The 24 references with contexts in paper John Barkoulas, Christopher F. Baum, Mustafa Caglayan (1998) “Fractional Monetary Dynamics” / RePEc:boc:bocoec:321

3
Barnett, W., E. Offenbacher and P. Spindt (1984), The new Divisia monetary aggregates, Journal of Political Economy, 92(6), 1049-1085.
Total in-text references: 1
  1. In-text reference with the coordinate start=17186
    Prefix
    However, a more disaggregated data set may be needed in order to fully address the aggregation argument. -8Analysis of Divisia Indices and Velocity Series We subsequently test for a fractional integration order in an alternative set of monetary aggregates: the Divisia indices (Thornton and Yue (1992)). The Divisia monetary aggregates were proposed by
    Exact
    Barnett et al. (1984)
    Suffix
    as superior to simple-sum aggregates which “implicitly view distant substitutes for money as perfect substitutes for currency.” (1984, p.1051) Barnett et al. found that the Divisia aggregates performed considerably better in terms of causality tests, tests of the structural stability of money demand functions, and forecasting.

4
Diebold, F. X. and G. D. Rudebusch (1989), Long memory and persistence in aggregate output, Journal of Monetary Economics, 24, 189-209.
Total in-text references: 1
  1. In-text reference with the coordinate start=2174
    Prefix
    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
    Exact
    Diebold and Rudebusch (1989) and Sowell (1992a).
    Suffix
    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)).

5
Diebold, F. X. and G. D. Rudebusch (1991), Is consumption too smooth? Long memory and the Deaton paradox, Review of Economics and Statistics, 71, 1-9.
Total in-text references: 1
  1. In-text reference with the coordinate start=2283
    Prefix
    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 Sowell (1992a). Such persistence is also evident in consumption
    Exact
    (Diebold and Rudebusch (1991)),
    Suffix
    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 Porter-Hudak (1990) to examine M1, M2 and M3 aggregates for fractional integration.

6
Fox, R. and M. S. Taqqu (1986), Large sample properties of parameter estimates for strongly dependent Gaussian time-series, Annals of Statistics, 14, 517-532.
Total in-text references: 1
  1. In-text reference with the coordinate start=7470
    Prefix
    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
    Exact
    Fox and Taqqu (1986)),
    Suffix
    which simultaneously estimate both the short-memory and long-memory parameters of the model. These estimation methods are computationally burdensome, rely on the correct specification of the high-frequency (ARMA) structure to obtain consistent parameter estimates, the final ARFIMA specification chosen generally varies across different selection

7
Friedman, B. and K. Kuttner (1992), Money, income, prices, and interest rates, American Economic
Total in-text references: 1
  1. In-text reference with the coordinate start=20665
    Prefix
    Although not every component of the simple-sum aggregates exhibits long memory, the overall evidence is substantial and robust in support of fractional monetary dynamics with long-memory features. Our findings of fractional integration orders between one and two (and statistically distinguishable from one and two) is contrary to the conclusion reached by
    Exact
    King et al. (1991) and Friedman and Kuttner (1992)
    Suffix
    that nominal money balances are I2() processes. A shock to the growth rate of the monetary series displays significant persistence, but it eventually dissipates. The money velocity series are best characterized as unit-root processes.

8
Geweke J. and S. Porter-Hudak (1983), The estimation and application of long memory time series models, Journal of Time Series Analysis, 4, 221-238.
Total in-text references: 3
  1. In-text reference with the coordinate start=3104
    Prefix
    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. More specifically, we -1test for fractional integration, using the spectral regression method developed by
    Exact
    Geweke and Porter-Hudak (1983),
    Suffix
    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

  2. In-text reference with the coordinate start=6196
    Prefix
    The process exhibits short memory for d=0, corresponding to stationary and invertible ARMA modeling. 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.
    Exact
    Geweke and Porter-Hudak (1983)
    Suffix
    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.

  3. In-text reference with the coordinate start=6993
    Prefix
    of the sample λξ πλ ==λ −    2 1 1 T ,...,, T is the number of observations, and ν = gT() << T2 T is the number of Fourier frequencies included in the spectral regression. 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.
    Exact
    Geweke and Porter-Hudak (1983)
    Suffix
    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).

9
Gould, J. P. and C. R. Nelson (1974), The Stochastic Structure of the Velocity of
Total in-text references: 1
  1. In-text reference with the coordinate start=18897
    Prefix
    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.
    Exact
    Gould and Nelson (1974), Nelson and Plosser (1982), and Haraf (1986)
    Suffix
    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.

