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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
0
50
100
150
200
250
-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
-4
-2
0
2
4
-6
-4
-2
0
2
4
60 65 70 75 80 85 90 95 00
Residual Actual Fitted
Histogram of Residuals
0
50
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
-4
-2
0
2
4
-6
-4
-2
0
2
4
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)
-6
-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
0
4
8
12
16
20
55 60 65 70 75 80 85 90 95 00 05
FORETBILL TBILL
T-bill Forecast
0
1
2
3
4
5
6
7
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.