The 17 reference contexts in paper John Barkoulas, Christopher F. Baum, Mustafa Caglayan (1998) “Fractional Monetary Dynamics” / RePEc:boc:bocoec:321

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    , whether an IS-LM based structure or a much more elaborate framework, will contain a number of economic variables which have been empirically identified as possessing fractional dynamics, or elements of strong persistence, in their time series representation. The model of fractionally integrated timeseries developed by Granger and Joyeux (1980) and
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    Hosking (1981)
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    allows for a fractional, as opposed to an integer, exponent in the differencing process of the time series. This avoids the 'knife-edge' unit root distinction while permitting a modelled series to exhibit the persistence, or 'long memory,' which characterizes many macroeconomic timeseries.
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    This avoids the 'knife-edge' unit root distinction while permitting a modelled series to exhibit the persistence, or 'long memory,' which characterizes many macroeconomic timeseries. For instance, fractionally integrated output series have been identified by Diebold and Rudebusch (1989) and
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    Sowell (1992a).
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    Such persistence is also evident in consumption (Diebold and Rudebusch (1991)), interest rates (Shea (1991)), and inflation rates (Baillie, Chung, and Tieslau (1996), Hassler and Wolters (1995), Baum, Barkoulas, and Caglayan (1997)).
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    For instance, fractionally integrated output series have been identified by Diebold and Rudebusch (1989) and Sowell (1992a). Such persistence is also evident in consumption (Diebold and Rudebusch (1991)), interest rates
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    (Shea (1991)), and
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    inflation rates (Baillie, Chung, and Tieslau (1996), Hassler and Wolters (1995), Baum, Barkoulas, and Caglayan (1997)). The importance of measures of money in a macroeconomic modelling framework led Porter-Hudak (1990) to examine M1, M2 and M3 aggregates for fractional integration.
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    Such persistence is also evident in consumption (Diebold and Rudebusch (1991)), interest rates (Shea (1991)), and inflation rates (Baillie, Chung, and Tieslau (1996), Hassler and Wolters (1995), Baum, Barkoulas, and Caglayan (1997)). The importance of measures of money in a macroeconomic modelling framework led
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    Porter-Hudak (1990) to
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    examine M1, M2 and M3 aggregates for fractional integration. The latter study provides the motivation for this paper, in which we extend Porter-Hudak's study of fractional integration in the monetary aggregates in several important ways in order to provide comprehensive evidence on the nature of fractional dynamic behavior in these series.
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    paper, in which we extend Porter-Hudak's study of fractional integration in the monetary aggregates in several important ways in order to provide comprehensive evidence on the nature of fractional dynamic behavior in these series. More specifically, we -1test for fractional integration, using the spectral regression method developed by Geweke and
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    Porter-Hudak (1983),
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    in both simple-sum and Divisia monetary aggregates, monetary base, money multipliers, and velocity series. Given clear evidence of fractional integration in the aggregates, we subsequently try to identify which components of the monetary aggregates might be responsible for fractional integration and therefore evaluate Granger's (1980) aggregation hypothesi
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    The stochastic process yt 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 nonstationary for d≥0. 5, as it possesses infinite variance, i.e. see Granger and Joyeux (1980). Assuming that d∈0, 0. 5() and d≠0,
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    Hosking (1981)
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    showed that the correlation function, ρ(⋅), of an ARFIMA process is proportional to 2d−1k as k→∞. Consequently, the autocorrelations of the ARFIMA process decay hyperbolically to zero as k→∞ which is contrary to the faster, geometric decay of a stationary ARMA process.
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    For d∈0. 5,1[) the process is mean reverting, even though it is not covariance stationary, as there is no long-run impact of an innovation on future values of the process. Geweke and
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    Porter-Hudak (1983)
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    suggest a semiparametric procedure to obtain an estimate of the fractional differencing parameter d based on the slope of the spectral density function around the angular frequency ξ=0.
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    Assuming that T→∞ limgT()=∞, T→∞ lim gT() T       =0, and T→∞ lim lnT()2 gT() =0, the negative of the OLS estimate of the slope coefficient in (3) provides an estimate of d. Geweke and
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    Porter-Hudak (1983)
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    prove consistency and asymptotic normality for d<0, while Robinson (1995) and Hassler (1993) prove consistency and asymptotic normality for d∈0, 0. 5() in the case of Gaussian ARMA innovations in (1).
