Forecasting by Smoothing Techniques

This site is a part of the JavaScript E-labs learning objects for decision making. Other JavaScript in this series are categorized under different areas of applications in the MENU section on this page.

Professor Hossein Arsham   

A time series is a sequence of observations which are ordered in time. Inherent in the collection of data taken over time is some form of random variation. There exist methods for reducing of canceling the effect due to random variation. Widely used techniques are "smoothing". These techniques, when properly applied, reveals more clearly the underlying trends.

Enter the time series Row-wise in sequence, starting from the left-upper corner, and the parameter(s), then click the Calculate button for obtaining one-period-ahead forecasting.

Blank boxes are not included in the calculations but zeros are.

In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.

Features of time series, which might be revealed by examining its graph, with the forecasted values, and the residuals behavior, condition forecasting modeling.

Moving Averages: Moving averages rank among the most popular techniques for the preprocessing of time series. They are used to filter random "white noise" from the data, to make the time series smoother or even to emphasize certain informational components contained in the time series.

Exponential Smoothing: This is a very popular scheme to produce a smoothed Time Series. Whereas in Moving Averages the past observations are weighted equally, Exponential Smoothing assigns exponentially decreasing weights as the observation get older. In other words, recent observations are given relatively more weight in forecasting than the older observations. Double Exponential Smoothing is better at handling trends. Triple Exponential Smoothing is better at handling parabola trends.

An exponenentially weighted moving average with a smoothing constant a, corresponds roughly to a simple moving average of length (i.e., period) n, where a and n are related by:

a = 2/(n+1)    OR    n = (2 - a)/a.

Thus, for example, an exponenentially weighted moving average with a smoothing constant equal to 0.1 would correspond roughly to a 19 day moving average. And a 40-day simple moving average would correspond roughly to an exponentially weighted moving average with a smoothing constant equal to 0.04878.

Holt's Linear Exponential Smoothing: Suppose that the time series is non-seasonal but does display trend. Holtís method estimates both the current level and the current trend.

Notice that the simple moving average is special case of the exponential smoothing by setting the period of the moving average to the integer part of (2-Alpha)/Alpha.

For most business data an Alpha parameter smaller than 0.40 is often effective. However, one may perform a grid search of the parameter space, with = 0.1 to = 0.9, with increments of 0.1. Then the best alpha has the smallest Mean Absolute Error (MA Error).

How to compare several smoothing methods: Although there are numerical indicators for assessing the accuracy of the forecasting technique, the most widely approach is in using visual comparison of several forecasts to assess their accuracy and choose among the various forecasting methods. In this approach, one must plot (using, e.g., Excel) on the same graph the original values of a time series variable and the predicted values from several different forecasting methods, thus facilitating a visual comparison.

You may like using the Past Forecasts by Smoothing Techniques JavaScript to obtain the past forecast values based on smoothing techniques that use only single parameter. Holt, and Winters methods use two and three parameters, respectively, therefore it is not an easy task to select the optimal, or even near optimal values by trial-and Ėerrors for the parameters.

The single exponential smoothing emphasizes the short-range perspective; it sets the level to the last observation and is based on the condition that there is no trend. The linear regression, which fits a least squares line to the historical data (or transformed historical data), represents the long range, which is conditioned on the basic trend. Holtís linear exponential smoothing captures information about recent trend. The parameters in Holtís model is levels-parameter which should be decreased when the amount of data variation is large, and trends-parameter should be increased if the recent trend direction is supported by the causal some factors.

Short-term Forecasting: Notice that every JavaScript on this page provides a one-step-ahead forecast. To obtain a two-step-ahead forecast, simply add the forecasted value to the end of you time series data and then click on the same Calculate button. You may repeat this process for a few times in order to obtain the needed short-term forecasts.

Moving Average
Forecast MA Error
Weighted Moving Average
Forecast MA Error
Single, Double, & Triple Exponential Smoothing
Forecast MA Error
Forecast MA Error
Forecast MA Error
Holt's Linear Smoothing
Forecast MA Error

For Technical Details, Back to:
Time Series Analysis and Forecasting Techniques

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Professor Hossein Arsham



Decision Tools in Economics & Finance

Probabilistic Modeling


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Professor Hossein Arsham   

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