# The 91 Day T-Bill Rate

```The 91 Day T-Bill Rate
Steven Carlson
Darren Egan
Christina Louie
Cambria Price
Pinar 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
2 0
1 6
1 2
8
4
0
5 5
6 0
6 5
7 0
7 5
8 0
8 5
T B IL L
9 0
9 5
0 0
T-Bill Correlogram
T-Bill Histogram
80
Series: TBILL
Sample 1955:01 2004:04
Observations 592
60
40
20
0
2
4
6
8
10
12
14
16
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
5.358851
5.020000
16.30000
0.830000
2.794218
1.101825
4.737383
Jarque-Bera
Probability
194.2394
0.000000
Dickey-Fuller Test
Transforming the Data
• Take the First Difference of the series
4
2
0
-2
-4
-6
55
60
65
70
75
80
85
DT B ILL
90
95
00
Histogram of Transformed
Data
250
Series: DTBILL
Sample 1955:01 2004:04
Observations 592
200
150
100
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
-0.000355
0.010000
2.610000
-4.620000
0.465580
-1.687016
26.62898
Jarque-Bera
Probability
14052.91
0.000000
50
0
-4
-3
-2
-1
0
1
2
Dickey-Fuller Test of
Transformed Data
Correlogram of First
Difference
The Model
Correlogram of the Model
Actual, Fitted, Residual
4
2
0
4
-2
2
-4
0
-6
-2
-4
60
65
70
Residual
75
80
85
Actual
90
95
Fitted
00
Histogram of Residuals
250
Series : R es iduals
Sample 1956:09 2004:04
Obs erv ations 572
200
Mean
Median
Max imum
Minimum
Std. D ev .
Sk ew nes s
Kurtos is
150
100
-5.52E-05
0.007656
2.168041
-3.182289
0.396788
-0.864306
16.35221
50
J arque-Bera
Probability
0
-3
-2
-1
0
1
2
4320.256
0.000000
Residuals Squared
ARCH/GARCH Model 1
ARCH/GARCH Model 2
Model 2 Actual, Fitted,
Residual
4
2
0
4
-2
2
-4
0
-6
-2
-4
60
65
70
Residual
75
80
85
Actual
90
95
Fitted
00
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
DTBILL
DTBILLF
03:09
03:11
04:01
DTBILLF+2*SEF2
DTBILLF-2*SEF2
04:03
Using the Model to Forecast
0.4
0.2
0.0
-0.2
-0.4
04:05
04:07
04:09
DTBILLF1
DTBILL
04:11
05:01
05:03
DTBILLF1+2*SEF2
DTBILLF1-2*SEF2
05:05
Plot of Entire Series
(Including Forecast)
4
2
0
-2
-4
-6
55
60
65
70
DTBILLF4
DTBILL
75
80
85
90
95
DTBILLF4+2*SEF4
DTBILLF4-2*SEF4
00
05
Forecast Recolored
T-bill Forecast
20
16
12
8
4
0
55
60
65
70
75
80
FORET BILL
85
90
95
T BILL
00
05
T-bill Forecast
7
6
5
4
3
2
1
0
96
97
98
99
00
FORET BILL
01
02
03
T BILL
04
05
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