:[7] Morvai, G., Weiss, B.: Estimating the lengths of memory words.IEEE Trans. Inform. Theory 54 (2008), 8, 3804-3807. Zbl 1329.60095, MR 2451043, 10.1109/tit.2008.926316; reference:[8] Morvai, G., Weiss, B.: On universal estimates for binary renewal processes.Ann. Appl. Probab. 18 (2008), 5, 1970-1992. Zbl 1158.62053, MR 2462556, 10.1214/07-aap512; reference:[9] Morvai, G., Weiss, B.: Estimating the residual waiting time for binary stationary time series.In: Proceedings of ITW2009, Volos 2009, pp. 67-70. 10.1109/itwnit.2009.5158543; reference:[10] Morvai, G., Weiss, B.: Universal tests for memory words.IEEE Trans. Inform. Theory 59 (2013), 6873-6879. MR 3106870, 10.1109/tit.2013.2268913; reference:[11] Morvai, G., Weiss, B.: Inferring the residual waiting time for binary stationary time series.Kybernetika 50 (2014), 869-882. Zbl 1308.62067, MR 3301776, 10.14736/kyb-2014-6-0869; reference:[12] Ryabko, B. Ya.: Prediction of random sequences and universal coding.Probl. Inform. Transmiss. 24 (1988), 87-96. Zbl 0666.94009, MR 0955983; reference:[13] Shields, P. C.: The Ergodic Theory of Discrete Sample Paths.Graduate Studies in Mathematics, American Mathematical Society, Providence 13 1996. Zbl 0879.28031, MR 1400225, 10.1090/gsm/013
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7
المؤلفون: Roelly, Sylvie, Vallois, Pierre
مصطلحات موضوعية: msc:60G10, msc:60H10, Mathematics::Probability, msc:60G15, Institut für Mathematik, ddc:510, msc:60G17
وصف الملف: application/pdf
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8Academic Journal
المؤلفون: Morvai, Gusztáv, Weiss, Benjamin
مصطلحات موضوعية: keyword:nonparametric estimation, keyword:stationary processes, msc:60G10, msc:60G25, msc:62G05
وصف الملف: application/pdf
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9Academic Journal
المؤلفون: Prášková, Zuzana, Vaněček, Pavel
مصطلحات موضوعية: keyword:multivariate RCA models, keyword:parameter estimation, keyword:asymptotic variance matrix, msc:60F05, msc:60G10, msc:60G46, msc:62M10
وصف الملف: application/pdf
Relation: mr:MR2884857; zbl:Zbl 1226.62084; reference:[1] Aue, A., Horváth, L., Steinebach, J.: Estimation in random coefficient autoregressive models.J. Time Ser. Anal. 27 (2006), 60–67. Zbl 1112.62084, MR 2235147; reference:[2] Hwang, S. Y., Basawa, I. V.: Parameter estimation for generalized random coefficient autoregressive processes.J. Statist. Plann. Inference 68 (1998), 323–337. Zbl 0942.62102, MR 1629591, 10.1016/S0378-3758(97)00147-X; reference:[3] Berkes, I., Horváth, L., Ling, S.: Estimation in nonstationary random coefficient autoregressive models.J. Time Ser. Anal. 30 (2009), 395–416. Zbl 1224.62046, MR 2536060, 10.1111/j.1467-9892.2009.00615.x; reference:[4] Billingsley, P.: The Lindeberg–Lévy theorem for martingales.Proc. Amer. Math. Soc. 12 (1961), 788–792. Zbl 0129.10701, MR 0126871; reference:[5] Brandt, A.: The stochastic equation $Y_{n+1} = A_n Y_n + B_n$ with stationary coefficients.Adv. Appl. Probab. 18 (1986), 211–220. MR 0827336, 10.2307/1427243; reference:[6] Bougerol, P., Picard, N.: Strict stationarity of generalized autoregressive processes.Ann. Probab. 