variations in one form or another. An example Where xi is the of such a series can be seen in the graph below. This is a sinusoidal signal. Mixed with a random variable.
When analyzing series. We are interested in identifying their structure and assessing all the main components – trend. Seasonality. Noise and other features. As well as the ability to make forecasts of changes in the value in future periods.
When working with series. The presence of germany phone number list noise often makes it difficult to analyze the structure of the series. To eliminate its influence and better see the structure of the series. You can use series smoothing methods.
The simplest method of smoothing a series is a moving average. The idea is that for any odd number of points in a series. Replace the central point with the arithmetic mean of the remaining points:
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Below you can see the result Where xi is the of applying this algorithm to our two series.
By default. We suggest using smoothing with clean data directly translates to higher a window size of 5 points (k in our formula above will be equal to 2). Note that the smoothed signal is no longer so susceptible to the influence of noise. However. Along with the noise. Naturally. Some useful information about the dynamics of the series also disappears. It is also visible. That the smoothed series does not have the first (and also the last) k points. This is due to the fact that smoothing is performed for the central point of the window (in our case. For the third point). After which the window is shifted by one point. And the calculations are repeated. For the second. Random series. I used smoothing with a window equal.
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