1. Case 2 Review Brad Barker, Benjamin Milroy, Matt Sonnycalb, Kristofer Still, Chandhrika Venkataraman Time Series - February 2013

2. Saving as Percent of Personal Income Case2 Topic Summary 100 quarterly observations of saving rates Already been seasonally adjusted by the publicist, US Dept of Commerce Appears to have constant variance by inspection

3. Three-stage UBJ Procedure Choose one or more ARIMA models as candidates Is model satisfactory? Forecast YesNo Stage 1: Identification Stage 2: Estimation Stage 3: Diagnostic checking

4. Identification Plots non-diff, Rapid drop off suggests stationary Consider AR(1) from acf, decay pattern Consider AR (1) from pacf, drop-off

5. Estimation

6. Diagnostic Checking Early spike (lag 2) over significance band Indicates residuals are correlated significantly

7. Model Satisfactory ? Not Really… we already saw spike on lag 2, would be more forgiving if weren’t the very next lag

8. Further Identification Our reidentification logic, need to change one of the three of our ARIMA parameters; p,d,q – AR: Increase AR? No, we would have seen a our residual acf decay, we did not. – Diff: Maybe, but initial plot seemed as though stationary enough. – MA: The residual autocorrelation is significant, but the remaining lags still drop off after 2. We’ll go with ARIMA(1,0,2). Alternatively, ARMA(1,1), but want to go far enough to make sure we get the 2 nd lag.

9. Further Estimation

10. Diagnostic Checking Both residual acf / pacf indicate that there are no significant residual correlations – Except residual pacf lag=21, but that’s our 1 in 20.

11. Model Satisfactory ? Yes, white noise has no significant correlations. Model is concise, we accept

12. Forecast Forecasts level out as expected

13. Don’t forecast too far ahead… History sometimes changes!?! Comparison with new estimates this process: http://www.bea.gov/faq/index.cfm?faq_id=512 http://www.bea.gov/faq/index.cfm?faq_id=512

14. Questions