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 independent variable.

Trend Analysis: Uses linear and nonlinear regression with time as the explanatory variable-used where pattern over time.

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 to update.

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 of events.

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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