ARIMA Using Stata
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)
AR(p)
MA(q)
ARMA(p,q)
Time Series Analysis Identification –Autocorrelation Function MA(q) –Partial Autocorrelation AR(p) –Hypothesis Testing Bartlett Test Box-Pierce Q Test
Time Series Analysis Estimation –Maximum Likelihood Estimation –Diagnostic Checking Forecasting –Dynamic Forecast
Seasonal ARMA(p,q) Example: U. S. Whole Sale Price Index, 1960Q1-1990Q4Example: U. S. Whole Sale Price Index, 1960Q1-1990Q4
Multiplicative ARMA(p,q) Example: Airline Passengers, January December 1960Example: Airline Passengers, January December 1960
ARMAX(p,q) Example: U.S. Consumption-Income RelationshipExample: U.S. Consumption-Income Relationship
Transfer Function The Model Impulse Response Function x t ~ARMA(p,q) Filterted y t
Transfer Function The Transformed Model Cross Covariance
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):
Transfer Function Example –U.S. Consumption-Income Relationship (dpi_pce8.do)dpi_pce8.do