The 19 reference contexts in paper John Barkoulas, Christopher F. Baum (2003) “Long-Memory Forecasting of U.S. Monetary Indices” / RePEc:boc:bocoec:558

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    Introduction In this study we investigate the presence of long memory and its usefulness as a forecast generating mechanism for the U.S. monetary aggregates. The fractional differencing model employed is the autoregressive fractionally integrated moving average (ARFIMA) type introduced by Granger and Joyeux (1980), Hosking (1981), and
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    Geweke and Porter-Hudak (1983).
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    Regarding macroeconomic time series, evidence of fractional integration has been found in output series (Diebold and Rudebusch (1989), Sowell (1992)), consumption (Diebold and Rudebusch (1991)), and inflation rates (Baillie, Chung, and Tieslau (1996), Hassler and Wolters (1995), Baum, Barkoulas, and Caglayan (1999)).
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    The fractional differencing model employed is the autoregressive fractionally integrated moving average (ARFIMA) type introduced by Granger and Joyeux (1980), Hosking (1981), and Geweke and Porter-Hudak (1983). Regarding macroeconomic time series, evidence of fractional integration has been found in output series
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    (Diebold and Rudebusch (1989), Sowell (1992)),
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    consumption (Diebold and Rudebusch (1991)), and inflation rates (Baillie, Chung, and Tieslau (1996), Hassler and Wolters (1995), Baum, Barkoulas, and Caglayan (1999)). Porter-Hudak (1990) reported evidence of long memory in simple sum monetary aggregates while Barkoulas, Baum, and Caglayan (1999) extended similar findings to components of simple-sum monetary aggregates, divisia monetary indices, t
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    The fractional differencing model employed is the autoregressive fractionally integrated moving average (ARFIMA) type introduced by Granger and Joyeux (1980), Hosking (1981), and Geweke and Porter-Hudak (1983). Regarding macroeconomic time series, evidence of fractional integration has been found in output series (Diebold and Rudebusch (1989), Sowell (1992)), consumption
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    (Diebold and Rudebusch (1991)), and
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    inflation rates (Baillie, Chung, and Tieslau (1996), Hassler and Wolters (1995), Baum, Barkoulas, and Caglayan (1999)). Porter-Hudak (1990) reported evidence of long memory in simple sum monetary aggregates while Barkoulas, Baum, and Caglayan (1999) extended similar findings to components of simple-sum monetary aggregates, divisia monetary indices, the monetary base, and money multipliers.
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    Regarding macroeconomic time series, evidence of fractional integration has been found in output series (Diebold and Rudebusch (1989), Sowell (1992)), consumption (Diebold and Rudebusch (1991)), and inflation rates (Baillie, Chung, and Tieslau (1996),
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    Hassler and Wolters (1995),
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    Baum, Barkoulas, and Caglayan (1999)). Porter-Hudak (1990) reported evidence of long memory in simple sum monetary aggregates while Barkoulas, Baum, and Caglayan (1999) extended similar findings to components of simple-sum monetary aggregates, divisia monetary indices, the monetary base, and money multipliers.
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    Regarding macroeconomic time series, evidence of fractional integration has been found in output series (Diebold and Rudebusch (1989), Sowell (1992)), consumption (Diebold and Rudebusch (1991)), and inflation rates (Baillie, Chung, and Tieslau (1996), Hassler and Wolters (1995), Baum, Barkoulas, and Caglayan (1999)).
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    Porter-Hudak (1990)
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    reported evidence of long memory in simple sum monetary aggregates while Barkoulas, Baum, and Caglayan (1999) extended similar findings to components of simple-sum monetary aggregates, divisia monetary indices, the monetary base, and money multipliers.
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    Despite the evidence of long memory in macroeconomic series, there are few applied studies in the literature regarding the predictive ability of ARFIMA models.1 Such forecasting evaluation would serve as a test of model adequacy, in discriminating among competing economic hypotheses, and be useful in guiding policy-making decisions (see
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    Fildes and Stekler (2002) and
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    references therein for a recent review of issues regarding macroeconomic forecasting). Granger and 1 Guegman (1994) points out that, despite the fundamental interest in forecasting, very few studies related to ARFIMA forecasts have been implemented.
