Polynomial trends in time series |
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Authors: | SK Zaremba |
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Institution: | Yr Hen Ysgol, Aberffrwd, Aberystwyth, Dyfed , Capel Bangor 329, Ffon, SY 23 3 ND, Wales |
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Abstract: | The J* test which was previously proposed by the present author for the detection of a trend in a time series does not depend on any quantitative assumptions, but in the case of a polynomial trend it depends on its degree; if this degree is too high, the test cannot be applied. The author finds a bound of the significance level at which the test can be applied when the sample size, as well as a bound of the degree of the trend, are given. Asymptotic results are used only when we trust the asymptotic distribution of J* under the null hypothesis. |
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Keywords: | Trend time series test function significance level orthogonal polynomials |
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