Locally adaptive estimation methods with application to univariate time series
- Elagin, Mstislav
2010 Mathematics Subject Classification
- 62M10 62F10, 62P20
- Adaptive estimation, local homogeneity, model selection, stagewise aggregation, volatility model, Poisson model, exponential model, Bernoulli model, propagation, oracle
The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical values is given. The underlying model encompasses all distributions from the exponential family providing for great flexibility. The procedures are applied to simulated and real financial data distributed according to the Gaussian, volatility, Poisson, exponential and Bernoulli models. Numerical results exhibit a very reasonable performance of the methods.