The 91 Day T-Bill Rate

Steven CarlsonMiguel Delgado HelleseterDarren EganChristina LouieCambria PricePinar Sahin

Outline Introduction The Data Transforming the Data The Model The Forecast Conclusion

Introduction Should those with student loans

consolidate? Consolidation allows the borrower

to roll multiple variable interest rate loans into a single fixed loan.

With interest rates at record lows and growing inflation concerns, consolidation can be a vehicle to significantly lower payments.

The Data The data is collected from the

Federal Reserve Economic Data (FRED) for the 91-day T-bill rate for the last auction date in May of each year.

T-Bill Trace

0

4

8

1 2

1 6

2 0

5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 0 0

T B I L L

T-Bill Correlogram

T-Bill Histogram

0

20

40

60

80

2 4 6 8 10 12 14 16

Series: TBILLSample 1955:01 2004:04Observations 592

Mean 5.358851Median 5.020000Maximum 16.30000Minimum 0.830000Std. Dev. 2.794218Skewness 1.101825Kurtosis 4.737383

Jarque-Bera 194.2394Probability 0.000000

Dickey-Fuller Test

Transforming the Data

• Take the First Difference of the series

-6

-4

-2

0

2

4

55 60 65 70 75 80 85 90 95 00

DT BILL

Histogram of Transformed Data

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100

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-4 -3 -2 -1 0 1 2

Series: DTBILLSample 1955:01 2004:04Observations 592

Mean -0.000355Median 0.010000Maximum 2.610000Minimum -4.620000Std. Dev. 0.465580Skewness -1.687016Kurtosis 26.62898

Jarque-Bera 14052.91Probability 0.000000

Dickey-Fuller Test of Transformed Data

Correlogram of First Difference

The Model

Correlogram of the Model

Actual, Fitted, Residual

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-2

0

2

4

-6

-4

-2

0

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60 65 70 75 80 85 90 95 00

Residual Actual Fitted

Histogram of Residuals

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100

150

200

250

-3 -2 -1 0 1 2

Series : Res idualsSample 1956:09 2004:04Observations 572

Mean -5.52E-05Median 0.007656Max imum 2.168041Minimum -3.182289Std. Dev . 0.396788Skewness -0.864306Kurtos is 16.35221

J arque-Bera 4320.256Probability 0.000000

Residuals Squared

ARCH/GARCH Model 1

ARCH/GARCH Model 2

Model 2 Actual, Fitted, Residual

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-2

0

2

4

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60 65 70 75 80 85 90 95 00

Residual Actual Fitted

Correlogram of Residuals

Squared Residuals

ARCH Lagrange Multiplier

Testing the Forecasting Capability

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

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

DTBILL DTBILLF

DTBILLF+2*SEF2 DTBILLF-2*SEF2

Using the Model to Forecast

-0.4

-0.2

0.0

0.2

0.4

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

DTBILLF1 DTBILL

DTBILLF1+2*SEF2 DTBILLF1-2*SEF2

Plot of Entire Series (Including Forecast)

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-4

-2

0

2

4

55 60 65 70 75 80 85 90 95 00 05

DTBILLF4 DTBILL

DTBILLF4+2*SEF4 DTBILLF4-2*SEF4

Forecast Recolored

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8

12

16

20

55 60 65 70 75 80 85 90 95 00 05

FORETBILL TBILL

T-bill Forecast

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1

2

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96 97 98 99 00 01 02 03 04 05

FORETBILL TBILL

T-bill Forecast

Conclusion The predicted result is an interest rate of

1.24% for May, 2005.

The forecasted rate is higher than the current rate. If you want to consolidate your loans, do so before the next rate, which the forecast shows to be higher.

While significant uncertainty exists in the model, the 91-day T-bill rate is expected to steadily increase.