Summary Statistics Final

Summary Statistics

CHF USD

Mean 53.57712 51.09375

Median 54.38260 49.24000

Maximum 74.72410 68.80000

Minimum 39.72070 43.90000

Std. Dev. 8.458609 5.929098

Skewness 0.363308 0.696679

Kurtosis 2.131772 2.323382

Jarque-Bera 69.59060 130.2596

Probability 0.000000 0.000000

Sum 69810.99 66575.16

Sum Sq. Dev. 93155.58 45770.78

Observations 1303 1303

0

20

40

60

80

100

120

140

40 45 50 55 60 65 70 75

Series: CHF

Sample 4/01/2009 3/31/2014

Observations 1303

Mean 53.57712

Median 54.38260

Maximum 74.72410

Minimum 39.72070

Std. Dev. 8.458609

Skewness 0.363308

Kurtosis 2.131772

Jarque-Bera 69.59060

Probability 0.000000

0

40

80

120

160

200

44 46 48 50 52 54 56 58 60 62 64 66 68

Series: USD

Sample 4/01/2009 3/31/2014

Observations 1303

Mean 51.09375

Median 49.24000

Maximum 68.80000

Minimum 43.90000

Std. Dev. 5.929098

Skewness 0.696679

Kurtosis 2.323382



36

40

44

48

52

56

60

64

68

72

76

2009 2010 2011 2012 2013

CHF

40

45

50

55

60

65

70

2009 2010 2011 2012 2013

USD

Correlogram of raw data - CHF

Date: 05/22/14 Time: 12:43

Sample: 4/01/2009 3/31/2014

Included observations: 1303

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

|******* |******* 1 0.997 0.997 1298.3 0.000

|******* | | 2 0.994 0.012 2590.2 0.000

|******* | | 3 0.991 0.007 3875.7 0.000

|******* | | 4 0.989 0.023 5155.3 0.000

|******* | | 5 0.986 -0.017 6428.7 0.000

|******* | | 6 0.983 -0.018 7695.7 0.000

|******* | | 7 0.980 -0.036 8955.7 0.000

|******* | | 8 0.977 0.000 10209. 0.000

|******* | | 9 0.974 -0.027 11455. 0.000

|******* | | 10 0.971 0.024 12694. 0.000

|******* | | 11 0.968 0.021 13927. 0.000

|******* | | 12 0.965 -0.031 15153. 0.000

|******* | | 13 0.962 0.003 16371. 0.000

|******* | | 14 0.959 0.021 17584. 0.000

|******* | | 15 0.956 0.037 18790. 0.000

|******* | | 16 0.953 0.011 19991. 0.000

|******* | | 17 0.951 -0.005 21186. 0.000

|******* | | 18 0.948 0.003 22375. 0.000

|******* | | 19 0.945 -0.057 23558. 0.000

|******* | | 20 0.942 -0.037 24733. 0.000

|******* | | 21 0.939 -0.013 25902. 0.000

|******* | | 22 0.935 0.006 27064. 0.000

|******* | | 23 0.933 0.029 28219. 0.000

|******* | | 24 0.930 0.031 29368. 0.000

|******* | | 25 0.927 -0.003 30511. 0.000

|******* | | 26 0.924 0.015 31648. 0.000

|******* | | 27 0.921 -0.005 32780. 0.000

|******* | | 28 0.919 0.020 33905. 0.000

|******* | | 29 0.916 0.006 35025. 0.000

|******* | | 30 0.913 -0.020 36139. 0.000

|******* | | 31 0.911 0.011 37248. 0.000

|******* | | 32 0.908 0.018 38351. 0.000

|******* | | 33 0.905 -0.033 39449. 0.000

|******* | | 34 0.903 -0.002 40541. 0.000

|******| | | 35 0.900 -0.005 41628. 0.000

|******| | | 36 0.897 -0.013 42709. 0.000

Correlogram of raw data – USD

Date: 05/22/14 Time: 12:48

Sample: 4/01/2009 3/31/2014



|******* |******* 1 0.998 0.998 1299.6 0.000

|******* | | 2 0.995 0.007 2594.0 0.000

|******* | | 3 0.993 0.054 3883.8 0.000

|******* | | 4 0.991 0.029 5169.4 0.000

|******* | | 5 0.989 -0.052 6450.2 0.000

|******* *| | 6 0.986 -0.081 7725.0 0.000

|******* | | 7 0.983 -0.005 8994.0 0.000

|******* | | 8 0.981 -0.025 10257. 0.000

|******* | | 9 0.978 0.012 11514. 0.000

|******* | | 10 0.976 0.010 12766. 0.000

|******* | | 11 0.973 -0.006 14011. 0.000

|******* | | 12 0.970 -0.041 15251. 0.000

|******* | | 13 0.967 -0.007 16483. 0.000

|******* | | 14 0.964 0.030 17710. 0.000

|******* | | 15 0.962 -0.012 18931. 0.000

|******* | | 16 0.959 -0.009 20145. 0.000

|******* | | 17 0.956 -0.004 21353. 0.000

|******* | | 18 0.953 0.038 22556. 0.000

|******* | | 19 0.950 -0.028 23752. 0.000

|******* | | 20 0.947 -0.031 24942. 0.000

|******* | | 21 0.944 -0.043 26125. 0.000

|******* | | 22 0.941 0.030 27301. 0.000

|******* | | 23 0.938 -0.022 28471. 0.000

|******* | | 24 0.936 0.048 29634. 0.000

|******* | | 25 0.933 0.013 30792. 0.000

|******* | | 26 0.930 -0.030 31943. 0.000

|******* | | 27 0.927 -0.021 33087. 0.000

|******* | | 28 0.924 0.003 34225. 0.000

|******* | | 29 0.921 0.010 35357. 0.000

|******* | | 30 0.918 -0.007 36483. 0.000

|******* | | 31 0.915 0.008 37602. 0.000

|******* | | 32 0.912 0.044 38715. 0.000

|******* | | 33 0.909 -0.007 39822. 0.000

|******* | | 34 0.907 0.018 40924. 0.000

|******* | | 35 0.904 -0.006 42020. 0.000

|******| | | 36 0.901 -0.040 43111. 0.000

Unit Root Tests

Augmented Dickey Fuller Test for CHF raw data

Null Hypothesis: CHF has a unit root

Exogenous: Constant

Lag Length: 0 (Automatic based on SIC, MAXLAG=22) t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -0.529650 0.8829

