Linear Time Series Models for Stationary data - Feweb

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ARIMA Model building In section §7.1 - §7.3, we study tools of linear analysis of time-series data starting with key concepts in §7.1. Model building philosophy is now specific to general with cycles: 1. Transform data to stationarity §7.3 (logs, differences, breaks) 2. Identify a parsimonious ARIMA model for stationary series, comparing model and data characteristics, §7.1.3- §7.1.5, §7.2.3 3. Estimate ARIMA model §7.2.2 4. Test ARMA model model, §7.2.4. If not OK, restart with 1. or 2. 5. Forecast with ARIMA model §7.1.6, §7.2.4 : conditional mean and variance, one-step and multi-step Chapter 7.1 Heij et al, TI Econometrics II 2006/2007 – p. 4/24
Key concepts of linear time series analysis Stationarity, second order / weak A stochastic process yt is said to be stationary in mean and variance, when the following conditions are satisfied: E(yt) = µ, Cov(yt, yt−k) = γk, for any t (that is, for any position in the time series) and for k = 0, 1, 2, . . .. This defines second order (weak) stationarity. Chapter 7.1 Heij et al, TI Econometrics II 2006/2007 – p. 5/24
Page 1 and 2: Econometrics II - Heij et al. Chapt
Page 3: Introduction Macroeconometrics and
Page 7 and 8: Key concept: SACF, White Noise (WN)
Page 9 and 10: Log Dow Jones: Nonstationary series
Page 11 and 12: Autocovariance, -correlation, corre
Page 13 and 14: Scatter plot log weekly Dow Jones v
Page 15 and 16: AR(∞) representation A simple ide
Page 17 and 18: AR(20) (+trend) Log Dow Jones Log D
Page 19 and 20: Practical purpose of linear time se
Page 21 and 22: Lag polynomials Examples of lag pol
Page 23 and 24: Linear Stochastic processes, Wold r

Linear Time Series Models for Stationary data - Feweb

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