
 Start

1824
 Prefix

Owners and managers of fixed
income portfolios will find accurate forecasts essential. Despite the sizable
body of research focusing on the term structure of interest rates, models based
on the analytics of this relationship–whether arbitragebased (e.g.
 Exact

Merton (1973),
 Suffix

Heath et al. (1992)) or of a general equilibrium nature (e.g. Cox et al.
(1985a,b), Longstaff and Schwartz (1992))–have not proven to be reliable in the
prediction of shortterm interest rate movements.
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 Start

4246
 Prefix

From an empirical
perspective, the presence of nonlinearities would form the basis for improved
predictability of interest rates.
Recent empirical research documents nonlinear dynamics both in the
mean and in the variance of interest rates.
 Exact

Hamilton (1988)
 Suffix

applies a Markov
switching model to U.S. shortterm interest rate data and finds that this
model fits the data better than a linear autoregressive model. Granger (1993)
shows that the U.
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 Start

4450
 Prefix

Hamilton (1988) applies a Markov
switching model to U.S. shortterm interest rate data and finds that this
model fits the data better than a linear autoregressive model.
 Exact

Granger (1993)
 Suffix

shows that the U.S. shortterm interest rate depends in a nonlinear manner
on the spread between long and short interest rates. Anderson (1994) provides
additional evidence for the types of nonlinear effects reported in Granger.
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 Start

4605
 Prefix

Hamilton (1988) applies a Markov
switching model to U.S. shortterm interest rate data and finds that this
model fits the data better than a linear autoregressive model. Granger (1993) shows that the U.S. shortterm interest rate depends in a nonlinear manner
on the spread between long and short interest rates.
 Exact

Anderson (1994)
 Suffix

provides
additional evidence for the types of nonlinear effects reported in Granger.
Kozicki (1994) finds asymmetry in the form of differing responses to positive
and negative shocks.
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 Start

4721
 Prefix

Granger (1993) shows that the U.S. shortterm interest rate depends in a nonlinear manner
on the spread between long and short interest rates. Anderson (1994) provides
additional evidence for the types of nonlinear effects reported in Granger.
 Exact

Kozicki (1994)
 Suffix

finds asymmetry in the form of differing responses to positive
and negative shocks. Naik and Lee (1993) and Das (1993) link the
nonlinearities to changes in economic regimes and stochastic jumps,
respectively.
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4873
 Prefix

Anderson (1994) provides
additional evidence for the types of nonlinear effects reported in Granger.
Kozicki (1994) finds asymmetry in the form of differing responses to positive
and negative shocks. Naik and Lee (1993) and
 Exact

Das (1993)
 Suffix

link the
nonlinearities to changes in economic regimes and stochastic jumps,
respectively. Finally, Pfann, Schotman, and Tscherning (1996) explore the
scope of nonlinear dynamics in shortterm interest rates and its implications
for the term structure.
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6527
 Prefix

Therefore, the nonparametric approach avoids the parametricmodel
selection problem and allows for a wider array of nonlinear behavior.
Following Diebold and
 Exact

Nason (1990),
 Suffix

we use the locally weighted regression
method (henceforth LWR), a nonparametric estimation method, to model
nonlinearities in mean returns of the 90day U.S. Tbill rate. We measure the
forecasting accurancy of our LWR model using both root mean square error
(RMSE) and mean absolute deviation (MAD) criteria.
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8058
 Prefix

The Locally Weighted Regression (LWR) Method
We attempt to uncover nonlinear relationships in the 90day Tbill rate
using the nonparametric locally weighted regression (LWR) method. LWR is
a nearestneighbor (NN) estimation technique, first introduced by
 Exact

Cleveland (1979) and
 Suffix

further developed by Cleveland and Devlin (1988) and Cleveland,
Devlin, and Grosse (1988). It is a way of estimating a regression surface
through a multivariate smoothing procedure, fitting a function of
independent variables locally and in a movingaverage manner.
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10001
 Prefix

To
set the observation weights, we use the tricube weighting function
wit=1−u
3
()
3
, where
u≡
xit−t
x∗
xq−t
x∗
(3)
The value of the regression surface at ∗x is then computed as
y ˆ ∗=ˆ g ∗x
()=∗x
′ˆ
,(4)
where
n
2
.(5)
ˆ =argmin
wt
t=1
∑ty−tx′()
 Exact

Stone (1977)
 Suffix

formulated the problem of consistent estimation through
regularity conditions on weights of the neighbors. Consistency of NN
estimators (and therefore LWR) requires that the number of NNs used go to
infinity with sample size, but at a slower rate, that is, as n→∞,q→∞,but
6q
n→0.
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12579
 Prefix

Tbill rate changes
are symmetric but leptokurtic.
We first investigate the lowfrequency properties of the TBill rate
series. To do so, we apply the PhillipsPerron tests (PP)
 Exact

(Phillips (1987),
 Suffix

Phillips and Perron (1988)) to both levels and first differences of the Tbill rate.
Table 2 presents the PP test results. Inference is robust to the order of serial
correlation allowed in the data.
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19476
 Prefix

The insample and outofsample superior performance of the LWR
methodology appears to be robust to autoregression order, window size, and
forecasting measure. This evidence is much more encouraging than that
found for exchange rates (Diebold and
 Exact

Nason (1990),
 Suffix

Meese and Rose (1990))
and stock returns (LeBaron (1988), Hsieh (1991)).
Our results could be extended to multiplestepahead forecasting
horizons. The empirical validity of the LWR methodology for other U.
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 Start

19552
 Prefix

The insample and outofsample superior performance of the LWR
methodology appears to be robust to autoregression order, window size, and
forecasting measure. This evidence is much more encouraging than that
found for exchange rates (Diebold and Nason (1990), Meese and Rose (1990))
and stock returns (LeBaron (1988),
 Exact

Hsieh (1991)).
 Suffix

Our results could be extended to multiplestepahead forecasting
horizons. The empirical validity of the LWR methodology for other U.S.
interest rate series as well as for international interest rate series should also
be investigated.
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22293
 Prefix

They recommend using between onehalf to
two times the standard deviation of the raw data. The accuracy of the
asymptotic distribution deteriorates for high embedding dimensions,
particularly when m is 10 and above.
14Endnotes
1
 Exact

Sims (1984), Abel (1988), Hodrick (1987),
 Suffix

Baldwin and Lyons (1988), and Nason (1988) have
shown that economic theory does not rule out the possibility of nonlinear dependence in
conditional means and higherorder conditional moments of asset returns.
2 The only exception was nonlinear autoregression of order one for which the performance of the
LWR fit was inferior to linear fits.
3 Note that i.i.d. implies that
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22375
 Prefix

The accuracy of the
asymptotic distribution deteriorates for high embedding dimensions,
particularly when m is 10 and above.
14Endnotes
1 Sims (1984), Abel (1988), Hodrick (1987), Baldwin and Lyons (1988), and
 Exact

Nason (1988)
 Suffix

have
shown that economic theory does not rule out the possibility of nonlinear dependence in
conditional means and higherorder conditional moments of asset returns.
2 The only exception was nonlinear autoregression of order one for which the performance of the
LWR fit was inferior to linear fits.
3 Note that i.i.d. implies that
Cm,T()=1C,T()
m but the converse is not tru
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