Test critical values: 1% level -3.435161

5% level -2.863552

10% level -2.567891

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(CHF)

Method: Least Squares

Date: 05/22/14 Time: 12:50

Sample (adjusted): 4/02/2009 3/31/2014

Included observations: 1302 after adjustments Coefficient Std. Error t-Statistic Prob.

CHF(-1) -0.000774 0.001462 -0.529650 0.5964

C 0.059582 0.079268 0.751648 0.4524

R-squared 0.000216 Mean dependent var 0.018110

Adjusted R-squared -0.000553 S.D. dependent var 0.445538

S.E. of regression 0.445662 Akaike info criterion 1.223021

Sum squared resid 258.1986 Schwarz criterion 1.230966

Log likelihood -794.1870 Hannan-Quinn criter. 1.226002

F-statistic 0.280529 Durbin-Watson stat 2.010680

Prob(F-statistic) 0.596445

KPSS test for CHF raw data

Null Hypothesis: CHF is stationary

Exogenous: Constant

Bandwidth: 30 (Newey-West using Bartlett kernel) LM-Stat.

Kwiatkowski-Phillips-Schmidt-Shin test statistic 3.913168

Asymptotic critical values*: 1% level 0.739000

5% level 0.463000

10% level 0.347000

*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)

Residual variance (no correction) 71.49315

HAC corrected variance (Bartlett kernel) 2149.707

KPSS Test Equation

Dependent Variable: CHF


Date: 05/22/14 Time: 12:52

Sample: 4/01/2009 3/31/2014

Included observations: 1303 Coefficient Std. Error t-Statistic Prob.

C 53.57712 0.234329 228.6402 0.0000


Adjusted R-squared 0.000000 S.D. dependent var 8.458609




Durbin-Watson stat 0.002777

Phillips Perron Test for CHF raw data

Null Hypothesis: CHF has a unit root

Exogenous: Constant

Bandwidth: 5 (Newey-West using Bartlett kernel) Adj. t-Stat Prob.*

Phillips-Perron test statistic -0.438790 0.9000


5% level -2.863552

10% level -2.567891




Phillips-Perron Test Equation

Dependent Variable: D(CHF)


Date: 05/22/14 Time: 12:53

Sample (adjusted): 4/02/2009 3/31/2014


CHF(-1) -0.000774 0.001462 -0.529650 0.5964

C 0.059582 0.079268 0.751648 0.4524








Augmented Dickey Fuller for USD raw data

Null Hypothesis: USD has a unit root

Exogenous: Constant




5% level -2.863556

10% level -2.567893



Dependent Variable: D(USD)


Date: 05/25/14 Time: 12:09

Sample (adjusted): 4/06/2009 3/31/2014


USD(-1) -0.000456 0.001561 -0.292183 0.7702

D(USD(-1)) -0.015744 0.027641 -0.569576 0.5691

D(USD(-2)) -0.107276 0.027646 -3.880350 0.0001

C 0.031855 0.080278 0.396805 0.6916








KPSS test for USD raw data

Null Hypothesis: USD is stationary

Exogenous: Constant




5% level 0.463000

10% level 0.347000




KPSS Test Equation

Dependent Variable: USD


Date: 05/22/14 Time: 12:57

Sample: 4/01/2009 3/31/2014

Included observations: 1303 Coefficient Std. Error t-Statistic Prob.

C 51.09375 0.164254 311.0651 0.0000







Phillips Perron test for USD raw data

Null Hypothesis: USD has a unit root

Exogenous: Constant




5% level -2.863552

10% level -2.567891





Dependent Variable: D(USD)