20 (1992), 1714–1730. Zbl 0763.60015, MR 1188039, 10.1214/aop/1176989526; reference:[7] Davidson, J.: Stochastic Limit Theory.Advanced Texts in Econometrics. Oxford University Press, Oxford 1994. MR 1430804; reference:[8] Feigin, P. D., Tweedie, R. L.: Random coefficient autoregressive processes: A Markov chain analysis of stationarity and finiteness of moments.J. Time Ser. Anal. 6 (1985), 1–14. Zbl 0572.62069, MR 0792428, 10.1111/j.1467-9892.1985.tb00394.x; reference:[9] Janečková, H., Prášková, Z.: CWLS and ML estimates in a heteroscedastic RCA(1) model.Statist. Decisions 22 (2004), 245–259. Zbl 1057.62071, MR 2125611, 10.1524/stnd.22.3.245.57064; reference:[10] Koul, H. L., Schick, A.: Adaptive estimation in a random coefficient autoregressive model.Ann. Statist. 24 (1996), 1025–1052. Zbl 0906.62087, MR 1401835, 10.1214/aos/1032526954; reference:[11] Nicholls, D. F., Quinn, B. G.: Random coefficient autoregressive models: An introduction.Lecture Notes in Statistics 11, Springer, New York 1982. Zbl 0497.62081, MR 0671255, 10.1007/978-1-4684-6273-9; reference:[12] Schick, A.: $\sqrt{n}$-consistent estimation in a random coefficient autoregressive model.Austral. J. Statist. 38 (1996), 155–160. MR 1442543, 10.1111/j.1467-842X.1996.tb00671.x; reference:[13] Schott, J.: Matrix Analysis for Statistics.Wiley Series in Probability and Statistics, Wiley, New York 1996. MR 2111601; reference:[14] Vaněček, P.: Rate of convergence for a class of RCA estimators.Kybernetika 6 (2006), 698–709. Zbl 1249.60034; reference:[15] Vaněček, P.: Estimators of multivariate RCA models.In: Bull. Internat. Statistical Institute LXII (M. I. Gomes at al., eds.), Instituto Nacional de Estatística, Lisbon 2007, pp. 4027–4030.; reference:[16] Vaněček, P.: Estimation of Random Coefficient Autoregressive Models.PhD Thesis, Charles University, Prague 2008.
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10Academic Journal
المؤلفون: Došlá, Šárka, Anděl, Jiří
مصطلحات موضوعية: keyword:non-positive autocorrelations, keyword:linear process, msc:60G10, msc:60G99, msc:60K99, msc:62H20, msc:62M10
وصف الملف: application/pdf
Relation: mr:MR2666898; zbl:Zbl 1187.62142; reference:[1] J. Beran: Statistics for Long-Memory Processes.Chapman & Hall, New York 1994. Zbl 0869.60045, MR 1304490; reference:[2] L. Bondesson: On a minimum correlation problem.Statist. Probab. Lett. 62 (2003), 361–370. Zbl 1116.60326, MR 1973311; reference:[3] P. Brockwell and R. Davis: Time Series: Theory and Methods.Second edition. Springer, New York 1991. MR 1093459; reference:[4] I. Gichman and A. V. Skorochod: Vvedenije v teoriju slučajnych processov.Nauka, Moskva 1965.; reference:[5] Y. Katznelson: An Introduction to Harmonic Analysis.Third edition. Cambridge University Press, Cambridge 2004. Zbl 1055.43001, MR 2039503; reference:[6] K. Meister and L. Bondesson: Some Real Time Sampling Methods.Technical Report 2, Dept. of Math. Statist., Umeåa Univ. 2001.; reference:[7] A. Zygmund: Trigonometric Series.Third edition. Cambridge University Press, Cambridge 2002. Zbl 1084.42003, MR 1963498
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11Academic Journal
المؤلفون: Hoffmann, Lars Michael
مصطلحات موضوعية: keyword:Boolean model, keyword:convex cylinder, keyword:direction distribution, keyword:least square estimator, keyword:parameter estimation, keyword:Poisson process, keyword:spherical measure, keyword:sine transform, msc:52A22, msc:60D05, msc:60G10, msc:62H11, msc:62M30, msc:65D15
