Zastosowanie teorii szarych systemów do przewidywania przyszłych ofert składanych na aukcjach pierwszej ceny poprzez pryzmat modelu szarego GM(1,1)

This paper presents the possibility of applying the theory of gray systems, with particular emphasis on the model GM (1,1) in the modeling of the first price auction. The paper presents the properties of the model GM (1,1) for the ultrashort time series representing the bid made by the participants at the first price auction. An analysis of the residuals simulation model based on the length of the time series and forecasting capabilities based on gray model GM (1,1). The analysis shows that with the decreasing the number of observations in time series (short time series) decreases the expost forecast error. This property is very important in modeling the course of the auction and in particular predicting possible future offerings. Model GM (1,1) can be considered in applications for masterpieces auctions.