以時空模型探討北台灣房地產價格

A Spatial-Temporal Model For House Prices In Northern Taiwan

王昱婷(Yu-Ting Wang)

指導教授 ： 張雅梅

淡江大學/商管學院/統計學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00723

摘要

本研究提出一時空模型來描述房地產價格的時空特性。此時空模型由三個部分組成，分別為總平均函數(global mean function)、一階自我迴歸模型(first-order autoregressive models)及非平穩空間模型(non-stationary spatial model)。模型中總平均函數用來描述房地產價格在空間中整體的平均趨勢；一階自我迴歸模型描述房地產價格時間上的相依性；非平穩空間模型則是描述房地產價格在空間上的相依性。其中，總平均函數可藉由數個基底函數所組成的線性組合來表示，而非平穩空間模型則表達為數個基底函數及數個平穩過程的線性組合。本研究中利用限制最小平方法(constrained least squares)來估計參數，此方法也被稱為正最小絕對壓縮機制(positive Lasso, Efron et al., 2004)，可使選取及估計參數同時進行。本文透過內政部地政司｢不動產實價｣資料，探討自民國101年7月至民國103年5月，台北市、新北市及桃園市45個行政區23個月平均的房地產價格，分析結果顯示，房地產價格在空間上呈現非平穩性質。

關鍵字

房地產價格 ； 時空模型 ； 限制最小平方法 ； 最小角度迴歸演算法 ； 正最小絕對壓縮機制 ； 一階自我迴歸模型

並列摘要

In this paper, a spatial-temporal model is proposed to describe the spatial-temporal distribution of house prices. The proposed model is divided into three parts, a global mean function, first order autoregressive models and a non-stationary spatial model. The global mean function and the non-stationary model are used to characterize the spatial trend and the spatial dependence of house prices, respectively. The temporal dependence of house prices is captured by the autoregressive models. The global mean function is decomposed as a linear combination of some basis functions. The non-stationary model is represented by a linear combination of some basis functions and some stationary processes. A constrained least squares is used to estimate the model parameters. This estimation approach is also known as the positive Lasso (Efron et al., 2004), which can select and estimate parameters simultaneously. The model is applied to 23-month house price data of 45 administrative districts in northern Taiwan. The result presents a non-stationary structures of the house price data.

並列關鍵字

House prices ； Spatial-temporal model ； Constrained least squares ； Least angle regression ； Positive Lasso ； Autoregressive model

參考文獻

Benth, J. c. and Saltyte, L. (2011). Spatial-temporal model for wind speed in Lithuania, Journal of Applied Statistics 38(6): 1151-1168.

Chang, Y.-M., Hsu, N.-J. and Huang, H.-C. (2010). Semiparametric estimation and selection for nonstationary spatial covariance functions, Journal of Conputational and Graphical Statistics 19(1): 117-139.

Chernobai, E., Reibel, M. and Carney, M. (2011). Nonlinear spatial and temporal eff ects of highway construction on house prices, The Journal of Real Estate Finance and Economics 42(3): 348-370.

Finazzi, F., Scott, M. E. and Fass o, A. (2013). A model-based framework for air quality indices and population risk evaluation, with and application to the analysis of Scottish air quality data, Journal of the Royal Statistical Society, series C 62. Part 2.

Hannonen, M. (2008). Predicting urban land prices: A comparison of four approaches, International Journal of Strategic Property Management 12: 217-236. Issue 4.