The 20 reference contexts in paper John Barkoulas, Christopher F. Baum, Joseph Onochie (1996) “Nonlinear Nonparametric Prediction of the 90-Day T-Bill Rate” / RePEc:boc:bocoec:320

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    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 arbitrage-based (e.g.
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    Merton (1973), Heath et al. (1992))
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    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 short-term interest rate movements. We are much better able to identify arbitrage opportunities at a point in time than we are able to forecast interest rate movements over a near-term horizon.
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    Despite the sizable body of research focusing on the term structure of interest rates, models based on the analytics of this relationship–whether arbitrage-based (e.g. Merton (1973), Heath et al. (1992)) or of a general equilibrium nature (e.g.
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    Cox et al. (1985a,b), Longstaff and Schwartz (1992))
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    –have not proven to be reliable in the prediction of short-term interest rate movements. We are much better able to identify arbitrage opportunities at a point in time than we are able to forecast interest rate movements over a near-term horizon.
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    We are much better able to identify arbitrage opportunities at a point in time than we are able to forecast interest rate movements over a near-term horizon. Models of these dynamics, such as
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    Cox et al. (1985b),
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    generally rely upon restrictive assumptions of linearity on the dynamics of the underlying processes and stability of their conditional moments. These assumptions would seem to be at odds with the data, as nonlinearities in many high-frequency asset returns have been well documented in the literature.
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    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.
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    Hamilton (1988)
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    applies a Markov switching model to U.S. short-term 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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    Hamilton (1988) applies a Markov switching model to U.S. short-term interest rate data and finds that this model fits the data better than a linear autoregressive model.
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    Granger (1993)
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    shows that the U.S. short-term 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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    Hamilton (1988) applies a Markov switching model to U.S. short-term interest rate data and finds that this model fits the data better than a linear autoregressive model. Granger (1993) shows that the U.S. short-term interest rate depends in a nonlinear manner on the spread between long and short interest rates.
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    Anderson (1994)
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    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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    Granger (1993) shows that the U.S. short-term 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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    Kozicki (1994)
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    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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    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.
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    Naik and Lee (1993) and Das (1993)
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    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 short-term interest rates and its implications for the term structure.
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    approaches, our nonparametric approach does not impose any specific type of nonlinearity in the estimation process but, instead, lets the data determine a suitable regression function. Therefore, the nonparametric approach avoids the parametric-model selection problem and allows for a wider array of nonlinear behavior. Following
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    Diebold and Nason (1990),
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    we use the locally weighted regression method (henceforth LWR), a nonparametric estimation method, to model nonlinearities in mean returns of the 90-day U.S. T-bill 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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    The Locally Weighted Regression (LWR) Method We attempt to uncover nonlinear relationships in the 90-day T-bill rate using the nonparametric locally weighted regression (LWR) method. LWR is a nearest-neighbor (NN) 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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    The Locally Weighted Regression (LWR) Method We attempt to uncover nonlinear relationships in the 90-day T-bill rate using the nonparametric locally weighted regression (LWR) method. LWR is a nearest-neighbor (NN) 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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    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′()
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    Stone (1977)
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    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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    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. Empirical Estimates A. Data and Preliminary Diagnostic Tests Our data are quarterly observations for the 90-day U.S. T-bill rate, referred to as the T-bill rate hereafter. The sample period is 1957:1 to 1988:4 (training set) and observations from 1989:1 to 1993:4 (test set) are used for one-7step ahead forecasts.
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    T-bill rate changes are symmetric but leptokurtic. We first investigate the low-frequency properties of the T-Bill rate series. To do so, we apply the Phillips-Perron tests (PP)
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    (Phillips (1987),
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    Phillips and Perron (1988)) to both levels and first differences of the T-bill 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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    The in-sample and out-of-sample 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
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    (Diebold and Nason (1990), Meese and Rose (1990)) and
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    stock returns (LeBaron (1988), Hsieh (1991)). Our results could be extended to multiple-step-ahead forecasting horizons. The empirical validity of the LWR methodology for other U.
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    The in-sample and out-of-sample 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
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    (LeBaron (1988), Hsieh (1991)).
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    Our results could be extended to multiple-step-ahead 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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    ,,T(). 4 Dividing the statistic by the estimate of the standard deviation gives -13W m (,T)= TmC,T()−1C,T()m() Vm,T() 12(A3) which converges to a normal distribution with unit variance, i.e., N0,1(). Simulations presented by BDS show that this test has good power against simple nonlinear deterministic systems as well as nonlinear stochastic processes. Brock, Hsieh, and
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    LeBaron (1991) and
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    Hsieh and LeBaron (1988) also report Monte Carlo simulations showing that the asymptotic distribution is a good approximation to the finite sample distribution when there are more than 500 observations.
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    Simulations presented by BDS show that this test has good power against simple nonlinear deterministic systems as well as nonlinear stochastic processes. Brock, Hsieh, and LeBaron (1991) and Hsieh and
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    LeBaron (1988)
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    also report Monte Carlo simulations showing that the asymptotic distribution is a good approximation to the finite sample distribution when there are more than 500 observations.
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    They recommend using between one-half 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
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    Sims (1984), Abel (1988), Hodrick (1987), Baldwin and Lyons (1988), and Nason (1988)
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    have shown that economic theory does not rule out the possibility of nonlinear dependence in conditional means and higher-order 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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    shown that economic theory does not rule out the possibility of nonlinear dependence in conditional means and higher-order 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 true.
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    Dechert (1988)
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    offers several counter examples. 4 See Brock, Dechert, and Scheinkman (1987) for definition of the variance V. -15
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