وصف الملف: application/pdf
Relation: mr:MR2476022; zbl:Zbl 1211.62092; reference:[1] Billingsley, P.: Convergence of Probability Measures.Wiley New York (1968). Zbl 0172.21201, MR 0233396; reference:[2] Gardner, R. J., Kiderlen, M., Milanfar, P.: Convergence of algorithms for reconstructing convex bodies and directional measures.Ann. Stat. 34 (2006), 1331-1374. Zbl 1097.52503, MR 2278360, 10.1214/009053606000000335; reference:[3] Hoffmann, L. M.: Mixed measures of convex cylinders and quermass densities of Boolean models.Submitted. Zbl 1180.52011; reference:[4] Hug, D., Schneider, R.: Stability results involving surface area measures of convex bodies.Rend. Circ. Mat. Palermo (2) Suppl. No. 70, part II (2002), 21-51. Zbl 1113.52013, MR 1962583; reference:[5] Kallenberg, O.: Foundations of Modern Probability, 2nd. ed.Springer New York (2002). Zbl 0996.60001, MR 1876169; reference:[6] Kiderlen, M.: Non-parametric estimation of the directional distribution of stationary line and fibre processes.Adv. Appl. Probab. 33 (2001), 6-24. Zbl 0998.62080, MR 1825313, 10.1239/aap/999187894; reference:[7] Kiderlen, M., Pfrang, A.: Algorithms to estimate the rose of directions of a spatial fibre system.J. Microsc. 219 (2005), 50-60. MR 2196184, 10.1111/j.1365-2818.2005.01493.x; reference:[8] Schladitz, K., Peters, S., Reinel-Bitzer, D., Wiegmann, A., Ohser, J.: Design of accoustic trim based on geometric modeling and flow simulation for non-woven.Comp. Mat. Sci. 38 (2006), 56-66. 10.1016/j.commatsci.2006.01.018; reference:[9] Schneider, R.: Convex Bodies: the Brunn-Minkowski Theory.Cambridge University Press Cambridge (1993). Zbl 0798.52001, MR 1216521; reference:[10] Schneider, R., Weil, W.: Integralgeometrie.Teubner Stuttgart (1992), German. Zbl 0762.52001, MR 1203777; reference:[11] Schneider, R., Weil, W.: Stochastische Geometrie.Teubner Stuttgart (2000), German. Zbl 0964.52009, MR 1794753; reference:[12] Spiess, M., Spodarev, E.: Anisotropic dilated Poisson $k$-flat processes.Submitted.; reference:[13] Stoyan, D., Kendall, W. S., Mecke, J.: Stochastic Geometry and Its Applications, 2nd ed.John Wiley & Sons Chichester (1995). Zbl 0838.60002, MR 0895588
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12Academic Journal
المؤلفون: Vaněček, Pavel
مصطلحات موضوعية: keyword:RCA, keyword:parameter estimation, keyword:rate of convergence, msc:60F05, msc:60G10, msc:62F10, msc:62M09, msc:62M10, msc:91B84
وصف الملف: application/pdf
Relation: mr:MR2296509; zbl:Zbl 1249.60034; reference:[1] Basu A. K., Roy S. Sen: On rates of convergence in the central limit theorem for parameter estimation in general autoregressive model.Statistics 21 (1990), 461–470 MR 1062852, 10.1080/02331889008802256; reference:[2] Basu A. K., Roy S. Sen: On rates of convergence in the central limit theorem for parameter estimation in random coefficient autoregressive models.J. Indian Statist. Assoc. 26 (1988), 19–25 MR 1002100; reference:[3] Davidson J.: Stochastic Limit Theory.