ARIMA

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
• xtARMA(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)