Time series interval forecast using GM(1,1) and NGBM(1, 1) models

Grey forecast is used for few and uncertain data, and its forecast results have very high accuracy. Although numerous researchers have developed various grey forecasting models, the forecast results of these models are limited to single-point forecast values and cannot provide more valuable information (e.g. possible estimation range) for decision-makers. In order to address this problem, this paper proposes two grey interval forecasting methods: interval GM(1, 1) and interval NGBM(1, 1), for few and uncertain time series data. To evaluate the forecast accuracy of the two grey interval methods, this study took the short-term forecast of the passenger volume of Taiwan High Speed Rail as an example and compared the forecast accuracy of the proposed two methods with that of three current grey forecasting methods. The forecast results showed that the proposed two methods have the highest forecast accuracy among the five grey forecasting methods. The grey interval forecast value provided by the proposed methods can help decision-makers make more accurate judgement within a probable variation range.

[1]  Deng Ju-Long,et al.  Control problems of grey systems , 1982 .

[2]  Robert Ivor John,et al.  Grey sets and greyness , 2012, Inf. Sci..

[3]  Zhiqiang Chen,et al.  Applying the Grey Forecasting Model to the Energy Supply Management Engineering , 2012 .

[4]  Chin-Tsai Lin,et al.  Forecast of the output value of Taiwan's opto-electronics industry using the Grey forecasting model , 2003 .

[5]  Chin-Tsai Lin,et al.  Developing an interval forecasting method to predict undulated demand , 2011 .

[6]  Li-Hsing Shih,et al.  Forecasting of electricity costs based on an enhanced gray-based learning model: A case study of renewable energy in Taiwan , 2011 .

[7]  Diyar Akay,et al.  Grey prediction with rolling mechanism for electricity demand forecasting of Turkey , 2007 .

[8]  J. Deng,et al.  Introduction to Grey system theory , 1989 .

[9]  Daisuke Yamaguchi,et al.  The development of stock exchange simulation prediction modeling by a hybrid grey dynamic model , 2008 .

[10]  Chaohui Wang,et al.  Predicting tourism demand using fuzzy time series and hybrid grey theory. , 2004 .

[11]  Chun-I Chen,et al.  Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate , 2008 .

[12]  Shuo-Pei Chen,et al.  Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1, 1) , 2008 .

[13]  Zuren Feng,et al.  A proposed grey model for short-term electricity price forecasting in competitive power markets , 2012 .

[14]  Chun-I Chen,et al.  Forecasting Taiwan's major stock indices by the Nash nonlinear grey Bernoulli model , 2010, Expert Syst. Appl..

[15]  Der-Chiang Li,et al.  Forecasting short-term electricity consumption using the adaptive grey-based approach—An Asian case , 2012 .

[16]  Hsin-Pin Fu,et al.  Grey theory analysis of online population and online game industry revenue in Taiwan , 2013 .

[17]  Yi Lin,et al.  Grey Information - Theory and Practical Applications , 2005, Advanced Information and Knowledge Processing.

[18]  M. Mao,et al.  Application of grey model GM(1, 1) to vehicle fatality risk estimation , 2006 .

[19]  Chao-Hung Wang,et al.  Using genetic algorithms grey theory to forecast high technology industrial output , 2008, Appl. Math. Comput..

[20]  Fang-Mei Tseng,et al.  Applied Hybrid Grey Model to Forecast Seasonal Time Series , 2001 .