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Tests for the presence of trends in linear processes

Seria
Rozprawy Matematyczne tom/nr w serii: 94 wydano: 1972
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Abstrakty
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CONTENTS
1. Introduction.............................................................................................................................................5
2. Assumptions and notations................................................................................................................6
3. An important asymptotic distribution..................................................................................................8
4. The asymptotic distribution of $K*_{μ, ν}$ under the null hypothesis.........................................14
5. The denominators of the test functions under the alternative hypothesis..................................18
6. The behaviour of $K*_{μ, ν}$ under the alternative hypothesis....................................................22
7. A class of alternative hypotheses for which the $K*_{μ, ν}$ test is consistent..........................23
8. The asymptotic distribution of under the null hypothesis..............................................................26
9. The behaviour of $J*_{μ, ν}$ under alternative hypotheses..........................................................28
10. Orthogonal polynomial.......................................................................................................................33
11. Polynomial trends...............................................................................................................................35
12. Comparisons between the powers of the three tests..................................................................38
13. The asymptotic independence of the three test functions under the null hypothesis............46
14. Numerical illustrations.......................................................................................................................53
References..................................................................................................................................................58
Słowa kluczowe
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Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 94
Liczba stron
58
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom XCIV
Daty
wydano
1972
Twórcy
Bibliografia
  • [1] F. E. Allan, The general form, of the orthogonal polynomials for simple series with proofs of their simple properties, Proc. Roy. Soc. Edinburgh, Sect, A, 50 (1930), pp. 310-320.
  • [2] H. Cramér, Mathematical Methods of Statistics, Princeton University Press 1946.
  • [3] J. H. Farley and M. J. Hinich, Detecting "small" mean shifts in time series, Management Sci. 17 (1970), pp. 189-199.
  • [4] J. H. Farley and M. J. Hinich, A test for a shifting slope coefficient in a linear model, J, Amer. Statist. Assoc., 65 (1970), pp. 1320-1329.
  • [5] M. G. Kendall, Tables of autoregresive series, Biometrika, 36 (1949), pp. 267-289.
  • [6] M. G. Kendall, and A. Stuart, The Advanced Theory of Statistics, vol. 2, London 1961.
  • [7] J. H. Laning, Jr. and R. H. Battin, Random Processes in Automatic Control, New York-Toronto-London 1956.
  • [8] Z. A. Łomnicki and S. K. Zaremba, On some moments and distributions occurring in the theory of linear stochastic processes, I, Monatsh. Math. 61 (1957), pp. 318-358.
  • [9] Z. A. Łomnicki and S. K. Zaremba, On some moments and distributions occurring in the theory of linear stochastic processes, II, Monatsh. Math. 63 (1959), pp. 128-168.
  • [10] E. Pleszczyńska, Further applications of the T* test to time series analysis, Zastosow. Mat. 12 (1971), pp. 33-61.
  • [11] J. Shohat, Théorie générale des polynômes orthogonaux de Tchebichef, Mémor. Sci. Math. 66, Paris 1934.
  • [12] E. T. Whittaker and G. N. Watson, A Course of Modem Analysis, 4th. éd., Cambridge 1940.
  • [13] S. K. Zaremba, Kurtosis and determinate components in linear processes, Rev. Inst. Internat. Statist. 33 (1965), pp. 378-413.
  • [14] S. K. Zaremba, Quartic Statistics in Spectral Analysis in B. Harris (Ed.), Spectral Analysis of Time Series, New York 1967.
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