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Introduction Simple time series models ARIMAValidating a model Spectral Analysis Wavelets Digital Signal Processing (DSP)Modeling volatility: GARCH models (Generalized Auto Regressive 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. 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.
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