By Manfred Gerstenfeld
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In the statistical literature, several digital filters are recommended for a wide range of applications. But even with only one filter, it is possible to construct an infinite number of different filters by the superposition of its application. For example, if the time series is smoothed two times, and if each time the smoothing value is the average of the two adjacent terms, it yields This filter is the Tukey filter, whose correlation and spectral characteristics are well-known (Jenkins and Watts, 1968).
5. It is impossible to list all of the smoothing filters that are used in applications. Identification of the filter parameters or construction of a new one is dictated by the statistical character of the observations as well as by the physical features of the problem under consideration. It is important to notice that the unsubstantiated or careless use of the smoothing technique can distort the real information of the observations and result in incorrect conclusions. 12), which show the transformation of the frequency composition of data by the process of smoothing (which is not always desirable).
As this illustration clearly shows, increasing the number of observations to more than 30 does not greatly decrease the point estimate variance (when m < 5). 3 to determine the sample size, which is necessary to obtain estimate (]0 with the required accuracy. The results of this section enable us to evaluate (within a constant factor cr 2 ) the accuracy of the point estimates of the least squares polynomials before making any calculations and estimations. 36)], which gives Cg0 = a2. 2. o estimate on the number of points and on the polynomial degree.