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

• Communications for Statistical Applications and Methods
• /
• v.10 no.1
• /
• pp.233-237
• /
• 2003

An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S$^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.67 no.2
• /
• pp.239-247
• /
• 2018

Adaptive Beamforming (ABF) algorithm, which is a typical jammer suppression algorithm, guarantees the performance on the assumption that the jamming characteristics of the TDS (Training Data Sample) are stationary, which are obtained immediately before and after transmitting the pulse signal. Therefore, effective jammer suppression can not be expected when the jamming characteristics are non-stationary. In this paper, we propose a new jammer suppression algorithm, of which power spectrum fluctuates fast. In this case, we assume that the location of the jammer station is fixed during the processing time. By applying the MPM (Matrix Pencil Method) to the jamming signal in TDS, we can estimate jammer parameters such as power and incident angle, of which the power will vary fast in time or range bins after TDS. Though we assume that the jammer station is fixed, the estimated jammer's incident angle has an error due to the noise, which degrades the performance of the jammer suppression as the jammer power increases fast. Therefore, the jammer's incident angle should be re-estimated at each range bin after TDS. By using the re-estimated jammer's incident angle, we can construct new covariance matrix under the non-stationary jamming environment. Then, the optimum weight for the jammer suppression is obtained by inversing matrix estimation method based on the matrix projection with the estimated jammer parameters as variables. To verify the performance of the proposed algorithm, the SINR (signal-to-interference plus noise ratio) loss of the proposed algorithm is compared with that of the conventional ABF algorithm.

• Journal of Broadcast Engineering
• /
• v.8 no.3
• /
• pp.278-287
• /
• 2003

Noise in an image degrades image quality and deteriorates coding efficiency. Recently, various edge-preserving noise filtering methods based on the nonstationary image model have been proposed to overcome this problem. In most conventional nonstationary image models, however, pixels are assumed to be uncorrelated to each other in order not to Increase the computational burden too much. As a result, some detailed information is lost in the filtered results. In this paper, we propose a computationally feasible adaptive noise smoothing algorithm which considers the nonstationary correlation characteristics of images. We assume that an image has a nonstationary mean and can be segmented into subimages which have individually different stationary correlations. Taking advantage of the special structure of the covariance matrix that results from the proposed image model, we derive a computationally efficient FFT-based adaptive linear minimum mean-square-error filter. Justification for the proposed image model is presented and effectiveness of the proposed algorithm is demonstrated experimentally.

• Water for future
• /
• v.28 no.5
• /
• pp.219-233
• /
• 1995

A non-stationary multivariate model is selected in which the mean and variance of rainfall are not temporally or spatially constant. And the rainfall prediction system is constructed which uses the recursive estimation algorithm, Kalman filter, to estimate system states and parameters of rainfall model simulataneously. The on-line, real-time, multivariate short-term, rainfall prediction for multi-stations and lead-times is carried out through the estimation of non-stationary mean and variance by the storm counter method, the normalized residual covariance and rainfall speed. The results of rainfall prediction system model agree with those generated by non-stationary multivariate model. The longer the lead time is, the larger the root mean square error becomes and the further the model efficiency decreases form 1. Thus, the accuracy of the rainfall prediction decreases as the lead time gets longer. Also it shows that the mean obtained by storm counter method constitutes the most significant part of the rainfall structure.

• The Korean Journal of Applied Statistics
• /
• v.21 no.3
• /
• pp.547-560
• /
• 2008

It is well known that spectral density function determines auto-covariance function of stationary time-series data and smoothed periodogram is a consistent estimator of spectral density function. Recently, Kim and Park (2007) showed that smoothed- periodogram based distances performs very well for the classification. In this paper, we introduce classification methods with smoothed periodogram and apply the approaches to the monthly precipitation measurements obtained from January, 1987 through December, 2007 at 22 locations in South Korea.

• Communications for Statistical Applications and Methods
• /
• v.30 no.4
• /
• pp.369-388
• /
• 2023

In this paper, we develop the two-step procedure that detects and estimates the position of structural changes for multivariate nonstationary time series, either on mean parameters or second-order structures. We first investigate the presence of mean structural change by monitoring data through the aggregated cumulative sum (CUSUM) type statistic, a sequential procedure identifying the likely position of the change point on its trend. If no mean change point is detected, the proposed method proceeds to scan the second-order structural change by modeling the multivariate nonstationary time series with a multivariate locally stationary Wavelet process, allowing the time-localized auto-correlation and cross-dependence. Under this framework, the estimated dynamic spectral matrices derived from the local wavelet periodogram capture the time-evolving scale-specific auto- and cross-dependence features of data. We then monitor the change point from the lower-dimensional approximated space of the spectral matrices over time by applying the dynamic principal component analysis. Different from existing methods requiring prior information on the type of changes between mean and covariance structures as an input for the implementation, the proposed algorithm provides the output indicating the type of change and the estimated location of its occurrence. The performance of the proposed method is demonstrated in simulations and the analysis of two real finance datasets.

• Journal of Wetlands Research
• /
• v.20 no.4
• /
• pp.338-344
• /
• 2018

In this study, the surface air temperature (SAT) and the dew-point temperature (DPT) are applied as the covariance of the location parameter among three parameters of GEV distribution to reflect the non-stationarity of extreme rainfall due to climate change. Busan station is selected as the study site and the monthly maximum daily rainfall depth from May to October is used for analysis. Various models are constructed to select the most appropriate co-variate(SAT and DPT) function for location parameter of GEV distribution, and the model with the smallest AIC(Akaike Information Criterion) is selected as the optimal model. As a result, it is found that the non-stationary GEV distribution with co-variate of exp(DPT) is the best. The selected model is used to analyze the effect of climate change scenarios on extreme rainfall quantile. It is confirmed that the design rainfall depth is highly likely to increase as the future DPT increases.

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

• Proceedings of the IEEK Conference
• /
• 2003.07e
• /
• pp.1711-1714
• /
• 2003

The noise in an image degrades image quality and deteriorates coding efficiency of compression. Recently, various edge-preserving noise filtering methods based on the nonstationary image model have been proposed to overcome this problem. In most conventional nonstationary image models, however, pixels are assumed to be uncorrelated to each other In order not to increase the computational burden too much. As a result, some detailed information is lost in the filtered results. In this paper, we propose a computationally feasible adaptive noise smoothing algorithm which considers the nonstationary correlation characteristics of images. We assume that an image has a nonstationary mean and can be segmented into subimages which have individually different stationary correlations. Taking advantage of the special structure of the covariance matrix that results from the proposed image model, we derive a computationally efficient FFT-based adaptive linear minimum mean square error filter. The justification for the proposed image model is presented and the effectiveness of the proposed algorithm is demonstrated experimentally.