Date: 05/22/14 Time: 12:58

Sample (adjusted): 4/02/2009 3/31/2014


USD(-1) -0.000755 0.001566 -0.481965 0.6299

C 0.045976 0.080518 0.570997 0.5681








Correlogram of CHF returns

Date: 05/22/14 Time: 12:59

Sample: 4/01/2009 3/31/2014



| | | | 1 -0.034 -0.034 1.5303 0.216

| | | | 2 -0.024 -0.025 2.2901 0.318

| | | | 3 -0.046 -0.048 5.0546 0.168

| | | | 4 -0.023 -0.027 5.7306 0.220

| | | | 5 0.010 0.006 5.8723 0.319

| | | | 6 0.025 0.023 6.7140 0.348

| | | | 7 -0.016 -0.016 7.0312 0.426

| | | | 8 0.049 0.050 10.177 0.253

*| | | | 9 -0.070 -0.065 16.672 0.054

| | | | 10 -0.041 -0.044 18.845 0.042

| | | | 11 0.045 0.043 21.536 0.028

| | | | 12 -0.038 -0.042 23.438 0.024

| | | | 13 -0.012 -0.020 23.615 0.035

| | | | 14 -0.047 -0.049 26.488 0.022

| | | | 15 -0.022 -0.023 27.117 0.028

| | | | 16 -0.008 -0.019 27.210 0.039

| | | | 17 0.051 0.049 30.700 0.022

| | | | 18 0.059 0.061 35.245 0.009

| | | | 19 0.054 0.050 39.151 0.004

| | | | 20 -0.013 0.008 39.390 0.006

| | | | 21 -0.004 0.006 39.415 0.009

| | | | 22 -0.024 -0.021 40.192 0.010

| | *| | 23 -0.065 -0.074 45.849 0.003

| | | | 24 -0.010 -0.026 45.989 0.004

| | | | 25 -0.035 -0.052 47.659 0.004

| | | | 26 0.005 -0.009 47.691 0.006

| | | | 27 -0.012 -0.014 47.881 0.008

| | | | 28 -0.011 -0.009 48.045 0.011

| | | | 29 0.044 0.047 50.593 0.008

| | | | 30 0.020 0.028 51.138 0.009

| | | | 31 -0.039 -0.019 53.194 0.008

| | | | 32 -0.008 -0.007 53.283 0.010

| | | | 33 -0.016 -0.009 53.638 0.013

| | | | 34 -0.015 -0.025 53.925 0.016

| | | | 35 0.021 -0.001 54.496 0.019

| | | | 36 -0.034 -0.052 56.074 0.018

Correlogram of USD returns

Date: 05/22/14 Time: 13:01

Sample: 4/01/2009 3/31/2014



| | | | 1 -0.019 -0.019 0.4611 0.497

*| | *| | 2 -0.083 -0.083 9.3846 0.009

| | | | 3 -0.017 -0.021 9.7848 0.020

| | | | 4 0.049 0.042 12.971 0.011

|* | |* | 5 0.081 0.081 21.553 0.001

| | | | 6 -0.015 -0.004 21.844 0.001

| | | | 7 -0.007 0.008 21.900 0.003

| | | | 8 0.000 -0.001 21.900 0.005

| | | | 9 -0.002 -0.009 21.903 0.009

| | | | 10 0.023 0.017 22.585 0.012

| | | | 11 0.047 0.050 25.523 0.008

| | | | 12 0.019 0.025 26.010 0.011

| | | | 13 -0.030 -0.020 27.178 0.012

| | | | 14 0.011 0.013 27.329 0.017

| | | | 15 0.017 0.007 27.731 0.023

| | | | 16 -0.005 -0.013 27.763 0.034

| | | | 17 -0.036 -0.035 29.451 0.031

| | | | 18 -0.007 -0.007 29.522 0.042

| | | | 19 0.026 0.017 30.427 0.047

| | | | 20 0.035 0.034 32.050 0.043

| | | | 21 -0.026 -0.018 32.935 0.047

| | | | 22 -0.003 0.004 32.950 0.063

| | *| | 23 -0.064 -0.071 38.439 0.023

| | | | 24 0.001 -0.009 38.439 0.031

| | | | 25 0.050 0.037 41.726 0.019

| | | | 26 0.024 0.027 42.478 0.022

| | | | 27 -0.008 0.008 42.563 0.029

| | | | 28 -0.050 -0.031 45.887 0.018

| | | | 29 0.025 0.020 46.719 0.020

| | | | 30 0.023 0.004 47.448 0.022

| | | | 31 -0.058 -0.062 51.940 0.011

| | | | 32 -0.037 -0.032 53.797 0.009

| | | | 33 -0.006 -0.008 53.850 0.012

| | | | 34 -0.001 -0.010 53.853 0.017

| | | | 35 0.023 0.028 54.559 0.019

| | | | 36 -0.040 -0.033 56.708 0.015

Graph of CHF returns

Graph of USD returns

-.10

-.08

-.06

-.04

-.02

.00

.02

.04

.06

2009 2010 2011 2012 2013

CHFR

-.04

-.03

-.02

-.01

.00

.01

.02

.03

.04

2009 2010 2011 2012 2013

USDR

Unit root tests of returns

Augmented Dickey Fuller Test of CHF returns

Null Hypothesis: CHFR has a unit root

Exogenous: Constant




5% level -2.863554

10% level -2.567892



Dependent Variable: D(CHFR)


Date: 05/22/14 Time: 13:04

Sample (adjusted): 4/03/2009 3/31/2014


CHFR(-1) -1.034250 0.027728 -37.30002 0.0000

C 0.000336 0.000223 1.507679 0.1319

R-squared 0.517153 Mean dependent var -8.40E-07


S.E. of regression 0.008026 Akaike info criterion -6.810693

Sum squared resid 0.083680 Schwarz criterion -6.802744

Log likelihood 4432.356 Hannan-Quinn criter. -6.807711



KPSS test of CHF returns

Null Hypothesis: CHFR is stationary

Exogenous: Constant




5% level 0.463000

10% level 0.347000


Residual variance (no correction) 6.44E-05

HAC corrected variance (Bartlett kernel) 5.44E-05

KPSS Test Equation

Dependent Variable: CHFR


Date: 05/22/14 Time: 13:05

Sample (adjusted): 4/02/2009 3/31/2014


C 0.000328 0.000222 1.476053 0.1402







Phillips Perron test of CHF returns

Null Hypothesis: CHFR has a unit root

Exogenous: Constant




5% level -2.863554

10% level -2.567892





Dependent Variable: D(CHFR)


Date: 05/22/14 Time: 13:05

Sample (adjusted): 4/03/2009 3/31/2014


CHFR(-1) -1.034250 0.027728 -37.30002 0.0000

C 0.000336 0.000223 1.507679 0.1319








Augmented Dickey Fuller test of USD returns

Null Hypothesis: USDR has a unit root

Exogenous: Constant




5% level -2.863556

10% level -2.567893



Dependent Variable: D(USDR)


