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
(Fitting) 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 bestfitting 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 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:
Smoothing models attempt to forecast by removing extreme changes in past
data. The following methods are available.
Seasonal Smoothing models attempt to forecast a deseasonalized version of past
data, and then apply seasonal effects back on the resultant forecast.

Method Descriptions

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.
y_{t} = a + bt

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.
y_{t} = ab^{t}

This method is similar to Exponential Function, but produces a forecast curve
that increases or decreases at a different rate.
y_{t} = at^{b}

This method is similar to Exponential
Function, but uses an alternate logarithmic model.
y_{t} = a + b log(t)

This method attempts to fit a 'Gompertz' or 'S' curve.
y_{t} = ca^{bt}

This method attempts to fit a 'Logistic' (a.k.a. PearlReed) curve.
1/y_{t} = c + ab^{t}

This method attempts to fit a 'Parabolic' (second order polynomial) curve.
y_{t} = a + bt +ct^{2}


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.

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.


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
oneperiod difference then a twoperiod difference until it finds the period difference
with the smallest forecast error.
y_{t} = y_{t1} * y_{t1}
/ y_{t1n }
where n is a variable number of periods

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.
S_{t} = ay_{t}
+ (1  a) S_{t1}
where S represents the 'smoothed estimate' and a the smoothing constant which has a value between 0 and 1

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: S_{t} = ay_{t}
+ (1  a) S_{t1}
Then DES is: S^{''}_{t}
= aS_{t} + (1  a) S^{''}_{t1}
where S represents the 'smoothed estimate' and a the smoothing constant which has a value between 0 and 1

This method (sometimes referred to as HoltWinters' NonSeasonal) 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 (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: S_{t} = ay_{t}
+ (1  a) S_{t1}
Then DES is: S^{''}_{t}
= aS_{t} + (1  a) S^{''}_{t1}
and TES is: S^{'''}_{t}
= aS^{''}_{t} + (1  a)
S^{'''}_{t1}
where S represents the 'smoothed estimate' and a the smoothing constant which has a value between 0 and 1

This method automatically adjusts its
smoothing parameters.


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.
y_{t} = T_{t} + S_{t} +
C_{t} + e_{t}
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.

Similar to the Additive method, but this version considers the effects of
seasonality to be Multiplicative, that is, growing (or decreasing) over time.
y_{t} = T_{t} x S_{t} x
C_{t} + e_{t}
where T represents the trend component, S the seasonality, C the
longterm cycle and e the error

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.
a_{t} = a (y_{t}
/ c_{ts}) + (1  a )(a_{t1}
+ b_{t1})
b_{t} = b (a_{t}
a_{t1}) + (1  b ) b_{t1}
c_{t} = g (y_{t}
/ a_{t}) + (1  g ) c_{ts}
where s = number of periods per year, a, b and g represent three smoothing constants with values between 0
and 1.

This advanced exponential smoothing method (a.k.a.
HoltWinters' 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.
a_{t} = a (y_{t}
/ c_{ts}) + (1  a )(a_{t1}
+ b_{t1})
b_{t} = b (a_{t}
a_{t1}) + (1  b ) b_{t1}
c_{t} = g (y_{t}
/ a_{t}) + (1  g ) c_{ts}
where s = number of periods per year, a, b and g represent three smoothing constants with values between 0
and 1.

The Moving Average method seeks to smooth out past data by averaging the
number of data periods and projecting it forward.

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.
y_{t} = y_{t1} * y_{t1n}
/ y_{t12n }
where n is a variable number of periods
