1. ARIMA Using Stata

2. Time Series Analysis Stochastic Data Generating Process –Stable and Stationary Process Autoregressive Process: AR(p) Moving Average Process: MA(q) ARMA(p,q) –Integrated Nonstationary Process ARIMA(p,d,q)

3. AR(p)

4. MA(q)

5. ARMA(p,q)

6. Time Series Analysis Identification –Autocorrelation Function MA(q) –Partial Autocorrelation AR(p) –Hypothesis Testing Bartlett Test Box-Pierce Q Test

7. Time Series Analysis Estimation –Maximum Likelihood Estimation –Diagnostic Checking Forecasting –Dynamic Forecast

8. Seasonal ARMA(p,q) Example: U. S. Whole Sale Price Index, 1960Q1-1990Q4Example: U. S. Whole Sale Price Index, 1960Q1-1990Q4

9. Multiplicative ARMA(p,q) Example: Airline Passengers, January 1949- December 1960Example: Airline Passengers, January 1949- December 1960

10. ARMAX(p,q) Example: U.S. Consumption-Income RelationshipExample: U.S. Consumption-Income Relationship

11. Transfer Function The Model Impulse Response Function x t ~ARMA(p,q) Filterted y t

12. Transfer Function The Transformed Model Cross Covariance

13. Transfer Function Cross Correlation Model Identification based on  uv (j) –Under null hypothesis  uv (j) = 0 –Identify the finite-parameter structure of  (B) Model Estimation using ARMAX(p,q):

14. Transfer Function Example –U.S. Consumption-Income Relationship (dpi_pce8.do)dpi_pce8.do