11
Granger, C. W. J. (1980), Long memory relationships and the aggregation of dynamic models, Journal of Econometrics, 25, 227-238.
Total in-text references: 2
  1. In-text reference with the coordinate start=13131
    Prefix
    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
    Exact
    Granger (1980),
    Suffix
    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

  2. In-text reference with the coordinate start=13281
    Prefix
    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.
    Exact
    Granger (1980)
    Suffix
    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.

12
Granger, C. W. J. and Z. Ding (1996), Varieties of Long Memory Models, Journal of Econometrics, 73, 61-77.
Total in-text references: 1
  1. In-text reference with the coordinate start=13664
    Prefix
    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 distribution with support 0,1(), then the aggregated series is asymptotically fractionally integrated with d<0. 5.
    Exact
    Granger and Ding (1996)
    Suffix
    extended the aggregation argument to mixtures of Ijd() processes for a range of distributions for dj; they also showed that other data generating mechanisms, like time-varying coefficient models and possibly nonlinear models, can have the long-memory property.

13
Granger, C. W. J. and R. Joyeux (1980), An introduction to long-memory time series models and fractional differencing, Journal of Time Series Analysis, 1, 15-39. -14-
Total in-text references: 2
  1. In-text reference with the coordinate start=1713
    Prefix
    Any dynamic macroeconomic model, 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
    Exact
    Granger and Joyeux (1980) and Hosking (1981)
    Suffix
    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.

  2. In-text reference with the coordinate start=5209
    Prefix
    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
    Exact
    Granger and Joyeux (1980).
    Suffix
    Assuming that d∈0, 0. 5() and d≠0, Hosking (1981) 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.

14
Haraf, W. S. (1986), Monetary Velocity and Monetary Rules, Cato Journal, 6, 641-62.
Total in-text references: 1
  1. In-text reference with the coordinate start=18897
    Prefix
    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.
    Exact
    Gould and Nelson (1974), Nelson and Plosser (1982), and Haraf (1986)
    Suffix
    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.

15
Hassler, U. (1993), Regression of spectral estimators with fractionally integrated time series, Journal of Time Series Analysis, 14, 369-380.
Total in-text references: 1
  1. In-text reference with the coordinate start=7091
    Prefix
    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
    Exact
    Robinson (1995) and Hassler (1993)
    Suffix
    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

16
Hassler, U. and J. Wolters (1995), Long memory in inflation rates: International evidence, Journal of Business and Economic Statistics, 13, 37-45.
Total in-text references: 1
  1. In-text reference with the coordinate start=2414
    Prefix
    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 (Shea (1991)), and inflation rates (Baillie, Chung, and Tieslau (1996),
    Exact
    Hassler and Wolters (1995),
    Suffix
    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.

17
Hosking, J. R. M. (1981), Fractional Differencing, Biometrika, 68, 165-176.
Total in-text references: 2
  1. In-text reference with the coordinate start=1713
    Prefix
    Any dynamic macroeconomic model, 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
    Exact
    Granger and Joyeux (1980) and Hosking (1981)
    Suffix
    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.

  2. In-text reference with the coordinate start=5279
    Prefix
    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,
    Exact
    Hosking (1981)
    Suffix
    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.

18
King, R., C. Plosser, J. Stock, and M. Watson (1991), Stochastic trends and economic fluctuations, American Economic Review, 81, 819-840.
Total in-text references: 1
  1. In-text reference with the coordinate start=20665
    Prefix
    Although not every component of the simple-sum aggregates exhibits long memory, the overall evidence is substantial and robust in support of fractional monetary dynamics with long-memory features. Our findings of fractional integration orders between one and two (and statistically distinguishable from one and two) is contrary to the conclusion reached by
    Exact
    King et al. (1991) and Friedman and Kuttner (1992)
    Suffix
    that nominal money balances are I2() processes. A shock to the growth rate of the monetary series displays significant persistence, but it eventually dissipates. The money velocity series are best characterized as unit-root processes.

20
Nelson, C. R. and C. I. Plosser (1982), Trends and Random Walks in Macroeconomic
Total in-text references: 1
  1. In-text reference with the coordinate start=18897
    Prefix
    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.
    Exact
    Gould and Nelson (1974), Nelson and Plosser (1982), and Haraf (1986)
    Suffix
    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.