(Advanced Texts in Econometrics.) Oxford University Press, New York, Reprinted 2002 Zbl 0904.60002, MR 1430804; reference:[5] Janečková H., Prášková Z.: CWLS and ML estimates in a heteroscedastic RCA(1) model.Statist. Decisions 22 (2004), 245–259 Zbl 1057.62071, MR 2125611, 10.1524/stnd.22.3.245.57064; reference:[6] Kato Y.: Rates of convergence in central limit theorem for martingale differences.Bull. Math. Statist 18 (1979), 1–8 MR 0517156; reference:[7] Michel R., Pfanzagl J.: The accuracy of the normal approximation for minimum contrast estimate.Z. Wahrsch. Verw. Gebiete 18 (1971), 73–84 MR 0288897, 10.1007/BF00538488; reference:[8] Nicholls D. F., Quinn B. G.: Random Coefficient Autoregressive Models: An Introduction.(Lecture Notes in Statistics 11.) Springer, New York 1982 Zbl 0497.62081, MR 0671255, 10.1007/978-1-4684-6273-9; reference:[9] Phillips P. C. B., Solo V.: Asymptotics for linear processes.Ann. Statist. 20 (1992), 971–1001 Zbl 0759.60021, MR 1165602, 10.1214/aos/1176348666; reference:[10] Schick A.: $\sqrt{n}$-consistent estimation in a random coefficient autoregressive model.Austral. J. Statist. 38 (1996), 155–160 MR 1442543, 10.1111/j.1467-842X.1996.tb00671.x; reference:[12] Vaněček P.: Estimators of generalized RCA models.In: Proc. WDS’04 Part I (2004), pp. 35–40
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13Academic Journal
المؤلفون: Marek, Tomáš
مصطلحات موضوعية: keyword:non-linear time series, keyword:invertibility, keyword:random coefficient moving average, msc:60G10, msc:62M09, msc:62M10
وصف الملف: application/pdf
Relation: mr:MR2193863; zbl:Zbl 1248.62154; reference:[1] Granger C. W. J., Andersen A. P.: An Introduction to Bilinear Time Series Models.Vandenhoek and Ruprecht, Gottingen 1978 Zbl 0379.62074, MR 0483231; reference:[2] Granger C. W. J., Andersen A. P.: On the invertibility of time series models.Stochastic Process. Appl. 8 (1978), 87–92 Zbl 0387.62076, MR 0511877; reference:[3] Marek T.: Maximum likelihood estimation in the simple NLMA model.In: Proc. WDS’99 (J. Šafránková, ed.), Matfyzpress, Praha 1999, pp. 28–33; reference:[4] McKenzie E.: Product autoregression: a time-series characterization of the gamma distribution.J. Appl. Probab. 19 (1982), 463–468 Zbl 0491.60034, MR 0649988, 10.2307/3213502; reference:[5] Robinson P. M.: The estimation of a nonlinear moving average models.Stochastic Process. Appl. 5 (1977), 81–90 MR 0428654; reference:[6] Štěpán J.: Probability Theory (in Czech).Academia, Praha 1986; reference:[7] Tjøstheim D.: Some doubly stochastic time series models.J. Time Ser. Anal. 7 (1986), 51–72 MR 0832352, 10.1111/j.1467-9892.1986.tb00485.x; reference:[8] Tong H.: Nonlinear Time Series.Clarendon Press, Oxford 1990 Zbl 1037.62092, MR 1079320
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14Academic Journal
المؤلفون: Anděl, Jiří, Ranocha, Pavel
مصطلحات موضوعية: keyword:absolute autoregression, keyword:stationary distribution, keyword:marginal distribution, msc:60G10, msc:62M05, msc:62M10
وصف الملف: application/pdf
