, where n is the number of observations.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