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Neglecting parameter changes in GARCH models. (English) Zbl 1337.62233
Summary: If a GARCH model is estimated on a time series that contains parameter changes in the conditional volatility process and these parameter changes are not accounted for, a distinct error in the estimation occurs: The sum of the estimated autoregressive parameters of the conditional variance converges to one. In finite samples, the sum of the estimated autoregressive parameters is heavily biased towards one. This paper shows that this convergence holds for all common estimators of GARCH. Simulations of the GARCH model show that the effect occurs for realistic parameter changes and sample sizes for financial volatility data.

MSC:
62M09 Non-Markovian processes: estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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