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Activity Number:
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368
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #301901 |
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Title:
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Bayesian Inference from Mixed Multivariate Time Series Data Using Copulas
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Author(s):
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Paul Dagum*+ and Leonardo Dagum and Vivek Vaidya
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Companies:
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Rapt, Inc. and Rapt, Inc. and Rapt, Inc.
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Address:
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625 2nd St., 2nd Floor, San Francisco, CA, 94107,
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Keywords:
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Bayesian inference ; copula ; Markov property ; time series ; semiparametric estimation
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Abstract:
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Pattern discovery and predictive inference from large-scale time series data has broad applicability from uncovering profitable opportunities in firms to preemptive inferences in homeland security. We propose a copula model for predictive Bayesian inference from mixed qualitative and quantitative time series data. Each quantitative time series is modeled as a stochastic process. We use a directed acyclic graph to express the Markov dependency structure among the random variables. We use nonparametric marginal distributions and model the dependencies in the graph using a copula that (1) is multivariate Gaussian conditional on the qualitative variables, and (2) has the Markov property with respect to the graph. Maximizing the pseudolog-likelihood gives the copula parameters. Predictive inference proceeds by sampling the copula's posterior distribution to simulate the stochastic processes. The technique is illustrated in a leading technology firm that makes frequent price and discount decisions over thousands of products. We obtain robust estimates of price elasticities and cross-elasticities. From these results we derive price decisions that optimize the firm's expected profits.
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