Relation: mr:MR2193862; zbl:Zbl 1249.60067; reference:[1] Anděl J.: Dependent random variables with a given marginal distribution.Acta Univ. Carolin. – Math. Phys. 24 (1983), 3–12 MR 0733140; reference:[2] Anděl J.: Marginal distributions of autoregressive processes.In: Trans. 9th Prague Conference Inform. Theory, Statist. Dec. Functions, Random Processes. Academia, Praha 1983 Zbl 0537.60027, MR 0757732; reference:[3] Anděl J., Bartoň T.: A note on the threshold AR(1) model with Cauchy innovations.J. Time Ser. Anal. 7 (1986), 1–5 Zbl 0587.60033, MR 0832348, 10.1111/j.1467-9892.1986.tb00481.x; reference:[4] Anděl J., Netuka, I., Zvára K.: On threshold autoregressive processes.Kybernetika 20 (1984), 89–106 Zbl 0547.62058, MR 0747062; reference:[5] Chan K. S., Tong H.: A note on certain integral equations associated with non-linear time series analysis.Probab. Theory Related Fields 73 (1986), 153–159 MR 0849071, 10.1007/BF01845999; reference:[6] Loges W.: The stationary marginal distribution of a threshold AR(1) process.J. Time Ser. Anal. 25 (2004), 103–125 Zbl 1051.62080, MR 2042113, 10.1111/j.1467-9892.2004.00339.x; reference:[7] Tong H.: Non-Linear Time Series.Clarendon Press, Oxford 1990 Zbl 0835.62076
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15Academic Journal
المؤلفون: Šindelář, Jan, Knížek, Jiří
مصطلحات موضوعية: keyword:AR(1) process, keyword:unequally spaced, keyword:autocorrelation coefficient, keyword:least squares estimate, keyword:maximum likelihood estimate, msc:60G10, msc:62M10
وصف الملف: application/pdf
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16Academic Journal
المؤلفون: Marhuenda, Marco A., Marhuenda, Yolanda, Morales, Domingo
مصطلحات موضوعية: keyword:multinomial distribution, keyword:algorithms, keyword:goodness-of-fit divergence tests, keyword:power divergence statistics, keyword:chi-squared tests, keyword:power comparisons, msc:60G10, msc:62G10, msc:62M10, msc:62Q05
وصف الملف: application/pdf
Relation: mr:MR1980124; zbl:Zbl 1249.60070; reference:[1] Aho A. V., Hopcroft J. E., Ullman J. D.: Data Structures and Algorithms.Addison–Wesley, Massachusetts 1983 Zbl 0487.68005, MR 0666695; reference:[2] Ali S. M., Silvey S. D.: A general class of coefficient of divergence of one distribution from another.J. Roy. Statist. Soc. Ser. B 286 (1966), 131–142 MR 0196777; reference:[3] Cressie N. A. C., Read T. R. C.: Multinomial goodness of fit tests.J. Roy. Statist. Soc. Ser. B 46 (1984), 440–464 Zbl 0571.62017, MR 0790631; reference:[4] Csiszár I.: Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten.Publ. Math. Inst. Hungarian Academy of Sciences, Series A, 8 (1963), 85–108 MR 0164374; reference:[5] Kulmann H.: Notes on the computation of the exact distribution function of the $\chi ^2$ and related tests statistics in the equiprobable case.Comput. Stat. Data Anal., The Statistical Software Newsletter 4 (1996), 707–710; reference:[6] Liese F., Vajda I.: Convex Statistical Distances.Teubner, Leipzig 1987 Zbl 0656.62004, MR 0926905; reference:[7] Marhuenda M. A., Marhuenda, Y., Morales D.: Algorithms to calculate the exact distribution function of power divergence statistics.Technical Report of the Operational Research Center, Miguel Hernández University of Elche 2001; reference:[8] Read T. R. C., Cressie N. A. C.: Goodness–of–fit Statistics for Discrete Multivariate Data.Springer–Verlag, New York 1988 Zbl 0663.62065, MR 0955054; reference:[9] Weiss M. A.: Data Structures and Algorithm Analysis.Benjamin/Cummings Publishing Company, Redwood City, CA 1992 Zbl 0879.68016; reference:[10] Zografos K., Ferentinos, K., Papaioannou T.: $\phi $-divergence statistics: sampling properties, multinomial goodness of fit and divergence tests.Comm. Statist. A – Theory Methods 19 (1990), 1785–1802 MR 1075502, 10.1080/03610929008830290
