Forecasting the US Dollar/Euro Forecasting the US Dollar/Euro Exchange RateExchange Rate

Group BGroup B

John HottingerJohn HottingerJingyu NieJingyu Nie

Katharina DenkKatharina DenkAlex BrownAlex Brown

Joel DemartiniJoel DemartiniYuanchen WangYuanchen Wang

Doug Skipper-DottaDoug Skipper-Dotta

Exchange RatesExchange Rates

• What are they?What are they?• We will be focusing on the U.S. Dollar We will be focusing on the U.S. Dollar

vs Euro Exchange Ratevs Euro Exchange Rate• An exchange rate is how much one An exchange rate is how much one

currency is worth compared to currency is worth compared to another currencyanother currency

• Current U.S./Euro 1.4272 i.e. it take Current U.S./Euro 1.4272 i.e. it take $1.43 to buy one Euro$1.43 to buy one Euro

GoalGoal

• We want to forecast what the We want to forecast what the exchange rate up to 6 months in the exchange rate up to 6 months in the futurefuture

A look at our dataA look at our data

• We gathered monthly exchange rate We gathered monthly exchange rate data from www.oanda.com from May data from www.oanda.com from May 2000 to May 2011. 2000 to May 2011.

A Trace of the DataA Trace of the Data

Things to noteThings to note

• Substantial drop for the U.S dollar Substantial drop for the U.S dollar compared to the Euro from 2002 to compared to the Euro from 2002 to 20082008

• Reasons: September 11, 2001. The Reasons: September 11, 2001. The war in Iraq and Afghanistan, the war in Iraq and Afghanistan, the housing bubble and the U.S. housing bubble and the U.S. accumulation of massive debt.accumulation of massive debt.

The HistogramThe Histogram

The CorrellogramThe Correllogram

Unit Root testUnit Root test

What does this all meanWhat does this all mean

• The trace is evolutionaryThe trace is evolutionary

• In order to forecast or to have a In order to forecast or to have a meaningful forecast we need to meaningful forecast we need to make the data stationarymake the data stationary

• We were able to make the data We were able to make the data stationary by using the box jenkins stationary by using the box jenkins methodmethod

Step 1: First differencingStep 1: First differencing

Whitened HistogramWhitened Histogram

The Whitened CorrellogramThe Whitened Correllogram

Whitened Unit Root TestWhitened Unit Root Test

Alternate ModelsAlternate Models

Building our Final ModelBuilding our Final Model

• We decided to use an intervention We decided to use an intervention model due to the drastic drop in the model due to the drastic drop in the exchange rate in 2002exchange rate in 2002

The Step Function Normal and The Step Function Normal and First DifferencedFirst Differenced

We begin to make our final We begin to make our final modelmodel

Actual Fitted Residual and Actual Fitted Residual and histogramhistogram

0

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-0.04 -0.02 0.00 0.02 0.04

Series: ResidualsSample 2000M07 2011M04Observations 130

Mean 5.79e-17Median -0.000926Maximum 0.049209Minimum -0.052183Std. Dev. 0.019727Skewness -0.193567Kurtosis 3.164628

Jarque-Bera 0.958616Probability 0.619212

Serial Correlation Test and Serial Correlation Test and CorrellogramCorrellogram

Looking for Looking for HeteroskidasticityHeteroskidasticity

Adding a MA(23)Adding a MA(23)

The CorrellogramThe Correllogram

Add an MA(26)Add an MA(26)

Actual Fitted Residual and Actual Fitted Residual and Histogram of ResidualsHistogram of Residuals

Correllogram of residuals and Correllogram of residuals and Serial Correlation TestSerial Correlation Test

Time to forecastTime to forecast

• 6 month whitened forecast6 month whitened forecast

-.06

-.04

-.02

.00

.02

.04

.06

M5 M6 M7 M8 M9 M10

2011

DUSD_EURF ± 2 S.E.

-.08

-.06

-.04

-.02

.00

.02

.04

.06

00 01 02 03 04 05 06 07 08 09 10 11

DUSD_EUR FORECASTFORECAST+2*SEF FORECAST-2*SEF

Forecasted ValuesForecasted Values

Forecasting 6 Months Forecasting 6 Months PreviousPrevious

-.06

-.04

-.02

.00

.02

.04

.06

M11 M12 M1 M2 M3 M4

2010 2011

DUSD_EURF1 ± 2 S.E.

Forecast: DUSD_EURF1Actual: DUSD_EURForecast sample: 2010M11 2011M04Included observations: 6Root Mean Squared Error 0.022872Mean Absolute Error 0.020886Mean Abs. Percent Error 126.5962Theil Inequality Coefficient 0.831111 Bias Proportion 0.001057 Variance Proportion 0.168977 Covariance Proportion 0.829967

-.08

-.06

-.04

-.02

.00

.02

.04

.06

00 01 02 03 04 05 06 07 08 09 10 11

DUSD_EUR FORECAST1FORECAST1+2*SEF1 FORECAST1-2*SEF1

Forecasted Values for Previous Forecasted Values for Previous 6 Months6 Months

Re-colored Forecast for Re-colored Forecast for Following 6 MonthsFollowing 6 Months

0.6

0.7

0.8

0.9

1.0

1.1

1.2

00 01 02 03 04 05 06 07 08 09 10 11

USD/EUR USD_EURFUSD_EURF+2*SEF USD_EURF-2*SEF

Re-Colored Forecast for Re-Colored Forecast for Previous 6 MonthsPrevious 6 Months

0.6

0.7

0.8

0.9

1.0

1.1

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USD/EUR USD_EURFUSD_EURF+2*SEF1 USD_EURF-2*SEF1

Just becauseJust because

• We decided to forecast using We decided to forecast using exponential smoothing and see how exponential smoothing and see how are model would lookare model would look

ResultsResults

• Exponential Model is very close to Exponential Model is very close to what our final model determined what our final model determined

• We will have to wait and see if our We will have to wait and see if our forecasts are correctforecasts are correct

Thank you!!Thank you!!