Wavelet-Based Trend Detection and Estimation
نویسندگان
چکیده
where it is assumed that the expected value of X(t) is zero. There is no commonly accepted precise definition for trend, but it is usually spoken of as a nonrandom (deterministic) smooth function representing long-term movement or systematic variations in a series (for example, Priestley (1981) refers to a trend as “. . . a tendency to increase (or decrease) steadily over time . . . [or to] fluctuate in [a] periodic manner,” while Kendall (1973) states that “the essential idea of trend is that it shall be smooth . . . ”). The problem of testing for or extracting a trend in the presence of noise is thus somewhat different from the closely related problem of estimating a function or signal S(t) buried in noise. While the model Y (t) = S(t) +X(t) has the same form as Equation (1), in general S(t) is not constrained to be smooth and thus can very well have discontinuities and/or rapid variations.
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