رگرسیون لجستیک در مزایده های مهر شده با دور چندگانه: کاربرد در حراج دادگاه کره ای

This paper proposes a forecasting method for court auction information system using logistic regression model with heterogeneity across the multiple round. The goal is to predict whether an individual auction item in a certain round will be sold or not. A simple linear regression and the least angle regression (LARS) containing random effect terms were used to select meaningful variables for our logit model. The link function of the proposed logit model is represented by two bundles of parameters. The former part consists of the parameters whose values do not change over rounds. The latter part has parameters whose values interact with rounds. The observed data corresponding to an appraiser price as well as an intercept term reflecting local characteristics are used without any change. Data that corresponds to all the other parameters is not directly used, but transformed based on similarities between the original item and the surrounding auction items being recommended by the court auction experts. We tested the Bayesian logistic regression by establishing different priors: Dunson’s prior, Gelman’s prior and Ansari’s prior. Dunson’s prior was found to perform the best. Little significant difference was found between the results of the other two priors. These findings indicate that logistic regression taking the heterogeneity of multi-round into account performs better than a one-layered neural network over all time periods.

Real estate auction market is one of the important markets in the capitalistic system. Despite of its importance, little research has been conducted on Korean court auction compared to researches on financial markets. Before 31 May 1993, Korean court auction had been operated in such a way that bidding applicants compete each other by orally asking their desired prices. As the oral based auction method was changed into the one that people should write a bidding price, more people started to show their interest in court auction. After Korean government seeking the IMF rescue package due to the foreign exchange crisis, overall price of real estate declined heavily and a number of Korean firms entered bankruptcy. As a consequence, the number of real properties took over by court auction was rapidly increased. On the contrary, increasing number of people accumulated wealth by taking advantage of it. Due to chronic housing shortage, people took consistent participation in purchasing residential housing through court auction paying more competitive price. However, few auction participants have applied scientific approaches except professional auction dealers up until now. Even in academic area, few scholars employ quantitative research methods on real estate auction. Assuming additional cost for the risk betided after a successful bid follows a certain type of probability distribution, Yang and Oh (2002) aimed to improve court auction system in the way that it maximizes a bidder’s profit. Oh (2006) proposed the predictive model for average winning price of items in the same group, call it as “average winning price for overall apartment”, by combining moving average (MA) and exponential smoothing (ES) commonly used in time series analysis. Since this model does not give us an individual price for each of the auction items, predicting an individual winning price with the overall average price of the group that it belongs to can be very demanding on auction participants. Oh’s incisive idea to segment items by its usage is deserving of so much praise. However, his assumption that individual winning price follows its group average cannot be generalized. If there are two identical apartments located at different places, their actual sale prices can be quite different. Thus, it is needed to develop a predictive model to forecast an individual winning price corresponding to each auction item instead of the overall average winning price.

This paper proposes a new forecasting method to predict whether an individual real estate in court auction will be sold by a successful bid or not. It is not an improvement upon the right analysis method but rather be a substitutional model that reflects external aspects of a given item whereas the right analysis only focuses on the calculation of its internal factors such as undertaken rights. That is, this paper does not use two negotiation algorithms to extend the statistical model with the right analysis. Both methods work independently. Since bidders cannot guarantee for a successful bid at their first try, they will choose several items but do not have specific rule for that. One of the things that affect their choice is, of course, their personal preferences. Through trimming out undesired items that cannot satisfy minimum levels of personal preferences, auctioneers get feasible set of items to potentially bid on, in which they can either order them again or randomly pick handful items out of them. This is one way that people normally do. Our proposed model filters thousands of given auction items with respect to the probability of successful bid for each item. It predicts whether each item gets more than one bid or no bid as well as gives a successful bid probability which we can get from the latent variable of logistic link and is on the range between 0 and 1 so that a bidder can manually set a cut-off level. See the following artificial example in Table 26. Table 26. Utility based approach for decision making. Estimated value of a latent variable Appraiser price – minimum bidding price Utility * (subjective probability) Option 1 0.3 4 million won 4 * (1 − 0.3) = 2.8 Option 2 0.45 8 million won 8 * (1 − 0.45) = 4.4 Option 3 0.6 10 million won 10 * (1 − 0.6) = 4 Option 4 0.8 12 million won 12 * (1 − 0.8) = 2.4 Table options It does not matter whatever a bidder chooses among the given four options above by strong intuition. A utility-based approach recommends us to choose the option 2 which offers the maximum utility. Here, we assume utility is equivalent to profit, which is proportional to the gap between appraiser price and minimum bidding price. This flow chart in Fig. 18 illustrates the complete flow sequence of decision making which narrows down the thousands of auction items to a considerable set to make actual bids. In the modeling of our Bayesian based predictive system, it is difficult to quantify the characteristics in a precise way of individual items, especially location parameters. Geographical distance using vector-valued parameter fails to detect correlation between two real estates in same district. Because it is common that the successful bid prices of different but adjacent apartments in percentage vary inconsistently across apartment brands. However, market prices of two apartments in the same apartment complex tend to be similar if the gross areas and other options of the two apartments are not too different from each other. Full-size image (19 K) Fig. 18. Recommended process for selecting auction items. Figure options An important component of Bayesian modeling is assessment of sensitivity of posterior corresponding to the specified prior distribution. In the experiment, the Dunson (2007)’s prior produces relatively higher true positive rate than other competitive priors when false positive rates are from 0.1 to 0.3. The Dunson (2007)’s prior also gives us a better accuracy rate. Hence, performance results differ depending on which prior to use for hyperparameter in normal inverse gamma distribution, and for the conjugate prior of univariate normal distribution.