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17Academic Journal
المؤلفون: Volf, Petr, Linka, Aleš
مصطلحات موضوعية: keyword:hazard function, keyword:goodness-of-fit test, msc:60G10, msc:60K10, msc:62M05, msc:62N02, msc:62N05
وصف الملف: application/pdf
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18Academic Journal
المؤلفون: Anděl, Jiří
وصف الملف: application/pdf
Relation: mr:MR1830645; zbl:Zbl 1248.62140; reference:[1] Anděl J.: On extrapolation in some non-linear AR(1) processes.Comm. Statist. – Theory Methods 26 (1997), 581–587 MR 1436289, 10.1080/03610929708831935; reference:[2] Anděl J., Dupač V.: Extrapolations in non-linear autoregressive processes.Kybernetika 35 (1999), 383–389 MR 1704673; reference:[3] Pemberton J.: Piecewise Constant Models for Univariate Time Series.Technical Report MCS-90-04, Department of Mathematics, University of Salford, Salford 1990; reference:[4] Pemberton J.: Measuring nonlinearity in time series.In: Developments in Time Series Analysis (T. Subba Rao, ed.), Chapman and Hall, London 1993, pp. 230–240 Zbl 0880.62091, MR 1292253; reference:[5] Tong H.: Non-linear Time Series.Clarendon Press, Oxford 1990 Zbl 0835.62076; reference:[6] Young P.: Time variable and state dependent modelling of non-stationary and nonlinear time series.In: Developments in Time Series Analysis (T. Subba Rao, ed.), Chapman and Hall, London 1993, pp. 374–413 Zbl 0880.62100
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19Academic Journal
المؤلفون: Klotz, Lutz
مصطلحات موضوعية: keyword:linear interpolation, msc:60G10, msc:60G25, msc:62H20, msc:62M20, msc:62M99
وصف الملف: application/pdf
Relation: mr:MR1773507; zbl:Zbl 1243.62124; reference:[1] Budinský P.: Improvement of interpolation under additional information.In: Proceedings of the 4th Prague Symposium on Asymptotic Statistics (P. Mandl and M. Hušková, eds.), Charles University, Prague 1989, pp. 159–167 Zbl 0711.62083, MR 1051435; reference:[2] Makagon A.: Interpolation error operator for Hilbert space valued stationary stochastic processes.Probab. Math. Statist. 4 (1984), 57–65 Zbl 0575.60040, MR 0764330; reference:[3] Makagon A., Weron A.: $q$-variate minimal stationary processes.Studia Math. 59 (1976), 41–52 Zbl 0412.60013, MR 0428419; reference:[4] Pringle R. M., Rayner A. A.: Generalized Inverse Matrices with Applications to Statistics.Griffin, London 1971 Zbl 0231.15008, MR 0314860; reference:[5] Rozanov, Yu. A.: Stationary Random Processes (in Russian).Fizmatgiz, Moscow 1963; reference:[6] Salehi H.: The Hellinger square–integrability of matrix–valued measures with respect to a non–negative hermitian measure.Ark. Mat. 7 (1967), 299–303 MR 0233951, 10.1007/BF02591023; reference:[7] Salehi H.: Application of the Hellinger integrals to $q$-variate stationary stochastic processes.Ark. Mat. 7 (1967), 305–311 MR 0236991, 10.1007/BF02591024; reference:[8] Weron A.: On characterizations of interpolable and minimal stationary processes.Studia Math. 49 (1974), 165–183 Zbl 0303.60034, MR 0341587
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20Academic Journal
المؤلفون: Anděl, Jiří, Hrach, Karel
مصطلحات موضوعية: keyword:AR(1) model, keyword:AR(2) model, msc:60G10, msc:62M10, msc:65C60
