GM(1,1) Model (Grey Forecast)

Grey forecast can be used to predict behavior of non-linear time series. This is a non-statistical forecasting method that is particularly effective when the number of observations is insufficient.

Define the observed time series as , where n is the number of observations.

Define the series x(1) in the following way: .

Where:

The GM(1,1) model is defined by a first order differential equation:

The solution can be obtained using the least-squares method:

,

where:

Discrete solution of differential equation:

Then the predicted series is calculated by the formula:

, where k = 2,3,…,n.

See also:

Library of Methods and Models | Modeling Container: Specification of the Grey Forecast Model | Time Series Analysis: Forecasting Using Grey Forecast | IModelling.Greyforecast | ISmGreyForecast