Correlograms for non-stationary autoregressions

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 68, Issue 4, 2006, Pages 707-720

  Nielsen, Bent ^a,b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b NUFFIELD COLLEGE   (United Kingdom)

Author keywords

Autoregression; Correlogram; Covariogram; Non stationarity; Partial correlogram

Indexed keywords

EID: 33746255365     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2006.00563.x     Document Type: Article

References (27)

1. Bartlett, M. S. (1935) Some aspects of the time-correlation problem in regard to tests of significance. J. R. Statist. Soc., 98, 536-543.
2. Bartlett, M. S. (1946) On the theoretical specification and sampling properties of autocorrelated time-series. J. R. Statist. Soc., suppl., 8, 27-41.
3. Billingsley, P. (1968) Convergence of Probability Measures. New York: Wiley.
4. Box, G. E. P. and Jenkins, G. M. (1970) Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.
5. Box, G. E. P. and Pierce, D. A. (1970) Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. J. Am. Statist. Ass., 65, 1509-1526.
6. Brockwell, P. J. and Davis, R. A. (1996) Introduction to Time Series and Forecasting. New York: Springer.
7. Doornik, J. A. (1999) Object-oriented Matrix Programming using Ox, 3rd edn. London: Timberlake.
8. Doornik, J. A., Hendry, D. F. and Nielsen, B. (1998) Inference in cointegrating models: UK M1 revisited. J. Econ. Surv., 12, 533-572.
9. Engle, R. F. and Granger, C. W. J. (1987) Co-integration and error correction: representation, estimation, and testing. Econometrica, 55, 251-276.
10. Gradshteyn, I. S. and Ryzhik, I. M. (1965) Tables of Integrals, Series and Products. New York: Academic Press.
11. Granger, C. W. J. and Joyeux, R. (1980) An introduction to long-memory time series models and fractional differencing. J. Time Ser. Anal., 1, 15-29.
12. Gujarati, D. N. (1995) Basic Econometrics. New York: McGraw-Hill.
13. Juselius, K. and Mladenović, Z. (2002) High inflation, hyperinflation and explosive roots: the case of Yugoslavia. Copenhagen. Discussion Paper. Institute of Economics, University of Copenhagen, Copenhagen. (Available from http://www.econ.ku.dk/okokj.)
14. Kendall, M. G. (1943) Oscillatory movements in English agriculture (with discussion). J. R. Statist. Soc., 106, 91-124.
15. Kendall, M. G. (1945) On the analysis of oscillatory time-series (with discussion). J. R. Statist. Soc., 108, 93-141.
16. Lai, T. L. and Wei, C. Z. (1983) Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters. J. Multiv. Anal., 13, 1-23.
17. Ljung, G. M. and Box, G. E. P. (1978) On a measure of lack of fit in time series models. Biometrika, 65, 297-303.
18. Nelson, C. R. and Plosser, C. I. (1982) Trends and random walks in macroeconomic time series: some evidence and implications. J. Monet. Econ., 10, 139-162.
19. Nielsen, B. (2001) Order determination in general vector autoregressions. Nuffield College, Oxford. (Available from www.nuf f.ox.ac.uk/Users/Nielsen.)
20. Paulsen, J. and Tjøstheim, D. (1985) On the estimation of residual variance and order in autoregressive time series. J. R. Statist. Soc, B, 47, 216-228.
21. Petrović, P. and Mladenović, Z. (2000) Money demand and exchange rate determination under hyperinflation: conceptual issues and evidence from Yugoslavia. J. Mon. Cred. Bankng, 32, 785-806.
22. Phillips, P. C. B. and Solo, V. (1992) Asymptotics for linear processes. Ann. Statist., 20, 971-1001.
23. Quenouille, M. H. (1947) A large-sample test for the goodness of fit of autoregressive schemes. J. R. Statist. Soc., 110, 123-129.
24. Quenouille, M. H. (1949) Approximate tests of correlation in time-series. J. R. Statist. Soc. B, 11, 68-84.
25. Rothenberg, T. J. (2002) Some elementary distribution theory for an autoregression fitted to a random walk. J. Econometr., 111, 355-361.
26. Wold, H. (1938) A Study in the Analysis of Stationary Time Series. Uppsala: Almqvist and Wiksell.
27. Yule, G. U. (1926) Why do we sometimes get nonsense-correlations between time-series? - a study in sampling and the nature of time-series (with discussion). J. R. Statist. Soc., 89, 1-63.