Advances and Applications in Statistics
Volume 27, Issue 1, Pages 27 - 45
(March 2012)
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http://dx.doi.org/10.17654/AS027011227
INFLUENCE IN STOCHASTIC VOLATILITY MODELS
Anderson C. O. Motta and Luiz K. Hotta
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Abstract: Peña [16] presented a new statistics to measure the influence of an observation based on how this observation is being influenced by the rest of the data. He developed the method for a linear regression model. We extend Peña’s approach to stochastic volatility models. The extension is not straightforward because we are now dealing with time series data, there is no analytical form for the likelihood and the prediction of the observable variable for the stochastic volatility model is always equal to zero. For these reasons, the observations cannot be deleted one by one, but treated as missing observation one by one, and the likelihood must be evaluated by a numerical method and one must choose another variable for the prediction. We show how to implement these modifications and how to find threshold values in order to decide whether an observation is influential or not. The results are applied to simulated and to empirical datasets. |
Keywords and phrases: influence in stochastic volatility models, outliers in stochastic volatility models, influential observations, influential observations in SV models. |
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