1. Final Project
FIN 335
Unknown Students

2. Non-Seasonal Data Set

3. USD/Euro Exchange Rate
Non-Seasonal
No apparent trend
Monthly data

4. Lag Plot No Autocorrelation
Lag 1 shows correlation, but as the lags get higher there is no autocorrelation

5. Acf Plot Autocorrelation significantly different from zero
Lower autocorrelation in upper lags

6. Simple Exponential Smoothing Model
Alpha of 0.6
RMSE of .03
MAE of .02
MAPE of 2.26%

7. Holts-Winter Model Our best model MAE of .019 RMSE of .02
MAPE of 1.71%

8. Holts-Winter Damped Model
RMSE of .03
MAE of .02
MAPE of 2.24%

9. Box Jenkins Model- ARIMA
Full data set
(2,1,1) model
RMSE of .03
MAE of .03
MAPE of 2.42%

10. Results Table
Model Type
RMSE($/Euro)
MAE($/Euro)
MAPE(%)
Basic Mean
.12
.11
10.57%
SES(ALPHA .6)
.03
.02
2.26%
Holts-Winter
1.71%
Holts-Damped
2.24%
ARIMA-(2,1,1)
2.42%

11. Seasonal Data Set

12. Retail Employees (Thousands of Persons)
Seasonal
Positive trend
Spikes during holiday season
Monthly data

13. Lag Plot
Strong autocorrelation all the way through

14. Seasonal Highs and Lows
Highest in December
Increasing every year
Low’s are frequently in February

15. Seasonal Highs and Lows
Highest in December
Lowest in February
Matches ggseasonplot

16. Seasonal Naive Model Best basic model since it is seasonal data
RMSE of
MAE of
MAPE of 17.46%

17. STLF (ETS) Model
RMSE of
MAE of
MAPE of 0.83%

18. STLF (ARIMA(0,2,1)+Robust) Model
RMSE of 59.47
MAE of 51.31
MAPE of 0.32%

19. ETS Model Overall the best model RMSE of 42.75 MAE of 29.93
MAPE of 0.13%

20. ARIMA (3,1,2)(0,1,1)(12) Full data set RMSE of 62.76 MAE of 53.24
MAPE of 0.33%

21. ARIMA (1,0,1)(0,1,0)(12) 2005-2018 RMSE of 83.68 MAE of 60.35
MAPE of 0.38%

22. Results Table Model Type RMSE (Thousands of People)
MAE (Thousands of People)
MAPE(%)
Seasonal Naive
287.27
276.19
17.46%
Linear Model cubic
376.8
295.51
18.66%
STLF(ETS)
143.39
132.44
0.83%
STLF(ARIMA(0,2,1)+Robust)
59.47
51.31
0.32%
ETS
42.75
29.93
0.13%
ARIMA- Full(3,1,2)(0,1,1)(12)
62.76
53.24
0.33%
ARIMA-
(1,0,1)(0,1,0)(12)
83.68
60.35
0.38%

23. Links to Time Series Used