
 Start

1977
 Prefix

Models of the term structure of interest rates fall into two categories:
those based upon arbitrage arguments and those based on a general equilibrium
formulation. In the former category, singlefactor models of the term structure of interest
rates have been proposed by
 Exact

Merton (1973), Vasicek (1977), Dothan (1978),
 Suffix

Schaefer and
Schwartz (1978), and many others. Multifactor term structure models have been proposed by
Richard (1987), Brennan and Schwartz (1979), Langetieg (1980), Schaefer and Schwartz
(1984), and Heath et al. (1992).
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2132
 Prefix

In the former category, singlefactor models of the term structure of interest
rates have been proposed by Merton (1973), Vasicek (1977), Dothan (1978), Schaefer and
Schwartz (1978), and many others. Multifactor term structure models have been proposed by
 Exact

Richard (1987),
 Suffix

Brennan and Schwartz (1979), Langetieg (1980), Schaefer and Schwartz
(1984), and Heath et al. (1992). Models representing a complete general equilibrium
specification of the term structure have been put forth by Cox, Ingersoll and Ross (1985a,b),
Longstaff and Schwartz (1992) and many others.
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 Start

2182
 Prefix

In the former category, singlefactor models of the term structure of interest
rates have been proposed by Merton (1973), Vasicek (1977), Dothan (1978), Schaefer and
Schwartz (1978), and many others. Multifactor term structure models have been proposed by
Richard (1987), Brennan and Schwartz (1979),
 Exact

Langetieg (1980),
 Suffix

Schaefer and Schwartz
(1984), and Heath et al. (1992). Models representing a complete general equilibrium
specification of the term structure have been put forth by Cox, Ingersoll and Ross (1985a,b),
Longstaff and Schwartz (1992) and many others.
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5031
 Prefix

Econometric Methodology
We attempt to uncover nonlinear relationships in U.S. Tbill and bond yields using the
nonparametric locally weighted regression (LWR) method. LWR is a nearestneighbor
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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6968
 Prefix

We also tried the tricube function,
wit=1−u
3
()
3
, suggested by Cleveland, as well as locally unweighted regression but (3)
proved slightly superior empirically.
The value of the regression surface at
x∗
is then computed as
yˆ∗=ˆg∗x
()=∗x
′ˆ
β,
(4)
where
n
2
.
(5)
βˆ=arg min
wt
t=1
∑ty−tx′β()
 Exact

Stone (1977)
 Suffix

addressed the issue 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
q
n→0.
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 Start

10185
 Prefix

As expected, yield changes for
short maturities exhibit greater variability than those for longer maturities.
We first investigate the lowfrequency properties of the yield 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 our sample series, with results presented in Table 2. Inference is
robust to the order of serial correlation allowed in the data.
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12199
 Prefix

i.i.d. null hypothesis in the BDS test is consistent with some type of
dependence in the data, which could result from a linear stochastic system, a nonlinear
stochastic system, or a nonlinear deterministic system. Under the null hypothesis, the BDS
test statistic asymptotically converges to a standard normal variate. However, Monte Carlo
simulations by Brock, Hsieh, and
 Exact

LeBaron (1991) and
 Suffix

Hsieh and LeBaron (1988) suggest that
the asymptotic distribution is a poor approximation to the finite sample distribution when
2 We also applied the KPSS test (Kwiatkowski, Phillips, Schmidt, and Shin (1992)) in which the null hypothesis
is stationarity.
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12228
 Prefix

the BDS test is consistent with some type of
dependence in the data, which could result from a linear stochastic system, a nonlinear
stochastic system, or a nonlinear deterministic system. Under the null hypothesis, the BDS
test statistic asymptotically converges to a standard normal variate. However, Monte Carlo
simulations by Brock, Hsieh, and LeBaron (1991) and Hsieh and
 Exact

LeBaron (1988)
 Suffix

suggest that
the asymptotic distribution is a poor approximation to the finite sample distribution when
2 We also applied the KPSS test (Kwiatkowski, Phillips, Schmidt, and Shin (1992)) in which the null hypothesis
is stationarity.
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15220
 Prefix

in linear models, extends to some nonlinear models but not to ARCH
models.
4 The orders for the conditional variance equation are chosen on the basis of superior performance of
diagnostic tests for serial correlation in the standardized and squared standardized residuals obtained from
estimating the corresponding ARARCH models.
5 Using the BDS test,
 Exact

Hsieh (1989)
 Suffix

found no evidence of inmean nonlinearities in daily foreign exchange rates
after properly specifying their conditional distributions and time variation in conditional volatility. However,
using neural networks, Kuan and Liu (1995) provided statistically significant out of sample forecasting
improvements over the random walk model for daily exchange rates.
nonlinear struct
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22943
 Prefix

Since it appears that the dynamical behavior of US interest
rates is very local in nature, letting the data determine the regression function pays
dividends in terms of improvements in the forecasting accuracy of interest rate models.
Although the LWR estimation method has failed to successfully predict stock returns
 Exact

(Hsieh (1991), LeBaron (1988)) and
 Suffix

exchange rates (Diebold and Nason (1990), Meese and Rose
(1990, 1991), Mizrach (1992)) it appears to be very useful in modeling conditional mean
changes in interest rate series.9 In addition to nonlinearities in variances and possibly higher
moments, significant nonlinearities in the mean clearly exist for U.
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23061
 Prefix

Although the LWR estimation method has failed to successfully predict stock returns (Hsieh (1991), LeBaron (1988)) and exchange rates (Diebold and Nason (1990), Meese and Rose
(1990, 1991),
 Exact

Mizrach (1992))
 Suffix

it appears to be very useful in modeling conditional mean
changes in interest rate series.9 In addition to nonlinearities in variances and possibly higher
moments, significant nonlinearities in the mean clearly exist for U.
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23947
 Prefix

Second, our positive results invite the use of alternative
nonparametric methods to be employed as forecasting tools for U.S. interest rates. Finally, an
obvious avenue of future research is to apply the LWR methodology to interest rate series
from other industrial countries.
9
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LeBaron (1992)
 Suffix

did provide some forecast improvements for stock returns and foreign exchange rates using
the locally unweighted regression method with the level of volatility as the crucial element of conditioning
information.
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