Date: 05/22/14 Time: 13:06

Sample (adjusted): 4/06/2009 3/31/2014


USDR(-1) -1.103242 0.039498 -27.93151 0.0000

D(USDR(-1)) 0.083107 0.027670 3.003500 0.0027

C 0.000153 0.000170 0.902412 0.3670








KPSS test of USD returns

Null Hypothesis: USDR is stationary

Exogenous: Constant




5% level 0.463000

10% level 0.347000




KPSS Test Equation

Dependent Variable: USDR


Date: 05/22/14 Time: 13:07

Sample (adjusted): 4/02/2009 3/31/2014


C 0.000135 0.000170 0.795918 0.4262







Phillips Perron test of USD returns

Null Hypothesis: USDR has a unit root

Exogenous: Constant




5% level -2.863554

10% level -2.567892





Dependent Variable: D(USDR)


Date: 05/22/14 Time: 13:08

Sample (adjusted): 4/03/2009 3/31/2014


USDR(-1) -1.018796 0.027729 -36.74062 0.0000

C 0.000143 0.000170 0.838830 0.4017

R-squared 0.509603 Mean dependent var 4.76E-06







Normality tests

CHF returns

USD returns

0

40

80

120

160

200

240

280

320

360

-0.075 -0.050 -0.025 0.000 0.025 0.050

Series: CHFR

Sample 4/01/2009 3/31/2014

Observations 1302

Mean 0.000328

Median 0.000235

Maximum 0.051633

Minimum -0.088578

Std. Dev. 0.008026

Skewness -0.902790

Kurtosis 17.31165



0

40

80

120

160

200

240

280

320

-0.025 0.000 0.025

Series: USDR

Sample 4/01/2009 3/31/2014

Observations 1302

Mean 0.000135

Median 0.000000

Maximum 0.037919

Minimum -0.037560

Std. Dev. 0.006132

Skewness -0.021088

Kurtosis 8.593096



Autocorrelation of CHF returns

Partial autocorrelation of CHF returns

-0.1

0-0

.05

0.0

00.0

5

Auto

co

rrela

tio

ns o

f chfr

0 10 20 30 40Lag

Bartlett's formula for MA(q) 95% confidence bands

-0.1

0-0

.05

0.0

00.0

5

Part

ial au

tocorr

ela

tions o

f ch

fr

0 10 20 30 40Lag

95% Confidence bands [se = 1/sqrt(n)]

Autocorrelation of USD returns

Partial autocorrelation of USDR

-0.1

0-0

.05

0.0

00.0

50.1

0

Auto

co

rrela

tio

ns o

f u

sd

r

0 10 20 30 40Lag

Bartlett's formula for MA(q) 95% confidence bands

-0.1

0-0

.05

0.0

00.0

50.1

0

Part

ial au

tocorr

ela

tions o

f u

sdr

0 10 20 30 40Lag

95% Confidence bands [se = 1/sqrt(n)]

Autoregressive Moving Average models

Model for CHF returns



Date: 05/22/14 Time: 14:39

Sample (adjusted): 3 1302

Included observations: 1300 after adjustments

Convergence achieved after 50 iterations

MA Backcast: 1 2 Coefficient Std. Error t-Statistic Prob.

C 0.000327 0.000216 1.510235 0.1312

AR(1) 1.587823 0.005041 314.9825 0.0000

AR(2) -0.977909 0.005074 -192.7272 0.0000

MA(1) -1.611383 0.002106 -765.2156 0.0000

MA(2) 0.994281 0.001994 498.5271 0.0000








Inverted AR Roots .79+.59i .79-.59i

Inverted MA Roots .81-.59i .81+.59i

Breusch-Godfrey Serial Correlation test for CHF returns

Null Hypothesis: There is no serial correlation

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 0.775958 Prob. F(8,1287) 0.6240

Obs*R-squared 6.240256 Prob. Chi-Square(8) 0.6203

Test Equation:

Dependent Variable: RESID


Date: 05/23/14 Time: 12:06

Sample: 3 1302


Presample missing value lagged residuals set to zero. Coefficient Std. Error t-Statistic Prob.

C -1.00E-06 0.000217 -0.004630 0.9963

AR(1) 0.001780 0.005177 0.343898 0.7310

AR(2) -0.000314 0.005219 -0.060233 0.9520

MA(1) 2.32E-05 0.001409 0.016493 0.9868

MA(2) -0.000220 0.000589 -0.373685 0.7087

RESID(-1) -0.030744 0.028373 -1.083556 0.2788

RESID(-2) -0.013592 0.028382 -0.478902 0.6321

RESID(-3) -0.032464 0.028363 -1.144597 0.2526

RESID(-4) -0.011870 0.028366 -0.418458 0.6757

RESID(-5) 0.015226 0.028362 0.536859 0.5915

RESID(-6) 0.018466 0.028356 0.651198 0.5150

RESID(-7) -0.026419 0.028350 -0.931862 0.3516

RESID(-8) 0.035837 0.028333 1.264834 0.2062








Model for USD returns



Date: 05/22/14 Time: 14:42





C 0.000137 0.000164 0.839178 0.4015

AR(1) 0.610026 0.032044 19.03721 0.0000

AR(2) -0.942548 0.031366 -30.05026 0.0000

MA(1) -0.621076 0.039651 -15.66345 0.0000

MA(2) 0.911523 0.038968 23.39135 0.0000








Inverted AR Roots .31+.92i .31-.92i

Inverted MA Roots .31+.90i .31-.90i

Breusch-Godfrey Serial Correlation test for USD returns

Null Hypothesis: There is no serial correlation




Test Equation:



