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Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function.Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.
The tracking signal is then used as the value of the smoothing constant for the next forecast. The idea is that when the tracking signal is large, it suggests that the time series has undergone a shift; a larger value of the smoothing constant should be more responsive to a sudden shift in the underlying signal.
Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways: . curve fitting often involves the use of an explicit function form for the result, whereas the immediate results from smoothing are the "smoothed" values with no later use made of a functional form if there is one;
If the smoothing or fitting procedure has projection matrix (i.e., hat matrix) L, which maps the observed values vector to predicted values vector ^ =, then PE and MSPE are formulated as: P E i = g ( x i ) − g ^ ( x i ) , {\displaystyle \operatorname {PE_{i}} =g(x_{i})-{\widehat {g}}(x_{i}),}
These methods are usually applied to short- or intermediate-range decisions. Examples of quantitative forecasting methods are [citation needed] last period demand, simple and weighted N-Period moving averages, simple exponential smoothing, Poisson process model based forecasting [15] and multiplicative seasonal indexes. Previous research shows ...
Exponential smoothing takes into account the difference in importance between older and newer data sets, as the more recent data is more accurate and valuable in predicting future values. In order to accomplish this, exponents are utilized to give newer data sets a larger weight in the calculations than the older sets.
The formula for a given N-Day period and for a given data series is: [2] [3] = = + (()) = (,) The idea is do a regular exponential moving average (EMA) calculation but on a de-lagged data instead of doing it on the regular data.
The default Expert Modeler feature evaluates a range of seasonal and non-seasonal autoregressive (p), integrated (d), and moving average (q) settings and seven exponential smoothing models. The Expert Modeler can also transform the target time-series data into its square root or natural log.