Forecasting Methods Used in ezForecaster
ezForecaster uses several different types of techniques in order to offer the best chance of creating an accurate forecast. These are Best Fit, Curve Fitting (or Regression) Methods, Smoothing Methods, and Seasonal Smoothing Methods. Best Method Firstly, ezForecaster provides the option of automatically sidestepping the issue of which is the best forecasting technique to choose. It does it for you. Select Best Method, and ezForecaster calculates the best-fitting forecast by attempting to fit each technique to the historic data you provide it. This means that ezForecaster chooses the technique that has minimized error. For the calculations ezForecaster uses to choose the Best Method, see the section How ezForecaster Chooses its Best Fit.   Curve Fitting (Regression) Methods Curve Fitting Methods attempt to explain variation using statistical techniques. By providing several methods, ezForecaster has a better opportunity to find a Best Fit forecast. None of these regression methods takes seasonal or cyclical effects into account, and each method weights back data equally. The following methods are available: Linear Regression Exponential Function Power Function Logarithmic Function Parabola Function Gompertz Function Logistic Function   Smoothing Methods Smoothing models attempt to forecast by removing extreme changes in past data. The following methods are available. Moving Average Double Moving Average Percent Difference Single Exponential Smoothing Double Exponential Smoothing Holt's Double Exponential Smoothing Triple Exponential Smoothing Adaptive Smoothing   Seasonal Smoothing Methods Seasonal Smoothing models attempt to forecast a deseasonalized version of past data, and then apply seasonal effects back on the resultant forecast. Additive Decomposition Multiplicative Decomposition Winters' Additive Winters' Multiplicative Annual Moving Average Annual Percent Difference
Curve Fitting Methods
Linear Regression A simple forecasting method that calculates a straight line. By its nature, the straight line it produces suggests that it is best suited to data that is expected to change by the same absolute amount in each time period. The mathematical equation shows that the variable y varies by a constant a and increasing (or decreasing) over time (denoted by t) by factor b. yt = a + bt
Exponential Function This method uses an increasing or decreasing curve rather than the straight line of the Linear Regression method. An exponential method is useful when it is known that there is, or has been, increasing growth or decline in past periods. yt = abt
Power Function This method is similar to Exponential Function, but produces a forecast curve that increases or decreases at a different rate. yt = atb
Logarithmic Function This method is similar to Exponential Function, but uses an alternate logarithmic model. yt = a + b log(t)
Gompertz Function This method attempts to fit a 'Gompertz' or 'S' curve. yt = cabt
Logistic Function This method attempts to fit a 'Logistic' (a.k.a. Pearl-Reed) curve. 1/yt = c + abt
Parabola Function This method attempts to fit a 'Parabolic' (second order polynomial) curve. yt = a + bt +ct2
Smoothing Methods
Moving Average The Moving Average method seeks to smooth out past data by averaging the last several periods and projecting that view forward. ezForecaster automatically calculates the optimal number of periods to be averaged.
Double Moving Average The Double Moving Average method smooth out past data by applying Moving Average twice, smoothing the already smoothed series. ezForecaster automatically calculates the optimal number of periods to be averaged.
Moving Annual Average The Moving Average method seeks to smooth out past data by averaging the last year and projecting it forward.
Percent Difference Percent Difference smoothes out past data by calculating the difference between one period ago versus a varying number of periods ago. Firstly, ezForecaster calculates a one-period difference then a two-period difference until it finds the period difference with the smallest forecast error. yt = yt-1 * yt-1 / yt-1-n   where n is a variable number of periods
Single Exponential Smoothing Single Exponential Smoothing (SES) largely overcomes the limitations of moving averages or percentage change models. It does this automatically by weighting past data with weights that decrease exponentially with time; that is, the more recent the data value, the greater its weighting. Effectively, SES is a weighted moving average system that is best suited to data that exhibits a flat trend. ezForecaster lets you specify a value for the smoothing constant, a, or you can let ezForecaster pick the most appropriate one. St = ayt + (1 - a) St-1 where S represents the 'smoothed estimate' and a the smoothing constant which has a value between 0 and 1
Double Exponential Smoothing Double Exponential Smoothing (DES) applies Single Exponential Smoothing twice. It is useful where the historic data series is not stationary. If we take SES to be: St = ayt + (1 - a) St-1 Then DES is: S''t = aSt + (1 - a) S''t-1 where S represents the 'smoothed estimate' and a the smoothing constant which has a value between 0 and 1
Holt's Double Exponential Smoothing This method (sometimes referred to as Holt-Winters' Non-Seasonal) is similar to regular Exponential Smoothing this technique allows for a different smoothing constant to be used for the second smoothing process.
Triple Exponential Smoothing Triple Exponential Smoothing (TES) applies SES three times. Along with DES, it is useful where the historic data series is not stationary. If we take SES to be: St = ayt + (1 - a) St-1 Then DES is: S''t = aSt + (1 - a) S''t-1 and TES is: S'''t = aS''t + (1 - a) S'''t-1 where S represents the 'smoothed estimate' and a the smoothing constant which has a value between 0 and 1
Adaptive Smoothing This method automatically adjusts its smoothing parameters.
Seasonal Smoothing Methods
Additive Decomposition Additive Decomposition breaks a series into component parts, Trend, Seasonality, Cyclical and Error, determines the value of each, projects them forward and reassembles them to create a forecast. yt = Tt + St + Ct + et T represents the trend component, S the seasonality, C the longterm cycle and e the error NB: Where historic data is less than a typical business cycle - say five to ten years - the Cyclical component is often left out of the calculation.
Multiplicative Decomposition Similar to the Additive method, but this version considers the effects of seasonality to be Multiplicative, that is, growing (or decreasing) over time. yt = Tt x St x Ct + et where T represents the trend component, S the seasonality, C the longterm cycle and e the error
Winters' Additive This advanced exponential smoothing method constructs three statistically related series, which are used to make the actual forecast: the smoothed data series, the seasonal index, and the trend series. This method requires at least two years of back data to calculate a forecast. It is calculated by solving the three 'updating formulas' below. at = a (yt / ct-s) + (1 - a )(at-1 + bt-1) bt = b (at- at-1) + (1 - b ) bt-1 ct = g (yt / at) + (1 - g ) ct-s where s = number of periods per year, a, b and g represent three smoothing constants with values between 0 and 1.
Winters' Multiplicative This advanced exponential smoothing method (a.k.a. Holt-Winters' Seasonal) constructs three statistically related series, which are used to make the actual forecast: the smoothed data series, the seasonal index, and the trend series. This method requires at least two years of back data to calculate a forecast. It is calculated by solving the three 'updating formulas' below. at = a (yt / ct-s) + (1 - a )(at-1 + bt-1) bt = b (at- at-1) + (1 - b ) bt-1 ct = g (yt / at) + (1 - g ) ct-s where s = number of periods per year, a, b and g represent three smoothing constants with values between 0 and 1.
Annual Percent Difference Annual Percent Difference calculates a forecast by calculating the difference from   a year ago versus two years ago. You need a minimum of two years of history for this technique. yt = yt-1 * yt-1-n / yt-1-2n  where n is a variable number of periods
Annual Percent Difference Annual Percent Difference calculates a forecast by calculating the difference from   a year ago versus two years ago. You need a minimum of two years of history for this technique. yt = yt-1 * yt-1-n / yt-1-2n  where n is a variable number of periods