Date: 05/23/14 Time: 12:10

Sample: 3 1302



C -1.50E-06 0.000164 -0.009175 0.9927

AR(1) 0.004821 0.038537 0.125108 0.9005

AR(2) -0.041009 0.037079 -1.105996 0.2689

MA(1) 0.018686 0.055479 0.336810 0.7363

MA(2) 0.059037 0.052572 1.122977 0.2617

RESID(-1) -0.038405 0.036405 -1.054924 0.2917

RESID(-2) -0.067930 0.035130 -1.933658 0.0534

RESID(-3) 0.007175 0.034751 0.206454 0.8365

RESID(-4) 0.045070 0.033628 1.340263 0.1804

RESID(-5) 0.061893 0.033537 1.845528 0.0652

RESID(-6) -0.019319 0.032630 -0.592051 0.5539

RESID(-7) 0.015678 0.032134 0.487889 0.6257

RESID(-8) 0.019595 0.031948 0.613344 0.5398








Vector Autoregression

Selection of lag length

VAR Lag Order Selection Criteria

Endogenous variables: USDR CHFR

Exogenous variables: C

Date: 05/23/14 Time: 12:23

Sample: 1 1302


Lag LogL LR FPE AIC SC HQ

0 9210.558 NA 2.26e-09 -14.23270 -14.22472 -14.22970

1 9233.397 45.57184 2.19e-09 -14.26182 -14.23787* -14.25283*

2 9239.104 11.37092* 2.19e-09* -14.26446* -14.22454 -14.24948

3 9240.428 2.634083 2.20e-09 -14.26032 -14.20444 -14.23935

4 9244.011 7.115732 2.20e-09 -14.25968 -14.18782 -14.23271

5 9248.227 8.359320 2.20e-09 -14.26001 -14.17219 -14.22705

6 9249.130 1.788678 2.21e-09 -14.25522 -14.15144 -14.21627

7 9249.965 1.651442 2.22e-09 -14.25033 -14.13058 -14.20539

8 9252.312 4.631530 2.22e-09 -14.24778 -14.11205 -14.19684

* indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level)

FPE: Final prediction error

AIC: Akaike information criterion

SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

Vector Autoregression results

Vector Autoregression Estimates

Date: 05/23/14 Time: 12:20



Standard errors in ( ) & t-statistics in [ ] USDR CHFR

USDR(-1) -0.031414 0.222680

(0.02876) (0.03726)

[-1.09232] [ 5.97653]

USDR(-2) -0.085347 -0.036559

(0.02913) (0.03774)

[-2.92972] [-0.96868]

CHFR(-1) 0.033861 -0.075762

(0.02227) (0.02885)

[ 1.52036] [-2.62571]

CHFR(-2) -0.013516 -0.023477

(0.02199) (0.02849)

[-0.61466] [-0.82407]

C 0.000149 0.000329

(0.00017) (0.00022)

[ 0.87500] [ 1.49282]

R-squared 0.009450 0.030067

Adj. R-squared 0.006390 0.027071

Sum sq. resids 0.048408 0.081252

S.E. equation 0.006114 0.007921

F-statistic 3.088563 10.03578

Log likelihood 4784.214 4447.589

Akaike AIC -7.352636 -6.834753

Schwarz SC -7.332751 -6.814868

Mean dependent 0.000139 0.000322

S.D. dependent 0.006134 0.008030

Determinant resid covariance (dof adj.) 2.17E-09

Determinant resid covariance 2.16E-09

Log likelihood 9280.993

Akaike information criterion -14.26307

Schwarz criterion -14.22330

. var chfr usdr, lags(1/2)

Vector autoregression

Sample: 04jan1960 - 26jul1963 No. of obs = 1300

Log likelihood = 9280.993 AIC = -14.26307

FPE = 2.19e-09 HQIC = -14.24814

Det(Sigma_ml) = 2.16e-09 SBIC = -14.2233

Equation Parms RMSE R-sq chi2 P>chi2

----------------------------------------------------------------

chfr 5 .007921 0.0301 40.29811 0.0000

usdr 5 .006114 0.0094 12.40195 0.0146

--------------------------------------------------------------------------------------

| Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+------------------------------------------------------------------------

chfr |

chfr |

L1. | -.0757623 .0287985 -2.63 0.009 -.1322064 -.0193182

L2. | -.023477 .0284342 -0.83 0.409 -.0792071 .0322531

|

usdr |

L1. | .2226804 .0371874 5.99 0.000 .1497944 .2955665

L2. | -.0365592 .0376688 -0.97 0.332 -.1103886 .0372702

|

_cons | .0003285 .0002197 1.50 0.135 -.000102 .0007591

-------------+----------------------------------------------------------------

usdr |

chfr |

L1. | .0338608 .0222287 1.52 0.128 -.0097066 .0774282

L2. | -.0135162 .0219475 -0.62 0.538 -.0565325 .0295001

|

usdr |

L1. | -.0314141 .0287038 -1.09 0.274 -.0876725 .0248443

L2. | -.0853467 .0290753 -2.94 0.003 -.1423333 -.0283601

|

_cons | .0001486 .0001695 0.88 0.381 -.0001837 .000481

------------------------------------------------------------------------------

Diagnostics – Serial correlation in residuals (Breusch-Godfrey Lagrange Multiplier test)

VAR Residual Serial Correlation LM Tests Null Hypothesis: no serial correlation at lag order h

Date: 05/23/14 Time: 12:39

Sample: 1 1302


Lags LM-Stat Prob

1 0.821498 0.9355

2 3.505578 0.4770

3 3.450986 0.4854

4 6.505030 0.1645

5 8.067981 0.0891

6 2.429257 0.6573

7 1.953323 0.7443

8 7.223321 0.1245

9 11.06779 0.0258

10 5.623677 0.2291

11 5.827624 0.2124

12 7.320485 0.1199

Probs from chi-square with 4 df.

