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时间序列(R语言实现)[精品].doc

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时间序列(R语言实现)[精品]

Time series Introduction Simple time series models ARIMA Validating a model Spectral Analysis Wavelets Digital Signal Processing (DSP) Modeling volatility: GARCH models (Generalized AutoRegressive Conditionnal Heteroscedasticity) Multivariate time series State-Space Models and Kalman Filtering Non-linear time series and chaos Other times Discrete-valued time series: Markov chains and beyond Variants of Markov chains Untackled subjects TO SORT This chapter contrasts with the topics we have seen up to now: we were interested in the study of several independant realizations of a simple statistical process (e.g., a gaussian random variable, or a mixture of gaussians, or a linear model); we shall now focus on a single realization of a more complex process. Here is the structure of this chapter. After an introduction, motivating the notion of a time series and giving several examples, simulated or real, we shall present the classical models of time series (AR, MA, ARMA, ARIMA, SARIMA), that provide recipes to build time series with desired properties. We shall then present spectral methods, that focus on the discovery of periodic elements in time series. The simplicity of those models makes them amenable, but they cannot describe the properties of some real-world time series: non-linear methods, built upon the classical models (GARCH) are called for. State-Space Models and the Kalman filter follow the same vein: they assume that the data is build from linear algebra, but that we do not observe everything -- there are hidden (unobserved, latent) variables. Some of those methods readily generalize to higher dimensions, i.e., to the study of vector-valued time-series, i.e., to the study of several related time series at the same time -- but some new phenomena appear (e.g., cointegration). Furthermore, if the number of time series to study becomes too large, the vector models have too many parameters to be useful: we enter the realm of panel data. We shall then present so

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