• Title/Summary/Keyword: moving average process

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A Laplacian Autoregressive Moving-Average Time Series Model

  • Son, Young-Sook
    • Journal of the Korean Statistical Society
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    • v.22 no.2
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    • pp.259-269
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    • 1993
  • A moving average model, LMA(q) and an autoregressive-moving average model, NLARMA(p, q), with Laplacian marginal distribution are constructed and their properties are discussed; Their autocorrelation structures are completely analogus to those of Gaussian process and they are partially time reversible in the third order moments. Finally, we study the mixing property of NLARMA process.

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PRECISE ASYMPTOTICS OF MOVING AVERAGE PROCESS UNDER ?-MIXING ASSUMPTION

  • Li, Jie
    • Journal of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.235-249
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    • 2012
  • In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.

An Extension of the Optimality of Exponential Smoothing to Integrated Moving Average Process (일반적인 IMA과정에 대한 지수평활 최적성의 확장)

  • Park, Hae-Chul;Park, Sung-Joo
    • Journal of the military operations research society of Korea
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    • v.8 no.1
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    • pp.99-107
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    • 1982
  • This paper is concerned with the optimality of exponential smoothing applied to the general IMA process with different moving average and differencing orders. Numerical experiments were performed for IMA(m,n) process with various combinations of m and n, and the corresponding forecast errors were compared. Results show that the higher differencing order is more critical to the optimality of exponential smoothing, i.e., the IMA process with the higher moving average order, forecasted by exponential smoothing, has comparatively smaller forecast error. If the difference between the differencing order and the moving average order becomes larger, the accuracy of forecast by exponential smoothing declines gradually.

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Consistency and Bounds on the Bias of $S^2$ in the Linear Regression Model with Moving Average Disturbances

  • Song, Seuck-Heun
    • Journal of the Korean Statistical Society
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    • v.24 no.2
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    • pp.507-518
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    • 1995
  • The ordinary least squares based estiamte $S^2$ of the disturbance variance is considered in the linear regression model when the disturbances follow the first-order moving-average process. It is shown that $S^2$ is weakly consistent estimate for the disturbance varaince without any restriction on the regressor matrix X. Also, simple exact bounds on the relative bias of $S^2$ are given in finite sample sizes.

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Fault Detection in the Semiconductor Etch Process Using the Seasonal Autoregressive Integrated Moving Average Modeling

  • Arshad, Muhammad Zeeshan;Nawaz, Javeria Muhammad;Hong, Sang Jeen
    • Journal of Information Processing Systems
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    • v.10 no.3
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    • pp.429-442
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    • 2014
  • In this paper, we investigated the use of seasonal autoregressive integrated moving average (SARIMA) time series models for fault detection in semiconductor etch equipment data. The derivative dynamic time warping algorithm was employed for the synchronization of data. The models were generated using a set of data from healthy runs, and the established models were compared with the experimental runs to find the faulty runs. It has been shown that the SARIMA modeling for this data can detect faults in the etch tool data from the semiconductor industry with an accuracy of 80% and 90% using the parameter-wise error computation and the step-wise error computation, respectively. We found that SARIMA is useful to detect incipient faults in semiconductor fabrication.

A Newton-Raphson Solution for MA Parameters of Mixed Autoregressive Moving-Average Process

  • Park, B. S.
    • Journal of the Korean Statistical Society
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    • v.16 no.1
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    • pp.1-9
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    • 1987
  • Recently a new form of the extended Yule-Walker equations for a mixed autoregressive moving-average process of orders p and q has been proposed. It can be used to obtain p+q+1 parameter values from the first p+q+1 autocovariance terms. The autoregressive part of the equations is linear and can be easily solved. In contrast the moving-average part is composed of nonlinear simultaneous equations. Thus some iterative algorithms are necessary to solve them. The iterative algorithm presented by Choi(1986) is very simple but its convergence has not been proved yet. In this paper a Newton-Raphson solution for the moving-average parameters is presented and its convergence is shown. Also numerical example illustrate the performance of the algorithm.

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On Stationarity of TARMA(p,q) Process

  • Lee, Oesook;Lee, Mihyun
    • Journal of the Korean Statistical Society
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    • v.30 no.1
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    • pp.115-125
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    • 2001
  • We consider the threshold autoregressive moving average(TARMA) process and find a sufficient condition for strict stationarity of the proces. Given region for stationarity of TARMA(p,q) model is the same as that of TAR(p) model given by Chan and Tong(1985), which shows that the moving average part of TARMA(p,q) process does not affect the stationarity of the process. We find also a sufficient condition for the existence of kth moments(k$\geq$1) of the process with respect to the stationary distribution.

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Economic Design of a Moving Average Control Chart with Multiple Assignable Causes when Two Failures Occur

  • Cben, Yun-Shiow;Yu, Fong-Jung
    • International Journal of Quality Innovation
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    • v.2 no.1
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    • pp.69-86
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    • 2001
  • The economic design of control charts has been researched for over four decades since Duncan proposed the concept in 1956. Few studies, however, have focused attention on the economic design of a moving average (MA) control chart. An MA control chart is more effective than the Shewhart chart in detecting small process shifts [9]. This paper provides an economic model for determining the optimal parameters of an MA control chart with multiple assignable causes and two failures in the production process. These parameters consist of the sample size, the spread of the control limit and the sampling interval. A numerical example is shown and the sensitivity analysis shows that the magnitude of shift, rate of occurrence of assignable causes and increasing cost when the process is out of control have a more significant effect on the loss cost, meaning that one should more carefully estimate these values when conducting an economic analysis.

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Unit Root Test for Temporally Aggregated Autoregressive Process

  • Shin, Dong-Wan;Kim, Sung-Chul
    • Journal of the Korean Statistical Society
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    • v.22 no.2
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    • pp.271-282
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    • 1993
  • Unit root test for temporally aggregated first order autoregressive process is considered. The temporal aggregate of fist order autoregression is an autoregressive moving average of order (1,1) with moving average parameter being function of the autoregressive parameter. One-step Gauss-Newton estimators are proposed and are shown to have the same limiting distribution as the ordinary least squares estimator for unit root when complete observations are available. A Monte-Carlo simulation shows that the temporal aggregation have no effect on the size. The power of the suggested test are nearly the same as the powers of the test based on complete observations.

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