Impulse response

-.002

.000

.002

.004

.006

.008

1 2 3 4 5 6 7 8 9 10

Response of USDR to USDR

-.002

.000

.002

.004

.006

.008

1 2 3 4 5 6 7 8 9 10

Response of USDR to CHFR

-.002

.000

.002

.004

.006

.008

1 2 3 4 5 6 7 8 9 10

Response of CHFR to USDR

-.002

.000

.002

.004

.006

.008

1 2 3 4 5 6 7 8 9 10

Response of CHFR to CHFR

Response to Cholesky One S.D. Innovations ± 2 S.E.

Granger Causality

VAR Granger Causality/Block Exogeneity Wald Tests

Date: 05/23/14 Time: 12:50

Sample: 1 1302


Dependent variable: USDR

Excluded Chi-sq df Prob.

CHFR 2.876262 2 0.2374

All 2.876262 2 0.2374

Dependent variable: CHFR


USDR 37.70582 2 0.0000

All 37.70582 2 0.0000

Cointegration tests

. vecrank CHF USD, trend(none) lags(8)

Johansen tests for cointegration

Trend: none Number of obs = 1295

Sample: 10jan1960 - 27jul1963 Lags = 8

-------------------------------------------------------------------------------

5%

maximum trace critical

rank parms LL eigenvalue statistic value

0 28 -1081.3614 . 8.0431* 12.53

1 31 -1078.3681 0.00461 2.0565 3.84

2 32 -1077.3398 0.00159

-------------------------------------------------------------------------------

Date: 05/25/14 Time: 14:48

Sample: 4/01/2009 3/31/2014


Series: USD CHF

Lags interval: 1 to 4

Selected

(0.05 level*) Number of

Cointegrating Relations by

Model

Data Trend: None None Linear Linear Quadratic

Test Type No Intercept Intercept Intercept Intercept Intercept

No Trend No Trend No Trend Trend Trend

Trace 0 0 0 0 0

Max-Eig 0 0 0 0 0

*Critical values based on MacKinnon-Haug-Michelis (1999)

Information Criteria by Rank and

Model

Data Trend: None None Linear Linear Quadratic

Rank or No Intercept Intercept Intercept Intercept Intercept

No. of CEs No Trend No Trend No Trend Trend Trend

Log Likelihood by Rank (rows) and Model (columns)

0 -1089.616 -1089.616 -1088.226 -1088.226 -1087.426

1 -1086.347 -1085.842 -1084.466 -1083.993 -1083.618

2 -1085.091 -1084.418 -1084.418 -1080.416 -1080.416

Akaike Information Criteria by

Rank (rows) and Model (columns)

0 1.703568* 1.703568* 1.704509 1.704509 1.706358

1 1.704695 1.705457 1.704878 1.705690 1.706654

2 1.708923 1.710967 1.710967 1.707883 1.707883

Schwarz Criteria by

Rank (rows) and Model (columns)

0 1.767280* 1.767280* 1.776184 1.776184 1.785997

1 1.784334 1.789078 1.792481 1.797275 1.802221

2 1.804490 1.814498 1.814498 1.819378 1.819378

ARCH/GARCH

Model and tests for CHF returns


Method: ML - ARCH (Marquardt) - Normal distribution

Date: 05/23/14 Time: 13:59

Sample: 1 1302



Presample variance: backcast (parameter = 0.7)

GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) Coefficient Std. Error z-Statistic Prob. Variance Equation

C 1.20E-06 2.09E-07 5.765298 0.0000

RESID(-1)^2 0.087763 0.011213 7.826985 0.0000

GARCH(-1) 0.895134 0.009514 94.08458 0.0000

R-squared -0.001675 Mean dependent var 0.000328






Residual tests

Heteroskedasticity Test: ARCH



Test Equation:

Dependent Variable: WGT_RESID^2


Date: 05/23/14 Time: 14:01



C 0.985346 0.064238 15.33909 0.0000

WGT_RESID^2(-1) 0.016764 0.027742 0.604277 0.5458








. regress CHFR

Source | SS df MS Number of obs = 1302

-------------+------------------------------ F( 0, 1301) = 0.00

Model | 0 0 . Prob > F = .

Residual | .083801293 1301 .000064413 R-squared = 0.0000

-------------+------------------------------ Adj R-squared = 0.0000

Total | .083801293 1301 .000064413 Root MSE = .00803

------------------------------------------------------------------------------

CHFR | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_cons | .0003283 .0002224 1.48 0.140 -.000108 .0007647

------------------------------------------------------------------------------

. estat archlm, lags(1)

LM test for autoregressive conditional heteroskedasticity (ARCH)

---------------------------------------------------------------------------

lags(p) | chi2 df Prob > chi2

-------------+-------------------------------------------------------------

1 | 8.219 1 0.0041

---------------------------------------------------------------------------

H0: no ARCH effects vs. H1: ARCH(p) disturbance

Model and tests for USD returns



Date: 05/23/14 Time: 14:13

Sample: 1 1302





C 1.37E-06 3.06E-07 4.480360 0.0000

RESID(-1)^2 0.056789 0.007951 7.142603 0.0000

GARCH(-1) 0.905510 0.014306 63.29536 0.0000







Residual tests




Test Equation:



Date: 05/23/14 Time: 14:18



C 0.995457 0.080357 12.38790 0.0000

WGT_RESID^2(-1) 0.005468 0.027746 0.197069 0.8438








. regress USDR


-------------+------------------------------ F( 0, 1301) = 0.00

Model | 0 0 . Prob > F = .


