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By Berhane K., Thomas D. C.

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A seasonal effect can also be eliminated by a simple linear filter called seasonal differencing. 4. Two general reviews of methods for seasonal adjustment are Butter and Fase (1991) and Hylleberg (1992). , 1998), which is used for estimating or removing both trend and seasonal variation. It is a fairly complicated procedure that employs a series of linear filters and adopts a recursive approach. Preliminary estimates of trend are used to get preliminary estimates of seasonal variation, which in turn are used to get better estimates of trend and so on.

These topics will be covered in the next two chapters and we will then be in a better position to interpret the correlogram of a given time series. 8 Other Tests of Randomness In most cases, a visual examination of the graph of a time series is enough to see that the series is not random, as, for example, if trend or seasonality is present or there is obvious short-term correlation. However, it is occasionally desirable to assess whether an apparently stationary time series is ‘random’. One type of approach is to carry out what is called a test of randomness in which one tests whether the observations x1,…, xN could have arisen in that order by chance by taking a simple random sample size N from a population assumed to be stationary but with unknown characteristics.

Thus when q=1, the weights are . As q gets large, the weights approximate to a normal curve. A third example is Spencer’s 15-point moving average, which is used for smoothing mortality statistics to get life tables. 6). This moving average aims to follow a cubic polynomial trend without distortion, and the choice of q depends on the degree of irregularity. The symmetric nine-term moving average, for example, is given by The general idea is to fit a polynomial curve, not to the whole series, but to a local set of points.

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