The Annals of Applied Statistics

Multilevel models with stochastic volatility for repeated cross-sections: An application to tribal art prices

Silvia Cagnone, Simone Giannerini, and Lucia Modugno

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In this paper, we introduce a multilevel specification with stochastic volatility for repeated cross-sectional data. Modelling the time dynamics in repeated cross sections requires a suitable adaptation of the multilevel framework where the individuals/items are modelled at the first level whereas the time component appears at the second level. We perform maximum likelihood estimation by means of a nonlinear state space approach combined with Gauss–Legendre quadrature methods to approximate the likelihood function. We apply the model to the first database of tribal art items sold in the most important auction houses worldwide. The model allows to account properly for the heteroscedastic and autocorrelated volatility observed and has superior forecasting performance. Also, it provides valuable information on market trends and on predictability of prices that can be used by art markets stakeholders.

Article information

Ann. Appl. Stat., Volume 11, Number 2 (2017), 1040-1062.

Received: February 2016
Revised: February 2017
First available in Project Euclid: 20 July 2017

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Multilevel model hedonic regression model dependent random effects stochastic volatility autoregression


Cagnone, Silvia; Giannerini, Simone; Modugno, Lucia. Multilevel models with stochastic volatility for repeated cross-sections: An application to tribal art prices. Ann. Appl. Stat. 11 (2017), no. 2, 1040--1062. doi:10.1214/17-AOAS1035.

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Supplemental materials

  • Supplement to “Multilevel models with stochastic volatility for repeated cross-sections: An application to tribal art prices”. The online supplement contains six technical Appendices with detailed material on the following topics: 1. Recursive algorithm for computing the likelihood; 2. Filtering, Smoothing, and Prediction; 3. Application to Tribal Art prices: full table of the estimates; 4. Application to Tribal Art prices: choice of the quadrature based method; 5. Application to Tribal Art prices: entropy based diagnostic tests for serial independence and nonlinearity; 6. Software implementation.