-------------+------------------------------ Adj R-squared = 0.0000

Total | .04891354 1301 .000037597 Root MSE = .00613

------------------------------------------------------------------------------

USDR | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_cons | .0001353 .0001699 0.80 0.426 -.0001981 .0004686

------------------------------------------------------------------------------

. estat archlm, lags(1)


---------------------------------------------------------------------------


-------------+-------------------------------------------------------------

1 | 74.578 1 0.0000

---------------------------------------------------------------------------


Truncated dataset

Unit root tests

CHF returns

ADF test

Null Hypothesis: CHFRI has a unit root

Exogenous: Constant




5% level -2.864111

10% level -2.568190



Dependent Variable: D(CHFRI)


Date: 05/25/14 Time: 14:10



CHFRI(-1) -1.057000 0.030998 -34.09873 0.0000

C 0.000253 0.000249 1.015789 0.3100








KPSS test

Null Hypothesis: CHFRI is stationary

Exogenous: Constant




5% level 0.463000

10% level 0.347000




KPSS Test Equation

Dependent Variable: CHFRI


Date: 05/25/14 Time: 14:12



C 0.000244 0.000249 0.978609 0.3280







USD Returns

ADF test

Null Hypothesis: USDRI has a unit root

Exogenous: Constant




5% level -2.864111

10% level -2.568190



Dependent Variable: D(USDRI)


Date: 05/25/14 Time: 14:13



USDRI(-1) -1.020336 0.031028 -32.88399 0.0000

C 8.52E-05 0.000174 0.490195 0.6241








KPSS test

Null Hypothesis: USDRI is stationary

Exogenous: Constant




5% level 0.463000

10% level 0.347000




KPSS Test Equation

Dependent Variable: USDRI


Date: 05/25/14 Time: 14:13



C 7.76E-05 0.000174 0.446696 0.6552







ARIMA Models

CHF Returns



Date: 05/25/14 Time: 14:14





C 0.000243 0.000246 0.988182 0.3233

AR(1) -1.063204 0.069953 -15.19888 0.0000

AR(2) -0.879592 0.060323 -14.58132 0.0000

MA(1) 1.037030 0.070387 14.73331 0.0000

MA(2) 0.878931 0.060638 14.49478 0.0000








Inverted AR Roots -.53+.77i -.53-.77i

Inverted MA Roots -.52-.78i -.52+.78i




Test Equation:



Date: 05/25/14 Time: 14:19

Sample: 3 1040



C 4.47E-07 0.000246 0.001818 0.9985

AR(1) 0.014618 0.071553 0.204298 0.8382

AR(2) 0.002295 0.063598 0.036081 0.9712

MA(1) -0.010088 0.073829 -0.136643 0.8913

MA(2) 0.006300 0.064318 0.097952 0.9220

RESID(-1) -0.029627 0.037115 -0.798255 0.4249

RESID(-2) -0.028110 0.036813 -0.763589 0.4453








USD Returns



Date: 05/25/14 Time: 14:19





C 8.43E-05 0.000174 0.484618 0.6280

AR(1) -1.841945 0.010730 -171.6579 0.0000

AR(2) -0.966332 0.010579 -91.34066 0.0000

MA(1) 1.865845 0.009159 203.7069 0.0000

MA(2) 0.983043 0.009041 108.7301 0.0000








Inverted AR Roots -.92-.34i -.92+.34i

Inverted MA Roots -.93+.34i -.93-.34i




Test Equation:



Date: 05/25/14 Time: 14:20

Sample: 3 1040



C -1.76E-08 0.000174 -0.000101 0.9999

AR(1) -9.37E-05 0.010979 -0.008538 0.9932

AR(2) 4.95E-05 0.010856 0.004558 0.9964

MA(1) 0.000194 0.009155 0.021228 0.9831

MA(2) 0.000207 0.009023 0.022993 0.9817

RESID(-1) -0.020707 0.032223 -0.642622 0.5206

RESID(-2) -0.020663 0.032194 -0.641842 0.5211








Vector Autoregression

Lag length selection

VAR Lag Order Selection Criteria

Endogenous variables: USDRI CHFRI

Exogenous variables: C

Date: 05/25/14 Time: 14:23

Sample: 1 1302


Lag LogL LR FPE AIC SC HQ

0 7407.838 NA 2.00e-09 -14.35240 -14.34283 -14.34877

1 7431.294 46.77471* 1.93e-09* -14.39010* -14.36139* -14.37921*

2 7432.890 3.176311 1.94e-09 -14.38545 -14.33758 -14.36728

3 7433.891 1.988292 1.95e-09 -14.37963 -14.31263 -14.35421

4 7436.930 6.024862 1.95e-09 -14.37777 -14.29162 -14.34508

5 7439.511 5.106776 1.96e-09 -14.37502 -14.26973 -14.33506

6 7440.053 1.071295 1.97e-09 -14.36832 -14.24388 -14.32110

7 7440.572 1.021836 1.99e-09 -14.36157 -14.21799 -14.30708

8 7442.384 3.564470 1.99e-09 -14.35733 -14.19461 -14.29558

* indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level)

FPE: Final prediction error

AIC: Akaike information criterion

SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

VAR results

Vector Autoregression Estimates

Date: 05/25/14 Time: 14:22



Standard errors in ( ) & t-statistics in [ ] USDRI CHFRI

USDRI(-1) -0.018996 0.285735

(0.03123) (0.04386)

[-0.60819] [ 6.51487]

CHFRI(-1) -0.008408 -0.079145

(0.02178) (0.03059)

[-0.38602] [-2.58760]

C 8.72E-05 0.000236

(0.00017) (0.00024)

[ 0.50105] [ 0.96703]

