Exponential Smoothing
It is a very popular technique to produce a smoothed time series. In this statistical scheme the changes in data are detected to produce a smooth data for presentation. Time series data is a sequence of operations. The weights are assigned to the observations where older data is given less relative weight and the newer data is assigned progressively greater weight. There are various smoothing parameters that need to be determined in the case of exponential smoothing. These methods are mostly written as recurrence relations where the next values are calculated from the previous ones. Numeric averaging places equal weights on all the information that has distinct time period. The formula for single exponential smoothing is very simple. This technique is commonly applied to the economic data and is used with any discrete set of measurements. The representation of raw data is done as {xt} and the output of this smoothing algorithm is written as {st}.
This method is also called averaging which is employed in making short-term forecasts. The ‘wait-and-see’ attitude of people is the spontaneous way in which the people use exponential smoothing in their daily living. It works really well for time series without an overall trend. However when the overall trend is not present, the smoothed values tend to lag behind the raw data. The beauty of this technique lies in its simplicity. In single exponential smoothing the entire operation can be done very easily inline, for instance with a simple awk script. The noisy signals from the file called data are read and the original signal is printed out together with the smoothed value. The transient behaviour is minimized at the beginning of time series and the final block is executed for every input line read and the smoothing operation is performed. The weights are adjusted on current values to check the effects of swings in the data.
Written by: Matt
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Tagged as algorithm, awk script, beginning of time, distinct time, economic data, expectancy theory, input line, noisy signals, presentation time, raw data, recurrence relations, relative weight, simplicity, term forecasts, time period, time series data, transient behaviour, Victor Vroom, weights + Categorized as Business, Economy articles, Ladership & Management