Ying & YenCarson MarriesAnthony MaderMickey SunEdgar TorresAlex Vicente

Ying & YenCarson MokoAnthony KamakaziMickey SumimatoEdgar TerriakiAlex Yamamuchi

Data From 1971 to Present (Monthly) 387 Observations Federal Reserve Bank St Louis

(Fred)

Exploratory Data Analysis

50

100

150

200

250

300

350

400

75 80 85 90 95 00

YEN

Exploratory Data Analysis

0

10

20

30

40

50

60

80 120 160 200 240 280 320 360

Series: YENSample 1971:01 2003:04Observations 388

Mean 187.9490Median 154.1100Maximum 358.0200Minimum 83.69000Std. Dev. 74.62085Skewness 0.455751Kurtosis 1.838691

Jarque-Bera 35.23484Probability 0.000000

Exploratory Data Analysis

Exploratory Data Analysis

Breaking Yen into Change $ Ln, Difference Fractional Change Pre-Whitening

Breaking Yen into Change $

Breaking Yen into Change $

-0.15

-0.10

-0.05

0.00

0.05

0.10

75 80 85 90 95 00

DLNYEN

Breaking Yen into Change $

0

10

20

30

40

50

-0.10 -0.05 0.00 0.05

Series: DLNYENSample 1971:02 2003:04Observations 387

Mean -0.002827Median -6.64E-05Maximum 0.080641Minimum -0.105212Std. Dev. 0.027848Skewness -0.560805Kurtosis 3.994162

Jarque-Bera 36.22266Probability 0.000000

Modeling ARMADependent Variable: DLNYEN Method: Least Squares Date: 05/27/03 Time: 19:55 Sample(adjusted): 1972:01 2003:04 Included observations: 376 after adjusting endpoints Convergence achieved after 5 iterations Backcast: 1971:11 1971:12

Variable Coefficient Std. Error t-Statistic Prob. C -0.002491 0.002324 -1.072022 0.2844

AR(1) 0.384827 0.050768 7.580106 0.0000 AR(11) 0.109029 0.047550 2.292930 0.0224 MA(2) -0.127598 0.055173 -2.312705 0.0213

R-squared 0.142849 Mean dependent var -0.002611 Adjusted R-squared 0.135936 S.D. dependent var 0.028097 S.E. of regression 0.026118 Akaike info criterion -4.441825 Sum squared resid 0.253754 Schwarz criterion -4.400021 Log likelihood 839.0632 F-statistic 20.66526 Durbin-Watson stat 1.997878 Prob(F-statistic) 0.000000 Inverted AR Roots .86 .73+.44i .73 -.44i .38 -.74i

.38+.74i -.08 -.80i -.08+.80i -.51 -.61i -.51+.61i -.76+.23i -.76 -.23i

Inverted MA Roots .36 -.36

Modeling ARMA

Residual^2 Checking Periods of High Variance

0.000

0.002

0.004

0.006

0.008

0.010

75 80 85 90 95 00

RES1

Residual^2

ARCH - GARCHDependent Variable: DLNYEN Method: ML - ARCH Date: 05/27/03 Time: 20:01 Sample(adjusted): 1972:01 2003:04 Included observations: 376 after adjusting endpoints Convergence achieved after 16 iterations Backcast: 1971:11 1971:12

Coefficient Std. Error z-Statistic Prob. C -0.003070 0.002464 -1.246078 0.2127

AR(1) 0.385571 0.049810 7.740781 0.0000 AR(11) 0.110189 0.047329 2.328143 0.0199 MA(2) -0.127388 0.057715 -2.207172 0.0273

Variance Equation C 6.60E-05 3.06E-05 2.155304 0.0311

ARCH(1) 0.025874 0.022354 1.157461 0.2471 GARCH(1) 0.878035 0.060674 14.47141 0.0000

R-squared 0.142704 Mean dependent var -0.002611 Adjusted R-squared 0.128765 S.D. dependent var 0.028097 S.E. of regression 0.026226 Akaike info criterion -4.441799 Sum squared resid 0.253797 Schwarz criterion -4.368642 Log likelihood 842.0582 F-statistic 10.23721 Durbin-Watson stat 1.998922 Prob(F-statistic) 0.000000 Inverted AR Roots .86 .73+.44i .73 -.44i .38 -.74i

.38+.74i -.08 -.80i -.08+.80i -.51 -.61i -.51+.61i -.76+.23i -.76 -.23i

Inverted MA Roots .36 -.36

ARCH - GARCH

-0.10

-0.05

0.00

0.05

0.10

-0.15

-0.10

-0.05

0.00

0.05

0.10

75 80 85 90 95 00

Residual Actual Fitted

Residual Squared of the ARCH-GARCH Model

0.000

0.002

0.004

0.006

0.008

0.010

75 80 85 90 95 00

RES2

Forecast Yen Exchange

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

03:05 03:07 03:09 03:11 04:01 04:03

DLNYENF ± 2 S.E.

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

03:05 03:07 03:09 03:11 04:01 04:03

DLNYENG ± 2 S.E.

0.00064

0.00065

0.00066

0.00067

0.00068

03:05 03:07 03:09 03:11 04:01 04:03

Forecast of Variance

ARMA- Forecast ARMA with ARCH-GARCH Forecast

Conclusion Our model forecasts a relatively flat

fractional change in the ¥/$ over the next twelve months.

We have more confidence in our second model because the ARCH-GARCH terms account for periods of high variance.

Questions?