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DATA SMOOTHING
This makes use of an algorithm to remove noise from a data set there by allowing important patterns to stand out.
It can be performed in a variety of different ways that is by including a random and random walk. It is also done using moving average and simple exponential as well as linear exponential and seasonal exponential smoothing.
It is mainly used to help predict trends such as trends in securities prices. These techniques eliminate "noise" and extract real trends as well as the patterns, below are some of the available smoothing methods.
Random which is considered as the best method as each period's data has no relationship to the patterns in the previous data. The best prediction for the next value in a series is made by simply taking the average of all previous data points which is represented as follows
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Random Walk
The method of random walk exists if the next data point is equal to the last data point plus some random deviation as many financial securities move in this manner. The best prediction for the next value in a series is just the last value which is represented as follows
Moving Average
The method of moving average works well if the data contains no trend or cyclic pattern which is represented as follows
Where n is a user-supplied constant which is greater than zero defining the number of consecutive points to average where the higher values cause greater smoothing.
Simple Exponential Smoothing
The method of Simple Exponential Smoothing works well if the data contains no trend or cyclic pattern. The most recent data points are more significant than earlier points which are represented as follows
Where a is the smoothing constant.
Linear Exponential Smoothing
The Linear Exponential Smoothing is method that works well if the data contains a trend but no cyclic pattern which is represented as follows
Where a can be level smoothing constant and b can be trend smoothing constant.
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Seasonal Exponential Smoothing (Winter's method)
The method of Seasonal Exponential Smoothing works well if the data contains a trend and a cyclic pattern which is represented as follows
Where a is the level smoothing constant, is the trend smoothing constant c is the seasonal smoothing constant, and p is the season period.
