Final Project FIN 335 Unknown Students.

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Presentation transcript:

Final Project FIN 335 Unknown Students

Non-Seasonal Data Set

USD/Euro Exchange Rate Non-Seasonal No apparent trend 1999-2018 Monthly data

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

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

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

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

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

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

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%

Seasonal Data Set

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

Lag Plot Strong autocorrelation all the way through

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

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

Seasonal Naive Model Best basic model since it is seasonal data RMSE of 287.27 MAE of 276.19 MAPE of 17.46%

STLF (ETS) Model RMSE of 143.39 MAE of 132.44 MAPE of 0.83%

STLF (ARIMA(0,2,1)+Robust) Model 2005-2018 RMSE of 59.47 MAE of 51.31 MAPE of 0.32%

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

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

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

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- 2005-2018 (1,0,1)(0,1,0)(12) 83.68 60.35 0.38%

Links to Time Series Used https://fred.stlouisfed.org/series/EXUSEU https://fred.stlouisfed.org/series/CEU4200000001