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    Assuming that T→∞ limgT()=∞, T→∞ lim gT() T       =0, and T→∞ lim lnT()2 gT() =0, the negative of the OLS estimate of the slope coefficient in (3) provides an estimate of d. Geweke and Porter-Hudak (1983) prove consistency and asymptotic normality for d<0, while
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    Robinson (1995) and Hassler (1993)
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    prove consistency and asymptotic normality for d∈0, 0. 5() in the case of Gaussian ARMA innovations in (1). Other authors have used maximum likelihood methods (i.e., the exact maximum likelihood method proposed by Sowell (1992b)) or the approximate frequency domain maximum likelihood method proposed by Fox and Taqqu (1986)), which simultaneously estima
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    Geweke and Porter-Hudak (1983) prove consistency and asymptotic normality for d<0, while Robinson (1995) and Hassler (1993) prove consistency and asymptotic normality for d∈0, 0. 5() in the case of Gaussian ARMA innovations in (1). Other authors have used maximum likelihood methods (i.e., the exact maximum likelihood method proposed by
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    Sowell (1992b))
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    or the approximate frequency domain maximum likelihood method proposed by Fox and Taqqu (1986)), which simultaneously estimate both the short-memory and long-memory parameters of the model.
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    The unit-root hypothesis in the growth rates of the simple-sum monetary indices is decidedly rejected and evidence of fractional dynamics with long memory features is established. If we compare the range of these estimates to those estimated by
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    Porter-Hudak (1990)
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    over the 19591986 period, we find values that are broadly comparable.2 1 We also applied the Phillips-Perron (PP, 1988) and Kwiatkowski, Phillips, Schmidt, and Shin (KPSS, 1992) unit-root tests to the growth rates of the monetary series.
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    of the sample period.3 3 Subsample estimates are not reported here, but are available upon request from the authors. -6Analysis of Components of the Monetary Aggregates Given the presence of a fractional exponent in the differencing process for the monetary aggregates, we now attempt to determine the sources of fractional dynamics. One explanation, attributed to
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    Granger (1980),
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    is that a persistent process can arise from the aggregation of constituent processes each of which has short memory. Granger (1980) showed that if a time series ty is the sum of an infinite number of independent first-order Markov processes which have equal variances and whose autoregressive parameters are drawn independently from a beta distributio
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    the Monetary Aggregates Given the presence of a fractional exponent in the differencing process for the monetary aggregates, we now attempt to determine the sources of fractional dynamics. One explanation, attributed to Granger (1980), is that a persistent process can arise from the aggregation of constituent processes each of which has short memory.
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    Granger (1980)
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    showed that if a time series ty is the sum of an infinite number of independent first-order Markov processes which have equal variances and whose autoregressive parameters are drawn independently from a beta distribution with support 0,1(), then the aggregated series is asymptotically fractionally integrated with d<0. 5.
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    The time series properties behavior of the velocity of money in the U.S. has attracted a great deal of attention in the literature given its implications for the monetarist position. Gould and
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    Nelson (1974),
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    Nelson and Plosser (1982), and Haraf (1986) conclude that money velocity contains a unit root. A similar conclusion is reached by Serletis (1995), even after allowing for the possibility of a -9one-time break in the intercept and the slope of the trend function at an unknown point in time.
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    The time series properties behavior of the velocity of money in the U.S. has attracted a great deal of attention in the literature given its implications for the monetarist position. Gould and Nelson (1974), Nelson and Plosser (1982), and
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    Haraf (1986)
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    conclude that money velocity contains a unit root. A similar conclusion is reached by Serletis (1995), even after allowing for the possibility of a -9one-time break in the intercept and the slope of the trend function at an unknown point in time.
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    The time series properties behavior of the velocity of money in the U.S. has attracted a great deal of attention in the literature given its implications for the monetarist position. Gould and Nelson (1974), Nelson and Plosser (1982), and Haraf (1986) conclude that money velocity contains a unit root. A similar conclusion is reached by
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    Serletis (1995),
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    even after allowing for the possibility of a -9one-time break in the intercept and the slope of the trend function at an unknown point in time. Table 4 reports the fractional-exponent estimates for the growth rates of both simple-sum and Divisia velocities.
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    Since long memory represents nonlinear dependence in the first moment of the distribution and hence a potentially predictable component in the series dynamics, the possibility of improved forecasting via the estimation of an ARFIMA model arises.
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    Porter-Hudak (1990)
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    found superior out-of-sample forecasting performance of an ARFIMA model for the M1 aggregate versus a benchmark ARIMA model. Given the substantial fractional exponent in the differencing process in our series, similar improvements in forecasting accuracy may be expected to result from the estimation of an appropriate ARFIMA model for our data series.
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