Leisure & Hospitality Employment in California

1. Leisure & Hospitality Employment in California Jesus Barragan Alex Killian Rasik Cauchon-Desai Ling Zhu Jeannette Figg Caitlin Hunsuck

2. Background • We chose to analyze the levels of leisure and hospitality employment in the state of California by looking at the number of people (in thousands) employed yearly in the industry over the past twenty years. • We believe this topic is of great interest because with the on-going recession this industry is particularly susceptible to change as it is dependent on people’s disposable incomes. • If disposable incomes decline, we expect the number of employees in the industry to decline as well

3. Examine the trace It appears highly seasonal and may be a random walk.

4. Histogram Non-normal

5. Correlogram The correlogram also indicates a random walk (large spike in the PACF and slow decay in the ACF).

6. Unit root test Unit root test confirms our data has a unit root (evolutionary).

7. Seasonal Difference Generate: SDCALEIHN= CALEIHN-CALEIHN(-12)

8. Unit root test There is a unit root so the series is a random walk. Thus, SDCALEIHN is also evolutionary.

9. First-Difference Generate: DSDCALEIHN= SDCALEIHN-SDCALEIHN(-1) Now the trace looks stationary Still non-normal

10. Unit root test Yes! Now we can reject the null hypothesis of a unit root. Our seasonally differenced and first differenced data is stationary

11. Examine the Correlogram to specify a model We may have overly seasonally adjusted because there are large spikes at lags 12 and 24. There are spikes for PACF at lag 5, lag 12, lag 24 and a spike for ACF at lag 12. Also, because T=230, 2/√T≈2/ √225=0.13. The values of PACF at lag 5, lag 12 lag 24 are all bigger than 0.13. AR(5), MA(12), and AR(24) to run the regression

12. Estimate the model Because the coefficient on AR(24) is not significant, drop it and run the regression again.

13. Re-estimate the model All the coeficcients are significant. Durbin watson is approximately 2

14. Correlogram of Residuals The values of PACF are still bigger than 0.13 at lag 2 and lag 4. Thus, add AR(2) and AR(4) into the model.

15. Re-estimate the model All the coefficients are significant except the constant term

16. Validate our model Correlogram of the residuals is clean. The probability for Q-statistics are all bigger than 0.05.

17. Serial Correlation Because the p-value of F-statistic is bigger than 0.05, there is no evidence of serial correlation.

18. Correlogram of residuals squared • Big spike at lag 6 • The Q-statistics are significant from lag 6 • There is conditional heteroskedasticity

19. ARCH LM Test The F-statistic is significant. We need an ARCH -GARCH model as a remedy.

20. ARCH-GARCH Model After trying various combinations of ARCH and GARCH terms, we decided to use GARCH(2,2) model.

21. Model Validation • Q-statistics are significant from lag 9 • Residuals are clean from lag 5 to lag 8.

22. ARCH Test for GARCH(2,2) • The F-statistic is now not significant • Problem of conditional Heteroskedasticity is solved

23. Further Validations The Actual, Fitted and Residuals plot looks good From the histogram, the residuals are WHITE noise.

24. Testing our model Now that we estimated a satisfactory model, let’s test it. We want to forecast the past 12 months based on the data up to May2009

25. Forecast: April 2009 – March 2010

26. Compare forecast to actual

27. Forecast for the rest of 2010 Use the full sample from 1990.01 to 2010.03

28. Forecast for the rest of 2010

29. Recolor • Our forecast shows a recovery to the same seasonal pattern. • However, their could be a permanent downward shift.

30. Conclusion • Unlike the past recessions, the latest great recession caused a dramatic shift downward Our forecast until 2012 does not indicate a recovery to pre-2008 levels.