Forecasting Fed Funds RateForecasting Fed Funds Rate

Group 4Neelima Akkannapragada

Chayaporn Lertrattanapaiboon

Anthony Mak

Joseph Singh

Corinna Traumueller

Hyo Joon You

BackgroundBackground

Fed funds rate (FFR) as an instrument of control. FFR as sign of economic strength/weakness. FFR is at 1.25%, the lowest since 1961. Greenspan intimates at possibility of deflation

(last week). Japanese Deflation and the Great Depression.

ObjectivesObjectives

What will happen to the FFR given indicators such as GDP, CPI, stock market price levels, etc?– Create a distributed lag model with FFR as the

dependent variable.– Provide one period ahead forecast of FFR.

And what does this forecast mean to us?– Provide economic context for the forecast.

The IdeaThe Idea

Supposing that the Fed made its decision solely on previous FFR would be naive.

Fed’s decision on future FFR depends on existing information.

We focus on these existing information to explain FFR.– GDP– CPI– SP500

Data StandardizationData Standardization

All data from Fred II. Different time range and frequencies But same time range and frequencies necessary for DL model Lower bound set by data with the latest start (SP5000 Jan 1970) Upper bound set by data with the earliest end (GDP Jan 2003) Frequency set by data with lowest frequency (GDP quarterly). Result is a shorter and less frequent data set (120 obs). Still enough data.

Trace of VariablesTrace of Variables

0

5

10

15

20

70 75 80 85 90 95 00

FFR

0

2000

4000

6000

8000

10000

12000

70 75 80 85 90 95 00

GDP

0

1000

2000

3000

4000

5000

70 75 80 85 90 95 00

SP

0

40

80

120

160

200

70 75 80 85 90 95 00

CPI

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

70 75 80 85 90 95 00

DLFFR

-0.02

0.00

0.02

0.04

0.06

70 75 80 85 90 95 00

DLGDP

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

70 75 80 85 90 95 00

DLSP

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

70 75 80 85 90 95 00

DDLCPI

Trace of Stationary VariablesTrace of Stationary Variables

Pairwise Granger Causality Tests

Date: 05/27/03 Time: 14:23

Sample: 1970:1 2003:2

Lags: 2

Null Hypothesis: Obs F-Statistic Probability

DLGDP does not Granger Cause DLFFR 130 12.8145 8.7E-06

DLFFR does not Granger Cause DLGDP 1.75070 0.17788

DLSP does not Granger Cause DLFFR 130 7.35499 0.00096

DLFFR does not Granger Cause DLSP 2.07473 0.12989

DDLCPI does not Granger Cause DLFFR 129 0.61862 0.54034

DLFFR does not Granger Cause DDLCPI 7.36316 0.00095

DLSP does not Granger Cause DLGDP 130 1.16482 0.31534

DLGDP does not Granger Cause DLSP 0.54295 0.58240

DDLCPI does not Granger Cause DLGDP 129 3.40096 0.03648

DLGDP does not Granger Cause DDLCPI 2.80740 0.06420

DDLCPI does not Granger Cause DLSP 129 1.48890 0.22963

DLSP does not Granger Cause DDLCPI 0.48034 0.61972

Time CausalityTime Causality

Cross Correlogram 1Cross Correlogram 1

Cross Correlogram 2Cross Correlogram 2

Dependent Variable: DLFFR

Method: Least Squares

Sample(adjusted): 1972:2 2003:1

Included observations: 124 after adjusting endpoints

Convergence achieved after 8 iterations

Variable Coefficient Std. Error t-Statistic Prob.

