ALMOST SURE CONVERGENCE FOR LINEAR PROCESS GENERATED BY ASYMPTOTICALLY LINEAR NEGATIVE QUADRANT DEPENDENCE PROCESSES

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CAI, GUANG-HUI (Department of Mathematics and Statistics Zhejiang Gongshang University)

In this paper, we obtain strong law of large numbers for linear process generated by asymptotically linear negative quadrant dependence processes.

H. C. Ho and T. Hsing, Limit theorems for functionals of moving average, Ann. Probab. 25 (1997), 1636-1669 https://doi.org/10.1214/aop/1023481106
T. Kim and J. Baek, A central limit theorem for Stationary linear processes under linear positive quadrant dependent process, Statist. Probab. Lett. 51 (2001), 299-305 https://doi.org/10.1016/S0167-7152(00)00168-1
T. Kim, M. Ko and D. Park, Almost sure convergence for linear processes generated by positively dependent processes, Stoch. Anal. Appl. 22(1) (2004), 143-153 https://doi.org/10.1081/SAP-120028027
P. Phillips, Time series regression with a unit root, Econometrica 55 (1987), 277-302 https://doi.org/10.2307/1913237
P. Phillips and V. Solo, Asymptotics for linear processes, Ann. Statist. 20 (1992), 971-1001 https://doi.org/10.1214/aos/1176348666
G. Salvadori, Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions, Stochastic Environmental Research and Risk Assessment. 17 (2003), 116-140 https://doi.org/10.1007/s00477-002-0121-5
Q. Y. Wang, Y. X. Lin and C. M. Gulati, The invariance principle for linear processes with applications, Econometric Theory 18 (2002), 119-139 https://doi.org/10.1017/S0266466602181072
L. X. Zhang, A functional central limit theorem for asymptotically negative dependence random fields, Acta Math. Hungar. 86(3) (2000), 237-259 https://doi.org/10.1023/A:1006720512467

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The limit theorem for dependent random variables with applications to autoregression models vol.24, pp.3, 2011, https://doi.org/10.1007/s11424-011-8119-z
Asymptotic Distribution for Products of Sums of Linear Processes Under Dependence vol.42, pp.13, 2013, https://doi.org/10.1080/03610926.2011.599011