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Weak dependence: models and applications to econometrics. (English) Zbl 1069.62070

Summary: We discuss weak dependence and mixing properties of some popular models. We also develop some of their econometric applications. Autoregressive models, autoregressive conditional heteroskedasticity (ARCH) models, and bilinear models are widely used in econometrics. More generally, stationary Markov modeling is often used. Bernoulli shifts also generate many useful stationary sequences, such as autoregressive moving average (ARMA) or ARCH\((\infty)\) processes. For Volterra processes, mixing properties are obtained given additional regularity assumptions on the distribution of the innovations. We recall associated probability limit theorems and investigate the nonparametric estimation of those sequences.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
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