• The Journal of the Acoustical Society of Korea
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• v.15 no.2E
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• pp.4-7
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• 1996

In this paper, we propose a formula to compute the exact autocorrelations of the autoregressive (AR) process. For an arbitrary value of N, we first review the Yule-Walker equation and some basic properties of the AR model. We then modify the Yule-Walker equation to construct a new system of N+1 linear equations that can be used to solve for the N+1 autocorrelation coefficients for lags 0, 1, …, N, provided that the AR parameters of order N and the power of the white noise of the AR process are given.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.35 no.3
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• pp.216-222
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• 2002

Autocorrelation in time series data can affect statistical inference in correlation or regression analyses. To improve a regression model from which the residuals are autocorrelated, Yule-Walker method, nonlinear least squares estimation, maximum likelihood method and 'prewhitening' method have been used to estimate the parameters in a regression equation. This study reviewed on the estimation methods of preventing spurious correlation in the presence of autocorrelation and applied the former three methods, Yule-Walker, nonlinear least squares and maximum likelihood method, to a 20-year real data set. Monte carlo simulation was used to compare the three parameter estimation methods. However, the simulation results showed that the mean squared error distributions from the three methods simulated do not differ significantly.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.446-450
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• 1987

In this paper, overdetermined method is used for high resolution spectral estimation in case of short data record length. To reduce the computational effort and to obtain recursive form of estimation algorithm, we modify data matrix to have near-Toeplitz structure. Then, new recursive algorithm is derived in the form of fast Kalman algorithm. Two stage procedure is used for the estimation of ARMA parameters. First AR parameters are estimated by using overdetermined modified Yule-walker equation, and then MA parameters are implicitly estimated by estimating numerator spectral coefficients(NS).

• Industrial Engineering and Management Systems
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• v.1 no.1
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• pp.64-72
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• 2002

In the field of plant maintenance, data that are gathered by sensors on multiple machines are handled and analyzed. Online or pseudo online data handling is required on such fields. When the data occurrence speed exceeds the data handling speed, multiple data should be handled at a time (batch data handling or pseudo online data handling). If l amount of data are received at one time following N amount of data, how to estimate the new parameters effectively is a great concern. A new simplified calculation method, which calculates the N data's weights, is introduced. Numerical examples show that this new method has a fairly god estimation accuracy and the calculation time is less than 1/10 compared with the case when the whole data are re-calculated. Even under the restriction calculation ability in the apparatus is limited, this proposed method makes the failure detection of equipments possible in early stages with a few new coming data. This method would be applicable in many data handling fields.