• 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.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.155-170
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• 1997

We propose an integer-valued MA(q) process with Poisson disturbance. Its various properties are discussed such as the joint distribution, time reversibility and regression. We derive the asymptotic distribution of autocovariance function and estimators of the parameters in the suggested model. We also consider the relationship between INMA(q) and M/D/.infty. processes.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.5
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• pp.1076-1082
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• 2013

The frequency bands were discovered which maximize the slopes of autocovariances of speech signals in frequency domain to increase the possibility of segregation between speech signals and background noise signal. A speech signal is divided into blocks which include multiples of sampled data, then those blocks are transformed to frequency domain using Fast Fourier Transform(FFT). To find linear equation by Linear Regression, the coefficients of autocovariance within blocks of some frequency band are used. The slope of the linear equation which is called the slope of autocovariance is varied from band to band according to the characteristics of the speech signal. Using speech signals of a man which consist of 200 files, the coefficients of the slopes of autocovariances are analyzed and compared from band to band.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.149-161
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• 2020

In this paper we extend the functional principal component analysis for real-valued random functions to the case of Hilbert-space-valued functional random objects. For this, we introduce an autocovariance operator acting on the space of real-valued functions. We establish an eigendecomposition of the autocovariance operator and a Karuhnen-Loève expansion. We propose the estimators of the eigenfunctions and the functional principal component scores, and investigate the rates of convergence of the estimators to their targets. We detail the implementation of the methodology for the cases of compositional vectors and density functions, and illustrate the method by analyzing time-varying population composition data. We also discuss an extension of the methodology to multivariate cases and develop the corresponding theory.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.91-95
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• 2004

Moments of skew t random vectors and their quadratic forms are derived. It is shown that the moments of the sample autocovariance function and of the sample variogram estimator do not depend on a skewness parameter.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.251-260
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• 2009

In this study, we propose a new estimation method based on autocovariance for selecting optimal estimators of the regression coefficients in the simple linear regression model. Although this method does not seem to be intuitively attractive, these estimators are unbiased for the corresponding regression coefficients. When the exploratory variable takes the equally spaced values between 0 and 1, under mild conditions which are satisfied when errors follow an autoregressive moving average model, we show that these estimators have asymptotically the same distributions as the least squares estimators. Additionally, under the same conditions as before, we provide a self-contained proof that these estimators converge in probability to the corresponding regression coefficients.

• Journal of the Korean Data and Information Science Society
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• v.22 no.5
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• pp.839-847
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• 2011

In this study, we derive an estimator based on autocovariance for the regression coefficients vector in the multiple linear regression model. This method is suggested by Park (2009), and although this method does not seem to be intuitively attractive, this estimator is unbiased for the regression coefficients vector. When the vectors of exploratory variables satisfy some regularity conditions, under mild conditions which are satisfied when errors are from autoregressive and moving average models, this estimator has asymptotically the same distribution as the least squares estimator and also converges in probability to the regression coefficients vector. Finally we provide a simulation study that the forementioned theoretical results hold for small sample cases.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.279-285
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• 2002

In this paper we consider the problem of testing for structural changes in ARIMA models based on a cusum test. In particular, the proposed test procedure is applicable to testing for a change of the status of time series from stationarity to nonstationarity or vice versa. The idea is to transform the time series via differencing to make stationary time series. We propose a graphical method to identify the correct order of differencing.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.209-222
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• 2006

Estimation of the spectral measure, covariance and spectral density functions of a strictly stationary r-vector valued time series is considered, under the assumption that some of the observations are missed. The modified periodograms are calculated using data window. The asymptotic normality is studied.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1071-1086
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• 2004

This paper is concerned with the strong consistency of the estimators of the autocovariance function and the spectral density function for the autoregressive process in the case where only an amplitude modulated process with missing data is observed. These results will give a simple and practical sufficient condition for the strong consistency of those estimators. Finally, some examples are given to illustrate the application of main result.