Modelling price paths in on-line auctions: smoothing sparse and unevenly sampled curves by using semiparametric mixed models

Summary.  On-line auctions pose many challenges for the empirical researcher, one of which is the effective and reliable modelling of price paths. We propose a novel way of modelling price paths in eBay's on-line auctions by using functional data analysis. One of the practical challenges is that the functional objects are sampled only very sparsely and unevenly. Most approaches rely on smoothing to recover the underlying functional object from the data, which can be difficult if the data are irregularly distributed. We present a new approach that can overcome this challenge. The approach is based on the ideas of mixed models. Specifically, we propose a semiparametric mixed model with boosting to recover the functional object. As well as being able to handle sparse and unevenly distributed data, the model also results in conceptually more meaningful functional objects. In particular, we motivate our method within the framework of eBay's on-line auctions. On-line auctions produce monotonic increasing price curves that are often correlated across auctions. The semiparametric mixed model accounts for this correlation in a parsimonious way. It also manages to capture the underlying monotonic trend in the data without imposing model constraints. Our application shows that the resulting functional objects are conceptually more appealing. Moreover, when used to forecast the outcome of an on-line auction, our approach also results in more accurate price predictions compared with standard approaches. We illustrate our model on a set of 183 closed auctions for Palm M515 personal digital assistants.     

网上拍卖竞买者出价水平的动态演变模式研究

网上拍卖是将传统拍卖与网络相结合的一种新商务模式,是对资源进行有效配置的一种市场机制。尽管有关参与者行为的研究是网上拍卖中的一个重要论题,但是国际上鲜有文献从统计视角对竞买者出价水平的动态演变模式及其变异性进行研究。本文利用函数性数据分析方法及基于MatLab编写的计算程序,对从eBay网站收集到的27个拍卖子类的出价数据进行了分析,结果显示竞买者出价水平的动态演变呈现“c”形模式且其形状随 拍卖的不同特征而变化,“c”形模式变异的两个主要方式是“前期变化”和“后期变化”,其显著变异的时段是拍卖的早期阶段。本文为网上拍卖问题的实证研究引入了新方法并提供了技术支持,所得结论丰富和发展了现有相关研究文献的结论。     

基于函数性数据方法的艺术品网上拍卖竞买者出价水平影响因素研究

在分析互联网艺术品拍卖中竞买者出价水平特有影响因素的基础上,运用函数性相平面图与线性回归方法,探究出价水平及各影响因素在整个拍卖期间的动态变化情况。结果表明,在拍卖的不同阶段,推动竞买者出价水平变化的影响因素各有不同,且作用大小与作用方向在整个拍卖期间不断变化。特别指出,拍卖次序在整个拍卖期间对出价水平具有正向影响,且作用程度随着拍卖的进行逐渐增强,即序号越大、越晚参与竞拍的艺术品的最终成交金额越大。     

Bayesian comparison of private and common values in structural second-price auctions

Private and common values (CVs) are the two main competing valuation models in auction theory and empirical work. In the framework of second-price auctions, we compare the empirical performance of the independent private value (IPV) model to the CV model on a number of different dimensions, both on real data from eBay coin auctions and on simulated data. Both models fit the eBay data well with a slight edge for the CV model. However, the differences between the fit of the models seem to depend to some extent on the complexity of the models. According to log predictive score the IPV model predicts auction prices slightly better in most auctions, while the more robust CV model is much better at predicting auction prices in more unusual auctions. In terms of posterior odds, the CV model is clearly more supported by the eBay data.     

Random-Time Aggregation in Partial Adjustment Models

Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis of the hierarchical Gaussian common value model with stochastic entry introduced by Bajari and Hortaçsu. A key component of our approach is an accurate and easily interpretable analytical approximation of the equilibrium bid function, resulting in a fast and numerically stable evaluation of the likelihood function. We extend the analysis to situations with positive valuations using a hierarchical gamma model. We use a Bayesian variable selection algorithm that simultaneously samples the posterior distribution of the model parameters and does inference on the choice of covariates. The methodology is applied to simulated data and to a newly collected dataset from eBay with bids and covariates from 1000 coin auctions. We demonstrate that the Bayesian algorithm is very efficient and that the approximation error in the bid function has virtually no effect on the model inference. Both models fit the data well, but the Gaussian model outperforms the gamma model in an out-of-sample forecasting evaluation of auction prices. This article has supplementary material online.     

Modelling concurrency of events in on-line auctions via spatiotemporal semiparametric models

Summary.  We introduce a semiparametric approach for modelling the effect of concurrent events on an outcome of interest. Concurrency manifests itself as temporal and spatial dependences. By temporal dependence we mean the effect of an event in the past. Modelling this effect is challenging since events arrive at irregularly spaced time intervals. For the spatial part we use an abstract notion of 'feature space' to conceptualize distances among a set of item features. We motivate our model in the context of on-line auctions by modelling the effect of concurrent auctions on an auction's price. Our concurrency model consists of three components: a transaction-related component that accounts for auction design and bidding competition, a spatial component that takes into account similarity between item features and a temporal component that accounts for recently closed auctions. To construct each of these we borrow ideas from spatial and mixed model methodology. The power of this model is illustrated on a large and diverse set of laptop auctions on eBay.com. We show that our model results in superior predictive performance compared with a set of competitor models. The model also allows for new insight into the factors that drive price in on-line auctions and their relationship to bidding competition, auction design, product variety and temporal learning effects.     

