Statistical Forecasting Methods
Multiple Regression Analysis: Used when
two or more independent factors are involved-widely used for intermediate
term forecasting. Used to assess which factors to include and which to
exclude. Can be used to develop alternate models with different factors.
Nonlinear Regression: Does not assume
a linear relationship between variables-frequently used when time is the
Trend Analysis: Uses linear and nonlinear
regression with time as the explanatory variable-used where pattern over
Decomposition Analysis: Used to identify
several patterns that appear simultaneously in a time series-time consuming
each time it is used-also used to deseasonalize a series
Moving Average Analysis: Simple Moving
Averages-forecasts future values based on a weighted average of past values-easy
Weighted Moving Averages: Very powerful
and economical. They are widely used where repeated forecasts required-uses
methods like sum-of-the-digits and trend adjustment methods.
Adaptive Filtering: A type of moving
average which includes a method of learning from past errors-can respond
to changes in the relative importance of trend, seasonal, and random factors.
Exponential Smoothing: A moving average
form of time series forecasting-efficient to use with seasonal patterns-
easy to adjust for past errors-easy to prepare follow-on forecasts-ideal
for situations where many forecasts must be prepared-several different
forms are used depending on presence of trend or cyclical variations.
Hodrick-Prescott Filter: This is a smoothing
mechanism used to obtain a long term trend component in a time series.
It is a way to decompose a given series into stationary and nonstationary
components in such a way that there sum of squares of the series from
the nonstationary component is minimum with a penalty on changes to the
derivatives of the nonstationary component.
Modeling and Simulation: Model describes
situation through series of equations-allows testing of impact of changes
in various factors-substantially more time-consuming to construct-generally
requires user programming or purchase of packages such as SIMSCRIPT. Can
be very powerful in developing and testing strategies otherwise non-evident.
Certainty models give only most likely outcome-advanced
spreadsheets can be utilized to do "what if" analysis-often
done e.g.; with computer-based spreadsheets.
Probabilistic Models Use Monte Carlo simulation techniques
to deal with uncertainty-gives a range of possible outcomes for each set
Forecasting error: All forecasting
models have either an implicit or explicit error structure, where error
is defined as the difference between the model prediction and the "true"
value. Additionally, many data snooping methodologies within the field
of statistics need to be applied to data supplied to a forecasting model.
Also, diagnostic checking, as defined within the field of statistics,
is required for any model which uses data.
Using any method for forecasting one must use a performance
measure to assess the quality of the method. Mean Absolute Deviation (MAD),
and Variance are the most useful measures. However, MAD doesn't lend itself
to further use making inferences, but that the standard error does. For
the error analysis purposes variance is preferred since variances of independent
(uncorrelated) errors are additive. MAD is not additive.
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