Grahn, T. A conditional least squares approach to bilinear time series estimation. (English) Zbl 0834.62077 J. Time Ser. Anal. 16, No. 5, 509-529 (1995). Summary: In this paper a conditional least squares (CLS) procedure for estimating bilinear time series models is introduced. This method is applied to a special superdiagonal bilinear model which includes the classical linear autoregressive moving-average model as a particular case and it is proven that the limiting distribution of the CLS estimates is Gaussian and that the law of the iterated logarithm holds. Cited in 14 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators 62M09 Non-Markovian processes: estimation 62E20 Asymptotic distribution theory in statistics Keywords:central limit theorem; conditional moments; Gaussian limiting distribution; Yule-Walker equations; conditional least squares; bilinear time series models; superdiagonal bilinear model; linear autoregressive moving-average model; law of the iterated logarithm PDFBibTeX XMLCite \textit{T. Grahn}, J. Time Ser. Anal. 16, No. 5, 509--529 (1995; Zbl 0834.62077) Full Text: DOI Link References: [1] DOI: 10.1080/02331888908802217 · Zbl 0685.62066 · doi:10.1080/02331888908802217 [2] T. Grahn (1993 ) A new approach to bilinear time series estimation . Ph.D. Thesis , University of Heidelberg. · Zbl 0840.62083 [3] Grahn T., A conditional least squares approach to bilinear time series (1993) · Zbl 0840.62083 [4] Granger C. W., An Introduction to Bilinear Time Series Models. (1978) · Zbl 0379.62074 [5] Guegan D., Scand. J. Statist. 16 pp 129– (1989) [6] Y. J. Jou (1989 ) On the bilinear time series model BL(p, 0, p, 1) . Ph.D. Thesis , University of Pennsylvania. [7] DOI: 10.1080/03610929008830255 · Zbl 0900.62460 · doi:10.1080/03610929008830255 [8] Kim W. K., J. Time Ser. Anal. 11 pp 215– (1990) [9] DOI: 10.1080/15326349908807167 · Zbl 0706.62079 · doi:10.1080/15326349908807167 [10] Liu J., Bilinear (p, 0, 1, 1) model and its consistent identification. Technical report (1990) [11] Mohler R. R., Bilinear Control Processes. (1973) · Zbl 0343.93001 [12] DOI: 10.2307/3213316 · Zbl 0466.62082 · doi:10.2307/3213316 [13] Seasay S. A. O., J. Time Ser. Anal. 9 pp 385– (1988) [14] Seasay S. A. O., J. Time Ser. Anal. 12 pp 159– (1991) [15] Seasay S. A. O., J. Time Ser. Anal. 13 pp 521– (1992) [16] Subba Rao T., An Introduction to Bispectral Analysis and Bilinear Time Series Models. Lecture Notes in Statistics, 24. (1984) · Zbl 0543.62074 [17] Subba Rao T., Statistica Sinica 2 (2) pp 465– (1992) [18] Tang Z., Nonlinear Time Series and Signal Processing (1988) [19] Tjostheim D., Nonlinear time series:a selective review. Preprint No. 694, SFB 123 (1992) [20] Tong H., Non-linear Time Series. (1990) · Zbl 0716.62085 [21] Velleman P., Applications, Basics and Computing of Exploratory Data Analysis. (1981) [22] DOI: 10.1137/0706001 · Zbl 0176.46401 · doi:10.1137/0706001 [23] DOI: 10.1080/02331888908802201 · Zbl 0685.62065 · doi:10.1080/02331888908802201 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.