وصف الملف: application/pdf
Relation: mr:MR1773506; zbl:Zbl 1248.62141; reference:[1] Anděl J.: Dependent random variables with a given marginal distribution.Acta Univ. Carolin. – Math. Phys. 24 (1983), 3–11 MR 0733140; reference:[2] Anděl J.: Marginal distributions of autoregressive processes.In: Trans. 9th Prague Conf. Inform. Theory, Statist. Decision Functions, Random Processes, Academia, Prague 1983, pp. 127–135 MR 0757732; reference:[3] Anděl J.: On linear processes with given moments.J. Time Ser. Anal. 8 (1987), 373–378 MR 0917790, 10.1111/j.1467-9892.1987.tb00001.x; reference:[4] Anděl J.: AR(1) processes with given moments of marginal distribution.Kybernetika 22 (1989), 337–347 Zbl 0701.62087, MR 1024709; reference:[5] Anděl J., Bartoň T.: A note on the threshold AR(1) model with Cauchy innovations.J. Time Ser. Anal. 7 (1986), 1–5 Zbl 0587.60033, MR 0832348, 10.1111/j.1467-9892.1986.tb00481.x; reference:[6] Anděl J., Garrido M.: On stationary distributions of some time series models.In: Trans. 10th Prague Conf. Inform. Theory, Statist. Decision Functions, Random Processes, Academia, Prague 1988, pp. 193–202 MR 1136274; reference:[7] Anděl J., Gómez M., Vega C.: Stationary distribution of some nonlinear AR(1) processes.Kybernetika 25 (1989), 453–460 Zbl 0701.60029, MR 1035151; reference:[8] Anděl J., Netuka I., Zvára K.: On threshold autoregressive processes.Kybernetika 20 (1984), 89–106 Zbl 0547.62058, MR 0747062; reference:[9] Bernier J.: Inventaire des modèles et processus stochastique applicables de la description des déluts journaliers des riviers.Rev. Inst. Internat. Statist. 38 (1970), 50–71 10.2307/1402324; reference:[10] Davis R. A., Rosenblatt M.: Parameter estimation for some time series models without contiguity.Statist. Probab. Lett. 11 (1991), 515–521 Zbl 0725.62079, MR 1116746, 10.1016/0167-7152(91)90117-A; reference:[11] Feller W.: An Introduction to Probability Theory and its Applications II.Wiley, New York 1966 MR 0210154; reference:[12] Gaver D. P., Lewis P. A. W.: First–order autoregressive gamma sequences and point processes.Adv. in Appl. Probab. 12 (1980), 727–745 Zbl 0453.60048, MR 0578846, 10.2307/1426429; reference:[13] Haiman G.: Upper and lower bounds for the tail of the invariant distribution of some AR(1) processes.In: Asymptotic Methods in Probability and Statistics (B. Szyszkowicz, ed.), North–Holland/Elsevier, Amsterdam 1998, pp. 723–730 Zbl 0926.62080, MR 1661513; reference:[14] Hamilton J. D.: Time Series Analysis.Princeton University Press, Princeton 1994 Zbl 0831.62061, MR 1278033; reference:[15] Loève M.: Probability Theory.Second edition. Van Nostrand, Princeton 1955 Zbl 0385.60001, MR 0203748; reference:[16] Rényi A.: Probability Theory.Akadémiai Kiadó, Budapest 1970; reference:[17] Sondhi M. M.: Random processes with specified spectral density and first–order probability density.Bell System Technical J. 62 (1983), 679–701 10.1002/j.1538-7305.1983.tb04411.x; reference:[18] Štěpán J.: Teorie pravděpodobnosti.Academia, Praha 1987; reference:[19] Tong H.: Non–linear Time Series.Clarendon Press, Oxford 1990 Zbl 0835.62076, MR 1079320; reference:[20] Research, Wolfram, Inc.: Mathematica, Version 2.2. Wolfram Research, Inc., Champaign, Illinois 1994