• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.257-265
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• 1996

We consider nonstationary autoregressive autoregressive process with infinite variance of error. In the case of infinite cariance, the limiting distribution of the estimated coefficient is different from that under the finite cariance assumption. In this paper we show that the bootstrap method can be used to approximate the distribution of ordinary least squares estimator of the coefficient in the first order random walk process with infinite variance through some empirical studies and we suggest a test procedure based on bootstrap method for the unit root test.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.31-46
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• 1997

Let $X_{t}$ = .beta. $X_{{t-1}}$ + .epsilon.$_{t}$ be an autoregressive process where $\mid$.beta.$\mid$ < 1 and {.epsilon.$_{t}$} is independent and identically distriubted with regularly varying tail probabilities. This process is called the asymptotically stationary first-order autoregressive process (AR(1)) with infinite variance. In this paper, we obtain a host of weak convergences of some point processes based on bootstrapping of { $X_{t}$}. These kinds of results can be generalized under the infinite variance assumption to ensure the asymptotic validity of the bootstrap method for various functionals of { $X_{t}$} such as partial sums, sample covariance and sample correlation functions, etc.ions, etc.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.295-303
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• 1997

Let ${X_k : k = 1, 2, \cdots}$ be a sequence of independent, identically distributed integer-valued random variables with common distribution function F.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1397-1403
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• 2006

This paper considers the testing problem for scale changes in autoregressive processes with heavy-tailed innovations. For a test, we propose the CUSUM test statistic based on the trimmed residuals. We perform a simulation study for the mixture normal and Cauchy innovations.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.507-513
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• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• Industrial Engineering and Management Systems
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• v.1 no.1
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• pp.29-45
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• 2002

In this study, we consider infinite supply of raw materials and backlogged demands as given two boundary conditions. And we need not make any specific assumptions about the inter-arrival of external demand and service time distributions. We propose a numeric model and an algorithm in order to compute the first two moments of inter-departure process. Entropy enables us to examine the convergence of this process and to derive measurable relations of this process. Also, lower bound on the variance of inter-departure process plays an important role in proving the existence and uniqueness of an optimal solution for a numeric model and deriving the convergence order of augmented Lagrange multipliers method applied to a numeric model. Through these works, we confirm some structural properties and numeric examples how the validity and applicability of our study.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.4
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• pp.185-205
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• 2002

In this study, we consider infinite supply of raw materials and backlogged demands as given two boundary conditions. And we need not make any specific assumptions about the inter-arrival of external demand and service time distributions. Under these situations, the ultimate objective of this study is to prove the variability propagation principle in a pull serial line and is to measure it in terms of the first two moments of the inter-departure process subject to number of cards in each cell. Two preparations are required to achieve this objective : The one is to derive a true lower bound of variance of the inter-departure process. The other is to establish a constrained discrete minimax problem for the no backorder (backlogging) probabilities in each cell. We may get some fundamental results necessary to a completion for the proof through the necessary and sufficient conditions for existence of optimal solution of a constrained discrete minimax problem and the implicit function theorem. finally, we propose a numeric model to measure the variability propagation principle. Numeric examples show the validity and applicability of our study.

• The Journal of Fisheries Business Administration
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• v.18 no.1
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• pp.37-57
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• 1987

This article discussed the characteristics of several Pareto-optimal incentive contracts between owner and labor, more specifically, four situations: reporting output jointly observable by labor ana owner; reporting both output and effort; incorporating other endogenous elements (like capital) that affect the production process and Pareto-optimal fee schedules; and ascertaining the effects of private pre-decision information private- decision information, and per-contact informational asymmetries. Also presented were several extensions of the basic contractual model, and the different components of agency costs associated with labor-owner contractual relations. In a single-period model, the agency problem exists because the uncertainty prevents the owner from using the cash flow to determine unambiguously the labor's action. Holmstrom(1979) suggests that "when the same situation repeats itself over time, the effects of uncertainty tend to be reduced and dystunctional behavior is more accurately revealed, thus alleviating the problem of moral hazard. " Under these conditions, if the labor selects the first-best level of effect in each period, the cash flow will be independent and identically distributed over time. As the number of periods increases, the variance of the labows average output, if he selects the first-best level of effort in each period, gets smaller. Note that for this diversification effect to occur, it is necessary that the owner evaluate the labor's effort over the entire history of his employment, rather than evaluate each period's performance separately. Radner(1980) and Rubinstein and Yaari(1980) consider the extreme case in which there are an infinite number of observations. They show that the owner can eventually detect and systematic shirking on the part of the labor by comparing the labor's average output with what would be expected if the labor had been selecting the first-best level of effort in each period. In a dynamic model with incentive problems we have demonstrated that the labor's second-period compensation will depend on his first-period performance. This allows the owner to diversify away some of the uncertainty surrounding the labor's actions. In addition, this allows the owner to smooth the labor's income over time by spreading the risk of the first-period outcome over both periods. At least some unexplored avenves in this area invite future accounting research: situations where owner has different incompatible objectives and negotiates a contract with labor; circumstances in which owner deals with multiple objectives and negotiates contracts with several labors simultaneously; the value of costly accounting information systems and communication in establishing, Pareto-optimal incentive contracts, and the value and effects of inside information, Thorough theoretical or empirical research on each of these topics not only would increase our knowledge about the role and significance of accounting information but could also provide explanations of the inherent differences among various organizations and in their economic behavior. behavior.