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    predictive ability of ARFIMA models.1 Such forecasting evaluation would serve as a test of model adequacy, in discriminating among competing economic hypotheses, and be useful in guiding policy-making decisions (see Fildes and Stekler (2002) and references therein for a recent review of issues regarding macroeconomic forecasting). Granger and 1
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    Guegman (1994)
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    points out that, despite the fundamental interest in forecasting, very few studies related to ARFIMA forecasts have been implemented. Joyeux (1980) discuss the forecasting potential of fractional models.
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    Granger and 1 Guegman (1994) points out that, despite the fundamental interest in forecasting, very few studies related to ARFIMA forecasts have been implemented. Joyeux (1980) discuss the forecasting potential of fractional models.
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    Cheung (1993)
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    finds that ARFIMA-generated forecasts fail to improve upon random-walk forecasts for foreign exchange rates. Lardic and Mignon (1996) however provide evidence that fractional forecasts have better predictive accuracy in the short term (relative to random-walk and structural model forecasts) for three major currencies.
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    1 Guegman (1994) points out that, despite the fundamental interest in forecasting, very few studies related to ARFIMA forecasts have been implemented. Joyeux (1980) discuss the forecasting potential of fractional models. Cheung (1993) finds that ARFIMA-generated forecasts fail to improve upon random-walk forecasts for foreign exchange rates.
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    Lardic and Mignon (1996)
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    however provide evidence that fractional forecasts have better predictive accuracy in the short term (relative to random-walk and structural model forecasts) for three major currencies. Franses and Ooms (1997) report that ARFIMA models fail to generate superior forecasts over competing models for the U.
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    Lardic and Mignon (1996) however provide evidence that fractional forecasts have better predictive accuracy in the short term (relative to random-walk and structural model forecasts) for three major currencies.
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    Franses and Ooms (1997)
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    report that ARFIMA models fail to generate superior forecasts over competing models for the U.K. inflation rate. Through extensive Monte Carlo analysis, Ray (1993a) and Crato and Ray (1996) find that simple ARMA models generally outperform or provide competitive forecasts compared to ARFIMA models.
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    Lardic and Mignon (1996) however provide evidence that fractional forecasts have better predictive accuracy in the short term (relative to random-walk and structural model forecasts) for three major currencies. Franses and Ooms (1997) report that ARFIMA models fail to generate superior forecasts over competing models for the U.K. inflation rate. Through extensive Monte Carlo analysis,
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    Ray (1993a) and Crato and Ray (1996)
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    find that simple ARMA models generally outperform or provide competitive forecasts compared to ARFIMA models. On the other hand, Ray (1993b) establishes that, by certain criteria, a fractional model provides more accurate forecasts than benchmark models for IBM product revenues.
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    Through extensive Monte Carlo analysis, Ray (1993a) and Crato and Ray (1996) find that simple ARMA models generally outperform or provide competitive forecasts compared to ARFIMA models. On the other hand,
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    Ray (1993b)
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    establishes that, by certain criteria, a fractional model provides more accurate forecasts than benchmark models for IBM product revenues. Barkoulas and Baum (1997) show that long-memory forecasts result in dramatic improvements in forecasting accuracy, especially over longer horizons, relative to rival models for several Eurocurrency deposit rates.
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    Through extensive Monte Carlo analysis, Ray (1993a) and Crato and Ray (1996) find that simple ARMA models generally outperform or provide competitive forecasts compared to ARFIMA models. On the other hand, Ray (1993b) establishes that, by certain criteria, a fractional model provides more accurate forecasts than benchmark models for IBM product revenues.
