“…In econometrics, forecasting economic or financial time series in an accurate and robust fashion has been the focus of many different researchers and practitioners. Some fundamental time series models, such as the autoregressive (AR), vector autoregressive (VAR), vector error correction (VEC) and a wide spectrum of their extensions and variations, have been investigated for various forecasting purposes and uses (Shimizu et al , 2006; Xu, 2018e; Kim et al , 2007; Xu, 2017c; Zohrabyan et al , 2008; Xu, 2014a; Hyvärinen et al , 2010; Xu, 2019c; Cabrera et al , 2011; Xu and Zhang, 2022i; Kawahara et al , 2011; Xu and Thurman, 2015a; Kouwenberg and Zwinkels, 2014; Xu, 2017a; Webb et al , 2016; Xu, 2017b; Wei and Cao, 2017; Xu, 2018b; Yang et al , 2018; Xu, 2019a; Liu and Wu, 2020; Xu, 2020; Milunovich, 2020; Xu and Zhang, 2021c; Silver and Goode, 1990; Xu and Zhang, 2023d; McGough and Tsolacos, 1995; Xu and Zhang, 2023j; Brooks and Tsolacos, 2000; Jackson, 2001; West and Worthington, 2006; Panagiotidis and Printzis, 2016; Gençay and Yang, 1996; Gencay and Yang, 1996; Glennon et al , 2018; Guo, 2020; Mei and Fang, 2017; Hepşen and Vatansever, 2011; Baroni et al , 2005). Recently, many machine learning approaches and algorithms, such as the neural network (NN), regression tree, nearest neighbor, support vector regression, random forest, bagging, ensemble learning, boosting and deep learning, have been found to be useful and promising tools to various forecasting problems regarding housing prices (Li et al , 2009; Wu et al , 2009; Gu et al , 2011; Wang et al , 2014; Park and Bae, 2015; Plakandaras et al , 2015; Rafiei and Adeli, 2016; Chen et al , 2017; Fu, 2018; Yu et al , 2018; Liu and Liu, 2019; Shahhosseini et al , 2019; Huang, 2019; Li et al , 2020; Yan and Zong, 2020; Milunovich, 2020; Pai and Wang, 2020…”