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In this chapter, we present the statistical tools used in risk management. The first section concerns estimation methods that are essential to calibrate the parameters of a statistical model. This includes the linear regression, which is the standard statistical tool to investigate the relationships between data in empirical research, and the method of maximum likelihood (ML), whose goal is to estimate parameters of non-linear and non-Gaussian financial models. We also present the generalized method of moments (GMM), which is very popular in economics because we can calibrate non-reduced forms or structural models. Finally, the last part of the first section is dedicated to non-parametric estimators. In the second section, we study time series modeling, in particular ARMA processes and error correction models. We also investigate state-space models, which encompass many dynamic models. A focus is also done on volatility modeling, which is an important issue in risk management. Finally, we discuss the application of spectral analysis. Most of statistical tools presented in this chapter are used in the next chapters, for example the estimation of copula models, the calibration of stressed scenarios or the implementation of credit scoring.
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