Showing papers on "Partial autocorrelation function published in 1981"
TL;DR: In this article, an extension of the partial autocorrelation function, which is called the generalized partial auto-correlation function (GAPF), is proposed for ARMA model identification.
Abstract: This paper investigates an extension of the partial autocorrelation function, which we call the generalized partial autocorrelation function. These generalized partial autocorrelations, which are not true correlations except when p = 0, are useful in examining the relationship between the S array method of Gray, Kelley, and McIntire (1978) and the Box-Jenkins approach to ARMA model identification. Also, the generalized partial autocorrelation is shown to be a useful model identification tool to be used along with the S array. Also discussed is a reformating of the S array into a shifted S array that the authors believe is easier to use in practice than the S array. The methods of this paper are illustrated by means of examples, including an analysis of the Makridakis (1978) metals series data.
76 citations
TL;DR: In this article, the authors develop approximate variances of the sample space-time autocorrelation function when the underlying process is white noise, which are needed to test significance of the observed autocorerelations.
Abstract: SUMMARY An important part of the diagnostic checking of space-time autoregressive moving average (STARMA) models is testing the temporal independence of the residuals. In the context of the three-stage modelling procedure,. such a test is based on the sample space-time autocorrelation function. This paper developes approximate variances of the sample space-time autocorrelation function when the underlying process is white noise, which are needed to test significance of the observed autocorrelations.
27 citations
TL;DR: In this article, the asymptotic probability of selecting the correct order tends to 1 as the number of the variates becomes large, and the distribution of the order selected by Akaike's information criterion is derived.
Abstract: First, statistical properties of partial autocorrelation matrices of multivariate autoregressive processes are briefly reviewed. Then, using the result, we derive the asymptotic distribution of the order selected by Akaike's information criterion. Contrary to our intuition, the asymptotic probability of selecting the correct order tends to 1 as the number of the variates becomes large.
7 citations
1 citations
Patent•
12 Oct 1981
TL;DR: In this article, the autocorrelation function operator was used to reduce the memory capacity of a partial auto-correlation type analyzer by using the deformation of equation I (where; gamma=0-P, Wt is window function, xt 0+t is sampling value, and n is window length).
Abstract: PURPOSE:To reduce a memory capacity required for operation remarkably, by multiplying window functions duplicated each other and operating autocorrelation function, in obtaining the autocorrelation function, in an autocorrelation function operator for a partial autocorrelation type analyzer. CONSTITUTION:The said operation device can reduce the memory capacity by devising the operation means to obtain Ugamma by using the deformation of equation I (where; gamma=0-P, Wt is window function, xt0+t is sampling value, and n is window length) as equation II. In the autocorrelation function operator as shown in Figure, since the windows are overlapping each other, the window functions overlapped are multiplied and the respective autocorrelation is obtained, allowing to obtain the autocorrelation function Ugamma. Thus, by operating the autocorrelation function like this, the number of samples for periodic operation can be reduced to about a half the sample number corresponding to the window length of the register 4. Thus, the memory capacity is reduced to about 1/3.
1 citations