24
Porter-Hudak, S. (1990), An application of the seasonal fractionally differenced model to the monetary aggregates, Journal of the American Statistical Association, 85, 338-344.
Total in-text references: 3
  1. In-text reference with the coordinate start=2574
    Prefix
    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
    Exact
    Porter-Hudak (1990) to
    Suffix
    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.

  2. In-text reference with the coordinate start=9936
    Prefix
    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
    Exact
    Porter-Hudak (1990)
    Suffix
    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.

  3. In-text reference with the coordinate start=21556
    Prefix
    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.
    Exact
    Porter-Hudak (1990)
    Suffix
    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.

25
Robinson, P. (1995), Log-periodogram regression of time series with long range dependence, Annals of Statistics, 23, 1048-1072.
Total in-text references: 1
  1. In-text reference with the coordinate start=7091
    Prefix
    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
    Exact
    Robinson (1995) and Hassler (1993)
    Suffix
    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

27
Serletis, A. (1995), Random Walks, Breaking Trend Functions, and the Chaotic Structure of the Velocity of Money, Journal of Business and Economic Statistics, 13(4), 453-
Total in-text references: 1
  1. In-text reference with the coordinate start=19073
    Prefix
    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
    Exact
    Serletis (1995),
    Suffix
    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.

28
Shea, G. S. (1991), Uncertainty and implied variance bounds in long-memory models of the interest rate term structure, Empirical Economics, 16, 287-312.
Total in-text references: 1
  1. In-text reference with the coordinate start=2334
    Prefix
    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
    Exact
    (Shea (1991)), and
    Suffix
    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.

29
Sowell, F. (1992a), Modeling long-run behavior with the fractional ARIMA model, Journal of Monetary Economics, 29, 277-302.
Total in-text references: 1
  1. In-text reference with the coordinate start=2174
    Prefix
    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
    Exact
    Diebold and Rudebusch (1989) and Sowell (1992a).
    Suffix
    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)).

30
Sowell, F. (1992b), Maximum likelihood estimation of stationary univariate fractionally-integrated time-series models, Journal of Econometrics, 53, 165188.
Total in-text references: 1
  1. In-text reference with the coordinate start=7370
    Prefix
    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
    Exact
    Sowell (1992b))
    Suffix
    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.

31
Thornton, D. and P. Yue (1992), An extended series of Divisia monetary aggregates, Federal Reserve
Total in-text references: 2
  1. In-text reference with the coordinate start=17106
    Prefix
    However, a more disaggregated data set may be needed in order to fully address the aggregation argument. -8Analysis of Divisia Indices and Velocity Series We subsequently test for a fractional integration order in an alternative set of monetary aggregates: the Divisia indices
    Exact
    (Thornton and Yue (1992)).
    Suffix
    The Divisia monetary aggregates were proposed by Barnett et al. (1984) as superior to simple-sum aggregates which “implicitly view distant substitutes for money as perfect substitutes for currency.” (1984, p.1051) Barnett et al. found that the Divisia aggregates performed considerably better in terms of causality tests, tests of the structural stability of money demand f

  2. In-text reference with the coordinate start=24106
    Prefix
    monetary series would be likely to trigger these effects. -12Appendix All data series are seasonally adjusted, monthly observations obtained from the Federal Reserve Bank of St Louis' FRED database, which contains series originally published by the Board of Governors of the Federal Reserve System. The Divisia aggregates series were originally published in
    Exact
    Thornton and Yue (1992).
    Suffix
    For the Divisia M1, M2, M3, and L series, the sample period is 1960:1 to 1992:12. The sample period is 1959:1 to 1995:10 for the following series: simple-sum M1, M2, M3, L, currency in circulation, demand deposits, total checkable deposits, small time deposits at commercial banks, small time deposits at thrift institutions, savings deposits at comm

32
Tsay, W. and C. Chung (1995), The spurious regression of fractionally integrated processes, working paper 9503, Michigan State University. -16-
Total in-text references: 1
  1. In-text reference with the coordinate start=23426
    Prefix
    The nonlinear relations arising in this context deserve further scrutiny. Finally, care must be exercised in interpreting results from regressions involving the growth rates of monetary series.
    Exact
    Tsay and Chung (1995)
    Suffix
    have shown the existence of spurious effects in regressions involving two -11independent long memory fractionally integrated processes whose orders of integration sum up to a value greater than 0.5.