基于灰色分数阶马尔科夫模型的房价预测

House Price Forecast Based on Grey Fractional Markov Model

摘要: 针对房价数据的非线性性和复杂性的特点，本文结合分数阶累加生成算子和马尔科夫修正模型建立了MKFGM(1,1)模型，并对成都市2017年4月~2018年5月房价进行预测分析。首先，利用粒子群算法在实数域内搜索累加生成算子的最优阶数r，结合GM(1,1)模型可以得到改变阶数后的FGM(1,1)模型，并对成都市房价数据做出初步预测。其次，将预测值与实际值的相对误差进行状态划分，然后使用马尔科夫模型进行误差修正，最终建立MKFGM(1,1)模型。对比分析GM(1,1)、FGM(1,1)和MKFGM(1,1)模型的拟合及预测结果，可以看出MKFGM(1,1)模型在房价预测方面有更高的精度。

Abstract: According to the nonlinearity and complexity of the house price data, this paper combines the fractional-order cumulative generation operator and the Markov correction model to establish the MKFGM(1,1) model, and forecasts and analyzes the house prices of Chengdu from April 2017 to May 1818. Firstly, the particle swarm optimization algorithm is used to search for the optimal order of the cumulative generation operator in the real number domain; combined with the GM(1,1) model, the FGM(1,1) model after changing the order can be obtained; and a preliminary prediction of Chengdu city’s house price is made. Secondly, the relative error between the predicted value and the actual value is divided depending on the states, then the Markov model is used for error correction, and finally the MKFGM(1,1) model is established. Comparing and analyzing the fitting and prediction results of GM(1,1), FGM(1,1) and MKFGM(1,1) models, it can be seen that the MKFGM(1,1) model has a higher accuracy in housing price forecasting.