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ARIMA

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.

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ARIMA

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  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, 1960Q1-1990Q4

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

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

  11. Transfer Function The Model Impulse Response Function xt~ARMA(p,q) Filterted yt

  12. Transfer Function The Transformed Model Cross Covariance

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

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

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