Time Series Analysis

Introduction with time-dependent data. Notions of stationarity. Properties of autocorrelation function in stationary time series. Additive model with deterministic components (trend and seasonality). Parametric and nonparametric estimation and elimination methods of deterministic components, difference method. Box-Cox transformations in eliminating heteroscedasticity. Classic randomness/normality tests for a stochastic component. Autocorrelation of linear filters in stationary time series. Representation of stationary time series as linear filters of uncorrelated noise and Wold theorem (concisely). Autoregressive and Moving Average (ARMA) models, conditions of existence-causality-invertibility of stationary linear solutions. Calculation of autocovariance function of causal stationary solutions in the general ARMA(p,q) model. Asymptotic properties of sample mean. Bartlett theorem and asymptotic statistical inference of autocorrelations. Forecasting of minimum mean square error. Algorithms for optimal linear forecasting (Durbin-Levinson, innovations) and application in ARMA models. Partial autocorrelation function and its estimation. Adaptive causal stationary ARMA models: a) preliminary estimators for autoregressive AR(p) models (Yule-Walker, mean squares), moving average MA(q) models (innovations algorithm), mixed ARMA(p,q) models (generalized Yule-Walker method, innovations algorithm), b) maximum likelihood estimation and asymptotic inference. Diagnostic tests and order selection criteria in ARMA models (FPE, AIC, BIC). Introduction to ARIMA and SARIMA models for non-stationary time series with unit root, Dickey-Fuller test.

• Brockwell P.J., Davis R.A., Introduction to Time Series and Forecasting, 3^rd ed., Springer, 2016
• Kirchgassner G., Wolters J., Hassler U., Introduction to Modern Time Series Analysis, 2nd ed., Springer, 2013
• Chatfield C., The Analysis of Time Series, An Introduction, 6^th ed., Chapman & Hall, 2004
• Kantz H. and Schreiber T., Nonlinear Time Series Analysis, Cambridge University Press, 2004