Efficient use of higher-lag autocorrelations for estimating autoregressive processes

Journal of Time Series Analysis

Volumn 23, Issue 3, 2002, Pages 287-312

  Broze, Laurence ^a   Francq, Christian ^b   Zakoïan, Jean Michel ^a  

^a UNIV LILLE   (France)

^b UNIVERSITÉ DU LITTORAL CÔTE D OPALE   (France)

Author keywords

Autoregressive process; Efficiency gains; Empirical autocorrelations; Yule Walker estimator

Indexed keywords

EID: 0040673658     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00265     Document Type: Article

References (20)

1. 1 BERLINET, A. and FRANCQ, C. (1997) On Barlett's formula for non‐linear processes. Journal of Time Series Analysis 18, 535–52.DOI: 10.1111/1467-9892.00067
2. 2 BROCKWELL, P. J. and DAVIS, R. A. (1991) Time Series: Theory and Methods. New York: Springer‐Verlag.
3. 3 CHANDA, K. C. (1996) Asymptotic properties of estimators for autoregressive models with errors in variables. The Annals of Statistics 24, 423–30.
4. 4 DEMPSTER, A. P., LAIRD, N. M. and RUBIN, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc., Ser. B 39, 1–38.
5. 5 DEVIJVER, P. A. (1986) Causal Markovian models of contextual information in speech and images. Proceedings of ICPR‐86, Paris, 115–48.
6. 6 FRANCQ, C. and ZAKOÏAN, J. M. (1998) Estimating linear representations of nonlinear processes. Journal of Statistical Planning and Inference 68, 145–65.DOI: 10.1016/S0378-3758(97)00139-0
7. 7 HAMILTON, J. D. (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–84.
8. 8 HELSTROM, C. W. (1996) Calculating the distribution of the serial correlation estimator by saddlepoint integration. Econometric Theory 12, 458–80.
9. 9 IBRAGIMOV, I. A. (1962) Some limit theorems for stationary processes. Theory of Probability and Applications 7, 349–82.
10. 10 KREISS, J. P. (1987) On adaptive estimation in stationary ARMA processes. The Annals of Statistics 15, 112–33.
11. 11 LE CAM, L. (1960) Locally asymptotically normal families of distributions. University of California Publications in Statistics 3, 27–98.
12. 12 MANN, H. B. and WALD, A. (1943) On the statistical treatment of linear stochastic differential equations. Econometrica 11, 173–200.
13. 13 MÉLARD, G., PAESMANS, M. and ROY, R. (1991) Consistent estimation of the asymptotic covariance structure of multivariate serial correlations. Journal of Time Series Analysis 12, 351–61.
14. 14 ROBINSON, P. M. (1977) Estimating variances and covariances of sample autocorrelations and autocovariances. Australian Journal of Statistics 19, 236–40.
15. 15 ROMANO, J. P. and THOMBS, L. A. (1996) Inference for autocorrelations under weak assumptions. Journal of the American Statistical Association 91, 590–600.
16. 16 STOCKIS, J. P. and TONG, H. (1998) On the statistical inference of a machine‐generated AR(1) model. J. Roy. Statist. Soc., Ser. B 60, 781–96.
17. 17 SWENSEN, A. R. (1985) The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. Journal of Multivariate Analysis 16, 54–70.
18. 18 WALKER, G. (1931) On periodicity in series of related terms. Proceedings of the Royal Society of London A131, 518–32.
19. 19 WHITE, J. S. (1958) The limiting distribution of the serial correlation coefficient in the explosive case. Annals of Mathematical Statistics 29, 1188–97.
20. 20 YULE, G. U. (1927) On a method of investigating periodicities in disturbed series, with special reference to Wolfer's sunspot numbers. Philosophical Transactions, Royal Society of London A226, 267–98.