Hongxu Wang

A Set of Three Variables Time Series Prediction Model Based on Difference Method

This paper proposed a set of three variables time series prediction model based on difference method(ASTD). When forecasting the registered number at the University of Alabama in 1971~1992 years, the computer can find prediction model as Fx(0.000004,0.9,0.000004) using automatic optimization search method, which can make the mean square error MSE=0 and the average prediction error rate AFER=0%. For any time series, this prediction accuracy can be obtained, which improved comprehensively the prediction accuracy of the existing fuzzy time series forecasting model. Introduction In year 1993, Song and Chissom[1-3] firstly proposed fuzzy time series prediction model and successfully predicted the registered number at the University of Alabama in year 1971~1992, based on the fuzzy set theory, but the prediction accuracy is not satisfactory. The registered number is shown in table A, and its distribution map is shown in figure 1, that is actually a time series, which is undulating change radically. And Yule proposed the Wolfer’s sunspot numbers firstly in year 1749~1771, as is shown in figure 2, which is undulating change radically, too. Since then, the fuzzy time series forecasting model are emerging[4-9],and the prediction accuracy is constantly improved. Hongxu WANG and Zhenxing WU[4] proposed a set of fuzzy time series forecasting models based on historical data(SD). This model can obtain satisfactory prediction accuracy, which is mean square error MSE=0 and the average prediction error rate of AFER=0% when it predicted the registered number at the University of Alabama in year 1971~1992. This paper prosed a set of prediction model based on three element time difference sequence (ASTD). The set of prediction model was expanded, there are more prediction models can obtain satisfactory prediction accuracy, which is MSE=0 and AFER=0% when it predicted the registered number at the University of Alabama in year 1971~1992. Figure 1. Distribution of enrollment numbers of Alabama University in year 1971~1992. 1200

The Set of Ternary Time Series Forecasting Models Based on the Difference

The set of ternary time series forecasting models based on difference is proposed (STD). For a time series, it can select the best time series forecasting model in STD by using the automatic optimal search method. For example, when forecast enrollments data of University of Alabama in 1971~1992, can select the best time series forecasting model Fq(0.000004,0.9,0.000004) in STD by using the automatic optimal search method, and can gain the MSE=0 and AFER=0%. Increasing the best time series forecasting models’ numbers of STD which forecast accuracy reaches its peak.

A Set of Ternary Time Series Forecasting Models Based on the Difference Rate

A set of ternary time series forecasting models based on the difference rate (ASTDR) is proposed. For an arbitrary time series, we can apply automatic optimization search method to sieve the ordinary time series forecasting model in ASTDR. For example, when simulating the prediction of the enrollments of University of Alabama in 1971–1992, we can apply automatic optimization search method to sieve the ordinary time series forecasting model Ft(0.000003,0.7, 0.000003) in ASTDR. The mean square error (MSE) and the average forecasting error rate (AFER) of the predicted values of the enrollments can reach MSE=0 and AFER=0%. The prediction accuracy of simulating the prediction of historical data of time series reaches the most ideal level.

The Set of Fuzzy Time Series Forecasting Models Based on the Ordered Difference Rate

Song and Chissom established fuzzy time series forecasting model in 1993. Stevenson and Porter improved the forecasting model of Jilani, Burney, and Ardil in 2009, and researched the forecasting problem of enrollments of the University of Alabama 1971–1992. Although they obtained the best prediction accuracy by 2009, the prediction accuracy was still not ideal. In this paper, we improved the forecasting model of Stevenson and Porter, and got the SFBODR (The Set of Fuzzy Time Series Forecasting Models Based on the Ordered Difference Rate). The forecasting model SFBODR(0.00004, 0.00003) can get the ideal state of AFER(Average Forecasting Error Rate) = 0% and MSE(Mean Square Error) = 0 in forecasting the enrollments of the University of Alabama. Keywords-fuzzy time series forecasting method; fuzzy number function of SFBODR; inverse fuzzy number function of SFBODR; forecasting function of SFBODR

Set of Fuzzy Time Series Forecasting Models Based on the Difference Rate

Song & Chissom introduced the concept of fuzzy time series in 1993[1], and many fuzzy time series methods have been proposed, however, the prediction accuracy is not high, among which, Jilani, Burney and Ardil (2007) proposed prediction model has achieved a high accuracy. This paper improves their predicted model, and proposed the set of fuzzy time series forecasting models Based on the difference rate, simplified as SFBDR, it contains the predicted model SFBDR (0.000001, 0.000003) and SFBDR (0.000003, 0.000001), in the historical enrollment of University of Alabama it can get the highest predicted accuracy of AFER=0% and MSE=0. Keywords-fuzzy time series forecasting method; SFBDR fuzzy number function; SFBDR inverse fuzzy number function; SFBDR Predicted function

A Set of Time Series Prediction Models Based on Difference Method

This paper proposed a set of time series prediction models based on difference method(ASD). For a time series, the computer can automatically find the time series search method to filter out the ideal in ASD prediction model. For example, the forecast number of registered at the University of Alabama in 1971~1992 years, the ideal forecasting model is Aj (0.000003,0.000003), which can make the mean square error MSE=0 and the average prediction error rate AFER=0%, that thoroughly solve the unsatisfactory prediction accuracy of the existing fuzzy time series forecasting model. Keywords-differential rate; a set of time series prediction models; ASDs sum of fraction functions Kj (U, V)

A Set of Time Series Forecasting Models Based on the Ordered Difference

A set of time series forecasting models based on the ordered difference of historical data (ASOD) is proposed. For a time series, the automatic optimization search method can be applied to sieve standard time series forecasting model Cp(k,h) in ASOD, so that in simulating the prediction of historical data of the time series, the predicted values can reach AFER (Average Forecasting Error Rate) = 0% and MSE (Mean Square Error) = 0. For instance, for the enrollment of the University of Alabama in 1971–1992, the automatic optimization search method can be applied to sieve standard time series forecasting model Cp(0.0003,0.0003), the problem that the prediction accuracy of fuzzy time series forecasting model is not ideal for many years has been solved. Keywords-time series; automatic optimization search method; the fractional sum function of ASOD; the inverse function of fractional sum function of ASOD; the forecasting function of ASOD

A Set of Time Series Forecasting Model Based on the Difference

A set of time series forecasting models based on difference is proposed (SD). For a time series, it can select the best time series forecasting model in SD by using the automatic optimal search method. For example, when forecast enrollments data of University of Alabama in 1971~1992, it can select the best time series forecasting model Dq(0.000003,0.000003) in SD by using the automatic optimal search method, and can gain the MSE=0 and AFER=0%. The fact that the prediction accuracy of the existing fuzzy time series prediction model is not very high has been fundamentally improved. Keywords-the difference; the function Xq(s,t) of SD’s sum of fraction; the inverse function Zq(s,t) of SD’s sum of fraction; the prediction function Dq(s,t) of SD; time series