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| GM(1,1) harmaan ennustemalli× | ARIMA (Autoregressive Integrated Moving Average) -malli× | |
|---|---|---|
| Tieteenala≠ | Pehmeä laskenta | Ekonometria |
| Menetelmäperhe | Regression model | Regression model |
| Syntyvuosi≠ | 1982 | 2015 |
| Kehittäjä≠ | Julong Deng | Box & Jenkins (Box-Jenkins methodology) |
| Tyyppi≠ | Small-sample grey forecasting model | Univariate time-series model |
| Alkuperäislähde≠ | Deng, J. L. (1982). Control problems of grey systems. Systems & Control Letters, 1(5), 288–294. DOI ↗ | Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021 |
| Rinnakkaisnimet≠ | GM(1,1), grey prediction model, grey forecasting, gri tahmin modeli | Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli |
| Liittyvät≠ | 2 | 5 |
| Tiivistelmä≠ | GM(1,1) is the core forecasting model of grey system theory, introduced by Julong Deng in 1982, designed to predict from very few observations and incomplete information — situations where classical time-series models like ARIMA need far more data. It accumulates the raw series to expose a hidden exponential trend, fits a first-order grey differential equation, and projects future values, making it popular in engineering, energy, and management forecasting with short data records. | ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015). |
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