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    Barkoulas and Baum (1997)
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    show that long-memory forecasts result in dramatic improvements in forecasting accuracy, especially over longer horizons, relative to rival models for several Eurocurrency deposit rates. In this paper we investigate the ability of ARFIMA-based forecasts to outperform benchmark linear forecasts on an out-of-sample basis for seasonally adjusted U.
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    The stochastic process ty is both stationary and invertible if all roots of Φ(L) and Θ(L) lie outside the unit circle and d<0.5. The process is said to exhibit long-memory behavior for ()1,0∈d. For d∈0.5,1[), yt is nonstationary (having an infinite variance) but it is mean reverting.
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    Robinson (1995a)
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    proposes a Gaussian semiparametric estimator, GS hereafter, of the self-similarity parameter H. Assume that the spectral density of the time series, denoted by ()⋅f, behaves as ξξ H fG 12 ()~ − as ξ→0+(2) for ()∞∈,0G and ()1,0∈H.
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    Given the GS estimates of d, we approximate the short-run series dynamics by fitting an AR model to the fractionally differenced series using BoxJenkins methods.2,3 A question arises as to the asymptotic properties of the AR parameter estimates in the second stage. Conditioning on the d estimate obtained in the first stage,
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    Wright (1995)
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    shows that the ARp() fitted by the YuleWalker procedure to the d- differenced series inherit the δT-consistency of the 2 All fractional forecasts are based on the GS estimates of the long-memory parameter.
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    We forecast the monetary series by casting the fitted fractional-AR model in infinite autoregressive form, truncating the infinite autoregression at the beginning of the sample (thus setting data points before the sample period equal to zero), and applying Wold's chain rule. A similar procedure was followed by
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    Diebold and Lindner (1996) to
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    forecast the real interest rate and Ray (1993b) to forecast IBM product revenues. The long memory forecasts are compared to those generated by a linear AR model.4 Observations corresponding to the sample period starting in 1991:1 until the end of the sample are our test set (post-prediction interval).5 We consider 1-, 2-, 3-, 4-, 5-, 6-, 7-, 8-, 9-, 10-, 11-, 12-, 15-, 18-, 21-, and 24-months ahe
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    We forecast the monetary series by casting the fitted fractional-AR model in infinite autoregressive form, truncating the infinite autoregression at the beginning of the sample (thus setting data points before the sample period equal to zero), and applying Wold's chain rule. A similar procedure was followed by Diebold and Lindner (1996) to forecast the real interest rate and
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    Ray (1993b) to
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    forecast IBM product revenues. The long memory forecasts are compared to those generated by a linear AR model.4 Observations corresponding to the sample period starting in 1991:1 until the end of the sample are our test set (post-prediction interval).5 We consider 1-, 2-, 3-, 4-, 5-, 6-, 7-, 8-, 9-, 10-, 11-, 12-, 15-, 18-, 21-, and 24-months ahead forecasting horizons.
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    to the forecasting 4 In specifying the lag length for the linear AR model, we follow the same procedure as for the choice of the short-memory (AR) order of the fractional model. 5 We maintain a validation set of adequate size in order to effectively compare the out-of-sample accuracy of competing forecasts for all prediction horizons. 6 See
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    Lardic and Mignon (1996)
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    for arguments on the comparative performance of fractional forecasts over short- and longer-term horizons. horizon. However, the AR forecasts dominate the fractional forecasts for the simple sum M3 aggregate.
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    Even though the fractional forecasts result in rather sizeable forecasting improvements over the benchmark forecasts, such superiority is not generally statistically significant. We also employ the forecasting encompassing testing approach for our competing forecasts suggested by
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    Clements and Hendry (1998).
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    Let 1=ARFIMA model, 2=AR model, =Eiforecast error for model 2,1=i, and =Dthe difference between the forecasts from the two models. The forecast encompassing test is based on running two regressions: the first involves regressing the forecast error from the ARFIMA model on the difference of forecasts, i.e., ε+β+α=tttDE,111,1, and the second involves the regression ε+β+α=tttDE,222,2.
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