R-squared 0.000558 0.042478

Adj. R-squared -0.001372 0.040630

Sum sq. resids 0.032538 0.064155

S.E. equation 0.005604 0.007869

F-statistic 0.289114 22.97999

Log likelihood 3913.652 3560.962

Akaike AIC -7.527722 -6.848819

Schwarz SC -7.513441 -6.834538

Mean dependent 8.36E-05 0.000239

S.D. dependent 0.005600 0.008034

Determinant resid covariance (dof adj.) 1.92E-09

Determinant resid covariance 1.91E-09

Log likelihood 7481.819

Akaike information criterion -14.39041

Schwarz criterion -14.36185

Residual tests

VAR Residual Serial Correlation LM Tests Null Hypothesis: no serial correlation at lag order h

Date: 05/25/14 Time: 14:24

Sample: 1 1302


Lags LM-Stat Prob

1 2.491034 0.6462

2 2.814043 0.5894

3 2.565945 0.6329

4 7.349331 0.1185

5 2.955851 0.5652

6 2.068058 0.7232

7 0.506624 0.9729

8 6.584033 0.1596

9 9.069696 0.0594

10 3.832363 0.4292

11 2.800565 0.5917

12 8.754036 0.0676

Probs from chi-square with 4 df.

Impulse response

-.001

.000

.001

.002

.003

.004

.005

.006

1 2 3 4 5 6 7 8 9 10

Response of USDRI to USDRI

-.001

.000

.001

.002

.003

.004

.005

.006

1 2 3 4 5 6 7 8 9 10

Response of USDRI to CHFRI

-.002

.000

.002

.004

.006

.008

.010

1 2 3 4 5 6 7 8 9 10

Response of CHFRI to USDRI

-.002

.000

.002

.004

.006

.008

.010

1 2 3 4 5 6 7 8 9 10

Response of CHFRI to CHFRI

Response to Cholesky One S.D. Innovations ± 2 S.E.

Granger Causality test

VAR Granger Causality/Block Exogeneity Wald Tests

Date: 05/25/14 Time: 14:25

Sample: 1 1302


Dependent variable: USDRI


CHFRI 0.149014 1 0.6995

All 0.149014 1 0.6995

Dependent variable: CHFRI


USDRI 42.44358 1 0.0000

All 42.44358 1 0.0000

Modelling volatility

ARCH/GARCH Models

CHF Returns



Date: 05/25/14 Time: 14:56






C 5.57E-07 2.04E-07 2.734451 0.0062

RESID(-1)^2 0.068714 0.010362 6.631598 0.0000

GARCH(-1) 0.923899 0.010134 91.17175 0.0000







Residual tests




Test Equation:



Date: 05/25/14 Time: 14:58



C 1.021320 0.068563 14.89619 0.0000

WGT_RESID^2(-1) -0.017387 0.031051 -0.559956 0.5756








. regress CHFRI


-------------+------------------------------ F( 0, 1039) = 0.00

Model | 0 0 . Prob > F = .


-------------+------------------------------ Adj R-squared = 0.0000

Total | .067024755 1039 .000064509 Root MSE = .00803

------------------------------------------------------------------------------

CHFRI | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_cons | .0002437 .0002491 0.98 0.328 -.000245 .0007324

------------------------------------------------------------------------------

. . estat archlm, lags(1)


---------------------------------------------------------------------------


-------------+-------------------------------------------------------------

1 | 0.938 1 0.3329

---------------------------------------------------------------------------


USD Returns



Date: 05/25/14 Time: 15:00






C 4.59E-07 1.67E-07 2.756415 0.0058

RESID(-1)^2 0.029916 0.004033 7.418559 0.0000

GARCH(-1) 0.955801 0.005013 190.6546 0.0000

R-squared -0.000192 Mean dependent var 7.76E-05






Residual tests




Test Equation:



Date: 05/25/14 Time: 15:01



C 0.996038 0.089839 11.08697 0.0000

WGT_RESID^2(-1) 0.013297 0.031052 0.428211 0.6686








. regress USDRI


-------------+------------------------------ F( 0, 1039) = 0.00

Model | 0 0 . Prob > F = .


-------------+------------------------------ Adj R-squared = 0.0000

Total | .032595071 1039 .000031372 Root MSE = .0056

------------------------------------------------------------------------------

USDRI | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_cons | .0000776 .0001737 0.45 0.655 -.0002632 .0004184

------------------------------------------------------------------------------

. . estat archlm, lags(1)


---------------------------------------------------------------------------


-------------+-------------------------------------------------------------

1 | 1.115 1 0.2909

---------------------------------------------------------------------------


Forecasting

Using ARMA models

CHF Returns

USD Returns

-.020

-.015

-.010

-.005

.000

.005

.010

.015

.020

1050 1100 1150 1200 1250 1300

CHFRF ± 2 S.E.

Forecast: CHFRFActual: CHFRForecast sample: 1041 1302Included observations: 262

Root Mean Squared Error 0.008006Mean Absolute Error 0.005444Mean Abs. Percent Error 109.9064Theil Inequality Coefficient 0.968407 Bias Proportion 0.002774 Variance Proportion 0.985738 Covariance Proportion 0.011489

-.020

-.015

-.010

-.005

.000

.005

.010

.015

.020

1050 1100 1150 1200 1250 1300

USDRFF ± 2 S.E.

Forecast: USDRFFActual: USDRFForecast sample: 1041 1302Included observations: 262

Root Mean Squared Error 0.000363Mean Absolute Error 0.000214Mean Abs. Percent Error 254.6316Theil Inequality Coefficient 0.793899 Bias Proportion 0.000065 Variance Proportion 0.999236 Covariance Proportion 0.000699

Forecasting using VAR

Using VAR (1 lag)

-.06

-.04

-.02

.00

.02

.04

.06

1050 1100 1150 1200 1250 1300

Actual CHFR (Baseline Mean)

CHFR

-.04

-.02

.00

.02

.04

1050 1100 1150 1200 1250 1300

Actual USDR (Baseline Mean)

USDR

Documents

Summary Statistics Final