The 18 reference contexts in paper John Barkoulas, Christopher F. Baum, Atreya Chakraborty (1996) “Nearest-Neighbor Forecasts of U.S. Interest Rates” / RePEc:boc:bocoec:313

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    1977
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    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, single-factor models of the term structure of interest rates have been proposed by
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    Merton (1973), Vasicek (1977), Dothan (1978), Schaefer and Schwartz (1978), and
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    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
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    In the former category, single-factor 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
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    Richard (1987), Brennan and Schwartz (1979), Langetieg (1980), Schaefer and Schwartz (1984), and Heath et al. (1992).
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    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. Chan, Karolyi, Longstaff and Sanders (1992) and Broze, Scaillet, and Zakoian (1995) provided empirical comparisons of the adequacy of the models’ explanation of the data.
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    2378
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    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). Models representing a complete general equilibrium specification of the term structure have been put forth by
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    Cox, Ingersoll and Ross (1985a,b), Longstaff and Schwartz (1992) and
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    many others. Chan, Karolyi, Longstaff and Sanders (1992) and Broze, Scaillet, and Zakoian (1995) provided empirical comparisons of the adequacy of the models’ explanation of the data. Both theoretical and empirical results from these two branches of research suggest that term structure models that allow yield nonlinearity can provide additional insight and explanatory powe
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    2459
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    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). 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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    Chan, Karolyi, Longstaff and Sanders (1992) and
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    Broze, Scaillet, and Zakoian (1995) provided empirical comparisons of the adequacy of the models’ explanation of the data. Both theoretical and empirical results from these two branches of research suggest that term structure models that allow yield nonlinearity can provide additional insight and explanatory power for the modelling of equilibrium interest rates.
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    5031
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    Econometric Methodology We attempt to uncover nonlinear relationships in U.S. T-bill and bond yields using the nonparametric locally weighted regression (LWR) method. LWR is a nearest-neighbor estimation technique, first introduced by
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    Cleveland (1979) and
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    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 moving-average manner.
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    5078
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    T-bill and bond yields using the nonparametric locally weighted regression (LWR) method. LWR is a nearest-neighbor estimation technique, first introduced by Cleveland (1979) and further developed by
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    Cleveland and Devlin (1988), and
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    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 moving-average manner.
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    6968
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    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() 
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    Stone (1977)
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    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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    8331
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    Although the exact distribution of the error sum of squares is not χ2 (as the eigenvalues of I−L() need not be all ones or zeros), it can be approximated by a constant multiplied by a χ2 variable. The constant and degrees of freedom are chosen so that the first two moments of the approximating distribution match those of the distribution of the error sum of squares
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    (Kendall and Stuart, 1977).
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    3. Data and Diagnostic Tests Our data set consists of a variety of short- and long-term U.S. Treasury interest rates: monthly observations on the Federal Funds rate, 3-month, 6-month, and 12-month U.
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    10185
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    As expected, yield changes for short maturities exhibit greater variability than those for longer maturities. We first investigate the low-frequency properties of the yield series. To do so, we apply the Phillips-Perron tests (PP)
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    (Phillips (1987), Phillips and Perron (1988)) to
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    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. All PP tests fail to reject the unit root null hypothesis in the yield series but strongly reject the unit root null in yield changes.
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    10742
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    All PP tests fail to reject the unit root null hypothesis in the yield series but strongly reject the unit root null in yield changes. The PP test results therefore strongly support the hypothesis of a single unit root in the yield series. Given the low power of standard unit root tests against fractional alternatives
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    (Diebold and Rudebusch (1991))
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    we apply the semi-nonparametric procedure suggested by Geweke and Porter-Hudak (GPH, 1983) to the yield series. The GPH test avoids the knifeedged I(1) and I(0) distinction in the PP test by allowing the integration order to take on any real value (fractional integration).
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    12199
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    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
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    LeBaron (1991) and Hsieh and LeBaron (1988)
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    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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    13609
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    19, 19, 6, and 22, respectively (the maximum order allowed is 24), and the ARCH orders are 3, 4, 2, 2, 2, and 4, respectively.4 We applied the BDS test to these three sets of series for embedding dimensions of m=2, 3, 4 and 5. For each m,ε is set to 0.5 and 1.0 standard deviations (σ) of the data. We use the quantiles from the small sample simulations reported by
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    Brock et al. (1991)
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    as approximations to the finite-sample critical values of our BDS statistics. The i.i.d. null hypothesis is overwhelmingly rejected in all cases for yield changes. When the BDS test is applied to the AR-filtered series we still obtain strong rejections of the i.i.d. null hypothesis suggesting that linear dependence in the first moments does not fully account for rejection
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    15220
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    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 AR-ARCH models. 5 Using the BDS test,
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    Hsieh (1989)
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    found no evidence of in-mean 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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    15458
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    correlation in the standardized and squared standardized residuals obtained from estimating the corresponding AR-ARCH models. 5 Using the BDS test, Hsieh (1989) found no evidence of in-mean nonlinearities in daily foreign exchange rates after properly specifying their conditional distributions and time variation in conditional volatility. However, using neural networks,
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    Kuan and Liu (1995)
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    provided statistically significant out of sample forecasting improvements over the random walk model for daily exchange rates. nonlinear structure in the conditional mean of yield-change series, we now turn to modeling nonlinearities in their first moments by means of local-fitting methodology. 4.
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    20573
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    Full results are available upon request from the authors. window size enhances the view that the estimated nonlinearities are not a statistical artifact, but rather capture essential aspects of the data generating process. In order to formally evaluate model performance, we apply the forecast comparison test of
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    Granger and Newbold (1986,
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    pp. 278-280) to test the hypothesis that there is no difference in the forecasting accuracy between the linear and nonlinear models. Given that the nonparametric fit generally achieves a lower RMSE, we test the null hypothesis of no difference in the forecasting performance between the AR and LWR models against the onesided alternative that the LWR model has superior forecas
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    22943
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    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
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    (Hsieh (1991), LeBaron (1988)) and
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    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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    22998
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    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 (Hsieh (1991), LeBaron (1988)) and exchange rates
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    (Diebold and Nason (1990), Meese and Rose (1990, 1991), Mizrach (1992))
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    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
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    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)
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    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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