论文标题
动态时空拱形模型
Dynamic Spatiotemporal ARCH Models
论文作者
论文摘要
地理参考的数据的特征是由于地理位置近接近而固有的空间依赖性。在本文中，我们介绍了动态时空自动回归有条件的异方差（ARC）过程，以描述（i）（i）日志式时列的时间段变量的影响，即时间效应，即时间效应，（ii），（ii）对日志结果的空间延迟，即对日志效果的空间效应，即空间效应，以及（III）的空格lag，以及（IIII）的序列lag，（III）的序列lag。变量，即时空效应，对结果变量的挥发性。此外，我们建议的过程允许在时间和空间中产生固定效果，以解释未观察到的异质性。对于这种动态时空拱形模型，我们根据特定变换的线性和二次矩情况得出了一种广义的矩（GMM）估计器。我们显示了GMM估计器的一致性和渐近正态性，并确定最佳矩函数集。我们在一系列具有不同模型规格和误差分布的蒙特卡洛模拟中研究了所提出的GMM估计量的有限样本特性。我们的仿真结果表明，我们建议的GMM估计量具有良好的有限样品特性。在经验应用中，我们使用1995年至2015年柏林每个邮政编码的平均公寓价格（190个空间单位，240个时间点）的每月日志归还，以证明使用我们建议的模型。我们的估计结果表明，日志方回报的时间，时空和时空滞后滞后对对数回收的波动性具有统计学上的显着影响。
Geo-referenced data are characterized by an inherent spatial dependence due to the geographical proximity. In this paper, we introduce a dynamic spatiotemporal autoregressive conditional heteroscedasticity (ARCH) process to describe the effects of (i) the log-squared time-lagged outcome variable, i.e., the temporal effect, (ii) the spatial lag of the log-squared outcome variable, i.e., the spatial effect, and (iii) the spatial lag of the log-squared time-lagged outcome variable, i.e., the spatiotemporal effect, on the volatility of an outcome variable. Furthermore, our suggested process allows for the fixed effects over time and space to account for the unobserved heterogeneity. For this dynamic spatiotemporal ARCH model, we derive a generalized method of moments (GMM) estimator based on the linear and quadratic moment conditions of a specific transformation. We show the consistency and asymptotic normality of the GMM estimator, and determine the best set of moment functions. We investigate the finite-sample properties of the proposed GMM estimator in a series of Monte-Carlo simulations with different model specifications and error distributions. Our simulation results show that our suggested GMM estimator has good finite sample properties. In an empirical application, we use monthly log-returns of the average condominium prices of each postcode of Berlin from 1995 to 2015 (190 spatial units, 240 time points) to demonstrate the use of our suggested model. Our estimation results show that the temporal, spatial and spatiotemporal lags of the log-squared returns have statistically significant effects on the volatility of the log-returns.