Interregional Price Difference in the New Orleans Auctions Market for Slaves

Our article investigates the variation of winning bids in slave auctions held in New Orleans from 1804 to 1862. Specifically, we measure the variation in the price of slaves conditional on their geographical origin. Previous work using a regression framework ignored the auction mechanism used to sell slaves. This introduced a bias in the conditional mean of the winning bid because it depended on the number of bidders participating in the auction. Unfortunately, the number of bidders is unobserved by the econometrician.We adopt the standard framework of a symmetric independent private value auction and propose an estimation strategy to attempt to deal with this omitted variable bias. Our estimate of the mean number of bidders doubled from 1804 to 1862. We find the number of bidders had a significant positive effect on the average winning bid. An increase from 20 to 30 bidders in an auction raised the average winning bid by around 10%%. The price variation according to the geographical origin of slaves found in earlier work continues to persist after accounting for the omitted variable. We also find a new result that a considerable premium is paid for slaves originating from New Orleans. However, this price variation disappears once we account for regional productivity differences.     

股指期货信息内含股价变动信息的挖掘 ――小波框架与支持向量回归的金融建模应用

 内容提要：中国股指期货的推出指日可待，交易者多了一种投资工具的同时也带来了新的风险。建立准确的金融时间序列预测模型是逐利及避险的方法之一，一直是学者专家研究的热点。本研究结合小波转换与支持向量回归，提出一个二阶段时间序列预测模型。先以离散小波框架将预测变量分解成不同尺度的多个子序列，揭示隐藏在预测变量内的信息，再以支持向量回归为工具，以这些子序列为预测变量建构SVR模型。本研究以日经225指数开盘价为预测目标，以期货开盘价为预测变量对模型进行实证研究，结果显示，该模型的预测绩效比单纯SVR模型及随机漫步模型好。未来可尝试以不同的基底函数作进一步研究。     

Integrated-Quantile-Based Estimation for First-Price Auction Models

This article considers nonparametric estimation of first-price auction models under the monotonicity restriction on the bidding strategy. Based on an integrated-quantile representation of the first-order condition, we propose a tuning-parameter-free estimator for the valuation quantile function. We establish its cube-root-n consistency and asymptotic distribution under weaker smoothness assumptions than those typically assumed in the empirical literature. If the latter are true, we also provide a trimming-free smoothed estimator and show that it is asymptotically normal and achieves the optimal rate of Guerre, Perrigne, and Vuong (2000). We illustrate our method using Monte Carlo simulations and an empirical study of the California highway procurement auctions. Supplementary materials for this article are available online.     

基于大数据的碳价预测

为了研究大数据是否能够帮助我们预测碳排放权价格,本文讨论了结构化数据和非结构化信息对预测碳价所起的作用。结构化数据选取了国际碳现货价格、碳期货价格和汇率,非结构化信息选择百度搜索指数和媒体指数。考虑到当解释变量很多时,平等对待每一个解释变量是不合理的,所以提出了网络结构自回归分布滞后（ADL）模型,在参数估计和变量选择的同时兼顾了解释变量之间的网络关系。实证分析表明,网络结构ADL模型明显优于其他模型,可以获得较高的预测准确性,更适合基于大数据的预测。     

A multilevel model with autoregressive components for the analysis of tribal art prices

In this paper, we introduce a multilevel model specification with time-series components for the analysis of prices of artworks sold at auctions. Since auction data do not constitute a panel or a time series but are composed of repeated cross-sections, they require a specification with items at the first level nested in time-points. Our approach combines the flexibility of mixed effect models together with the predicting performance of time series as it allows to model the time dynamics directly. Model estimation is obtained by means of maximum likelihood through the expectation–maximization algorithm. The model is motivated by the analysis of the first database ethnic artworks sold in the most important auctions worldwide. The results show that the proposed specification improves considerably over classical proposals both in terms of fit and prediction.     

Functional Autoregression for Sparsely Sampled Data

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with nonnegligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation process, with broader applicability and improved computational efficiency over standard Gaussian process models. We prove finite-sample forecasting and interpolation optimality properties of the proposed model, which remain valid with the Gaussian assumption relaxed. An efficient Gibbs sampling algorithm is developed for estimation, inference, and forecasting, with extensions for FAR(p) models with model averaging over the lag p. Extensive simulations demonstrate substantial improvements in forecasting performance and recovery of the autoregressive surface over competing methods, especially under sparse designs. We apply the proposed methods to forecast nominal and real yield curves using daily U.S. data. Real yields are observed more sparsely than nominal yields, yet the proposed methods are highly competitive in both settings. Supplementary materials, including R code and the yield curve data, are available online.     