C -0.17718962391 0.0332222708495 -5.33345913387 4.6565699798e-07

DLGDP(-1) 5.74253059866 1.3480009163 4.26003464036 4.10881431448e-05

DLGDP(-3) 3.12720392868 1.31542817995 2.37732776016 0.0190325621418

DLSP(-1) 0.429515053545 0.162069622027 2.65018853116 0.00913844465895

AR(5) 0.246953114484 0.0878659566173 2.8105665037 0.00578442215627

R-squared 0.27792384769 Mean dependent var -0.00836815797483

Adjusted R-squared 0.253652380385 S.D. dependent var 0.15270778165

S.E. of regression 0.13192640994 Akaike info criterion -1.17365786942

Sum squared resid 2.07114473911 Schwarz criterion -1.05993683855

Log likelihood 77.766787904 F-statistic 11.4506405485

Durbin-Watson stat 1.79038035224 Prob(F-statistic) 6.75508422109e-08

Inverted AR Roots .76 .23+.72i .23 -.72i -.61 -.44i

-.61+.44i

Estimation Output DL ModelEstimation Output DL Model

Residual Correlogram of the DL ModelResidual Correlogram of the DL Model

0

2

4

6

8

10

12

14

-0.500 -0.375 -0.250 -0.125 0.000 0.125 0.250

Series: ResidualsSample 1972:2 2003:1Observations 124

Mean 3.00E-13Median 0.001774Maximum 0.328370Minimum -0.530533Std. Dev. 0.129764Skewness -0.700145Kurtosis 4.887927

Jarque-Bera 28.54626Probability 0.000001

Residual DiagnosticsResidual Diagnostics

Year FFR FFR_0LB FFR_0F FFR_0UB FFR FFR_FLB FFR_F FFR_FUB2001:01 5.98 4.66552 6.415033 8.820591 5.98 4.596384 6.034882 7.9235752001:02 4.8 4.285685 5.892765 8.102478 4.8 3.977865 5.222789 6.8573272001:03 3.77 3.440015 4.729978 6.503662 3.77 3.062946 4.021534 5.2801252001:04 2.49 2.701845 3.715004 5.108084 2.49 2.500064 3.282491 4.3097882002:01 1.73 1.784508 2.453676 3.373774 1.73 1.560487 2.048861 2.6900782002:02 1.75 1.239839 1.704763 2.344028 1.75 1.261908 1.656838 2.1753672002:03 1.73 1.254172 1.724471 2.371127 1.73 1.153964 1.515112 1.9892852002:04 1.75 1.239839 1.704763 2.344028 1.75 1.160605 1.523831 2.0007332003:01 1.24 1.254172 1.724471 2.371127 1.24 1.178243 1.546989 2.0311392003:02 NA 0.888671 1.221911 1.680113 NA 0.860899 1.130329 1.484079

Forecast AR Model Forecast DL Model

ForecastForecast

SummarySummary

Standardization of data for DL modeling causes results in fewer observations.

Granger test is useful in isolating independent variables.

dlSP500 did not have AR structure. Creating the transformed dependent variable may have been more difficult.

Result is more plausible than ARMA model. Fed funds rate will go down next quarter.

What Now?What Now?

Assuming that fed funds will continue to go down, one can…– buy treasury bonds now and sell them later at a

higher price when interest rate drops– simply try harder to find a job in the sluggish

economy– start a business now in anticipation of next

boom

Dependent Variable: DLFFR

Method: Least Squares

Sample(adjusted): 1970:3 2003:1

Included observations: 131 after adjusting endpoints

Convergence achieved after 3 iterations

Variable Coefficient Std. Error t-Statistic Prob.

C -0.014695 0.016465 -0.892533 0.3738

AR(1) 0.166843 0.088232 1.890959 0.0609

R-squared 0.026971 Mean dependent var -0.014326

Adjusted R-squared 0.019428 S.D. dependent var 0.158538

S.E. of regression 0.156991 Akaike info criterion 0.850112

Sum squared resid 3.179341 Schwarz criterion -0.806216

Log likelihood 57.68233 F-statistic 3.575725

Durbin-Watson stat 1.961340 Prob(F-statistic) 0.060873

Estimation Output AR ModelEstimation Output AR Model

Residual Correlogram AR ModelResidual Correlogram AR Model

0

5

10

15

20

25

-0.6 -0.4 -0.2 0.0 0.2 0.4

Series: ResidualsSample 1970:3 2003:1Observations 131

Mean -2.52E-13Median 0.017630Maximum 0.473354Minimum -0.696105Std. Dev. 0.156386Skewness -0.706809Kurtosis 5.937029

Jarque-Bera 57.99183Probability 0.000000

Residual of the AR ModelResidual of the AR Model