• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.269-284
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• 2000

We show asymptotic normality of the sample mean and sample autocovariances function generated from first-order integer valued autoregressive process(INAR(1)) with a negative binomial or a Poisson marginal. It is shown that a Poisson INAR(1) process is a special case of a negative binomial INAR(1) process.

• The Korean Journal of Applied Statistics
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• v.9 no.1
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• pp.111-124
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• 1996

In this paper, we consider the first-order integer valued autoregressive(INAR(1)) model where correlation structure is similar to that of the continuous valued AR(1) process. Several methods for estimating the parameters of the INAR(1) process with negative binomial marginal are discussed. We derive asymptotic distributions of these estimators. The results of a simulation study for these estimators methods show that the estimator which we present in this paper is better than the estimator which Klimko and Nelson(1978) presented. As an application we considered the estimator of M/M/1 queue length.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.159-165
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• 2005

Recently, as a result of the growing interest in modelling stationary processes with discrete marginal distributions, several models for integer valued time series have been proposed in the literature. One of theses models is the integer-valued autoregressive(INAR) models. However, when modelling with integer-valued autoregressive processes, there is not yet distributional properties of forecasts, since INAR process contain an accrued level of complexity in using the Steutal and Van Harn(1979) thinning operator 'o'. In this study, a manageable expression for the asymptotic mean square error of predicting more than one-step ahead from an estimated poisson INAR(1) model is derived. And, we present a bootstrap methods developed for the calculation of forecast interval limits of INAR(p) model. Extensive finite sample Monte Carlo experiments are carried out to compare the performance of the several bootstrap procedures.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.483-498
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• 1994

Suppose that a stationary process ${X_t}$ has a marginal distribution whose support consists of sufficiently large integers. We are concerned with some analogous law of large numbers for such distribution function F. In particular, we determine a weak law of large numbers for maximum queueing length in $M/M\infty$ system. We also present a limiting behavior for the maxima based on AR(1) process with binomial thining and poisson marginals (INAR(1)) introduced by E. Mckenzie. It turns out that the result of AR(1) process is the same as that of $M/M/\infty$ queueing process in limit when we observe the queues at regularly spaced intervals of time.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.37-47
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• 2006

Recently, as a result of the growing interest in modeling stationary processes with discrete marginal distributions, several models for integer valued time series have been proposed in the literature. One of these models is the integer-valued autoregressive (INAR) models. However, when modeling with integer-valued autoregressive processes, the distributional properties of forecasts have been not yet discovered due to the difficulty in handling the Steutal Van Ham thinning operator 'o' (Steutal and van Ham, 1979). In this study, we derive the mean squared error of h-step-ahead prediction from a Poisson INAR(1) process, reflecting the effect of the variability of parameter estimates in the prediction mean squared error.

• Journal of Welding and Joining
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• v.12 no.1
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• pp.102-115
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• 1994

This paper is to evaluate the fatigue strength of lap joints of materials applied to LNG carrier cargo containment of GAZ-TRANSPORT(GT) type, which was welded by manual and automatic TIG welding process. The thicknesses of lapped members were 1.5mm/1.5mm or 1.5mm/0.7mm in Invar to Invar joint, and 1.5mm/8.0mm in Invar to stainless steel joint, respectively. These lap joints were mainly applied to the membrance fabrication of GT-LNG carrier. Fatigue tests of Invar/Inar lap joints were conducted under the stress ratio R=0 at room temperature. The effect of mean stress and cumulative fatigue damage on the allowable stress of Invar lap joint was evaluated on the basis of test results. Fatigue test was also conducted on Inver/Stainless steel lap joints welded by automatic TIG process without filler metals. The fatigue test of the joint was carried out under the same conditions as those of Invar/invar lap joints. The fatigue strength of the joint welded without filler metal was comparable to those welded with filler metal quoted from reference. The fatigue strength of Invar/stainless steel lap joint was only dependent on the lap throat thickness, and not on the welding process. Based on test results, the applicability of TIG welding process without filler metal in Invar/stainless steel lap joint was reviewed by controlling welding variables to assure the valid throat thickness of lap joints.