网上拍卖中竞买者出价数据的特征及分析方法研究

在传统统计分析中，研究者面对的数值型数据有三种形式，即横截面数据、时间序列数据以及混合数据。这些类型的数据具有离散、等间隔分布、密度均匀等特点，它们是传统的描述性统计和推断性统计中最主要的数据分析对象。然而，从拍卖网站收集到的诸如竞买者出价等数据，却不具备这些特点，对传统统计分析方法提出了挑战。因此需要从数据容量、数据的混合性、不等间隔分布及数据密度等方面，对网上拍卖数据的产生机制进行阐释，对其特征进行分析，并结合实际网上拍卖资料给出分析此类数据的方法和过程。     

Beta seasonal autoregressive moving average models

In this paper, we introduce the class of beta seasonal autoregressive moving average (βSARMA) models for modelling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta autoregressive moving average models [Rocha AV and Cribari-Neto F. Beta autoregressive moving average models. Test. 2009;18(3):529–545] by incorporating seasonal dynamics to the model dynamic structure. Besides introducing the new class of models, we develop parameter estimation, hypothesis testing inference, and diagnostic analysis tools. We also discuss out-of-sample forecasting. In particular, we provide closed-form expressions for the conditional score vector and for the conditional Fisher information matrix. We also evaluate the finite sample performances of conditional maximum likelihood estimators and white noise tests using Monte Carlo simulations. An empirical application is presented and discussed.     

Short-Term GDP Forecasting With a Mixed-Frequency Dynamic Factor Model With Stochastic Volatility

In this article, we develop a mixed frequency dynamic factor model in which the disturbances of both the latent common factor and of the idiosyncratic components have time-varying stochastic volatilities. We use the model to investigate business cycle dynamics in the euro area and present three sets of empirical results. First, we evaluate the impact of macroeconomic releases on point and density forecast accuracy and on the width of forecast intervals. Second, we show how our setup allows to make a probabilistic assessment of the contribution of releases to forecast revisions. Third, we examine point and density out of sample forecast accuracy. We find that introducing stochastic volatility in the model contributes to an improvement in both point and density forecast accuracy. Supplementary materials for this article are available online.     

Modeling Financial Return Dynamics via Decomposition

While the predictability of excess stock returns is detected by traditional predictive regressions as statistically small, the direction-of-change and volatility of returns exhibit a substantially larger degree of dependence over time. We capitalize on this observation and decompose the returns into a product of sign and absolute value components whose joint distribution is obtained by combining a multiplicative error model for absolute values, a dynamic binary choice model for signs, and a copula for their interaction. Our decomposition model is able to incorporate important nonlinearities in excess return dynamics that cannot be captured in the standard predictive regression setup. The empirical analysis of U.S. stock return data shows statistically and economically significant forecasting gains of the decomposition model over the conventional predictive regression.     

The determinants of price in online auctions: more evidence from unbalanced panel data

This study provides an alternative approach that takes account of the unobserved effects of each seller under a sample selection framework while using online auction data. We use data collected from Yahoo! Kimo Auction (Taiwan) to demonstrate that earlier empirical results of online auction studies may be biased due to violating the assumption of independence of the error terms between sample observations. Empirical findings show that seller reputation is no longer as the most important factor for buyers to bid on items, while the sample data confirm the unobserved heterogeneity of sellers and sample selection problem.     

基于Boosting-ARMA的碳价预测

自回归滑动平均(ARMA)模型是最流行的预测模型之一,而模型选择却是使用ARMA进行预测的难点,尤其是当真实模型的阶数较高时,因此提出Boosting-ARMA预测算法,利用Boosting算法进行最优子集ARMA寻找,自动且高效地完成ARMA模型的识别。模拟实验显示,Boosting-ARMA优于其他方法,用新算法预测碳价实证分析发现,Boosting-ARMA算法可以获得较高的碳价预测准确性并且方便快捷。     

双效应面板ELES模型的构建与实证研究

本文在拓展ELES模型传统假设的基础上,将ELES模型推广到面板数据模型。构建同时包含时间效应和个体效应的双效应面板ELES模型,提出实证研究中模型形式的识别检验流程,并利用面板ELES模型实证研究了2002-2012年期间我国城镇居民消费结构的变动特征。     

Predictability of Interest Rates and Interest-Rate Portfolios

Due to the near unit-root behavior of interest rates, changes in individual interest-rate series are difficult to forecast. We propose an innovative way of applying dynamic term structure models to predict future changes in interest-rate portfolios. Instead of directly forecasting the movements based on the estimated factor dynamics, we use the dynamic term structure model as a decomposition tool and decompose each interest-rate series into two components: a persistent component captured by the dynamic factors, and a strongly mean-reverting component given by the pricing residuals of the model. With this decomposition, we form interest-rate portfolios that are first-order neutral to the persistent dynamic factors, but are exposed to the strongly mean-reverting residuals. We show that the predictability on the changes of these interest-rate portfolios is significant both statistically and economically. We explore the implications of the predictability in future interest-rate modeling.