- 22
- Hosking, J. R. M. 1981. Fractional differencing.. 68:165176.

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- Prefix
- An explanation for this conflicting evidence was recently provided by modeling inflation rates as fractionally integrated processes. Using the fractional differencing model developed by Granger and Joyeux (1980),
- Exact
- Hosking (1981), and
- Suffix
- Geweke and Porter-Hudak (1983), Baillie, Chung, and 4 Tieslau (1996) find strong evidence of long memory in the inflation rates for the Group of Seven (G7) countries (with the exception of Japan) and those of three high inflation countries: Argentina, Brazil, and Israel.

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- Prefix
- The stochastic process is both stationary and invertible if all roots ofandlie outside the unit circle and. The process is nonstationary for, as 7 t \b( )-( ) 0505 jjd< :d : it possesses infinite variance, i.e. see Granger and Joyeux (1980). 26 d;: d -k k k d;:-j n (0 0 5)= 0 () Assuming thatand,
- Exact
- Hosking (1981)
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- showed that the correlation function, , of an ARFIMA process is proportional to as. Consequently, the autocorrelations of the ARFIMA process decay hyperbolically to zero asin contrast to the faster, geometric decay of a stationary ARMA process.

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- 23
- Kim, Chang-Jin. 1993. Unobserved-component time series models with Markov-switching heteroscedasticity: Changes in regime a

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- Prefix
- Despite extensive research following the pioneering work of Nelson and Plosser (1982), disagreement remains in the literature on a key question: does the postwar inflation rate possess a unit root? Although there is considerable evidence in support of a unit root (e.g. Barsky 1987; MacDonald and Murphy 1989; Ball and Cecchetti 1990; Wickens and Tzavalis 1992; and
- Exact
- Kim 1993),
- Suffix
- Rose (1988) provided evidence of stationarity in inflation rates. Mixed evidence has been provided by Kirchgassner and Wolters (1993). Brunner and Hess (1993) argue that the inflation rate was stationary before the 1960s, but that it possesses a unit root since that time.

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- Porter-Hudak, Susan. 1990. An application of the seasonal fractionally differenced model to the monetary aggregates. . 85:338-344.

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- Prefix
- argument put forth by Granger (1980), which states that persistence can arise from the aggregation of constituent processes, each of which has short memory.Granger and Ding (1996) show that the long-memory property could also arise from time-varying coefficient models or nonlinear models. An alternative conjecture is that inflation inherits the long-memory property from money growth.
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- Porter-Hudak (1990) and
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- Barkoulas, Baum, and Caglayan (1998) have shown that the U.S. monetary aggregates exhibit the long-memory property, which will be transmitted to inflation, given the dependence of long-run inflation on the growth rate of money.

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- 36
- Robinson, Peter. 1995a. Log-periodogram regression of time series

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- Assuming that lim, lim, and lim , the negative of the OLS estimate of the slope coefficient in (2) provides an estimate of . Geweke and Porter-Hudak (1983) prove consistency and asymptotic normality for, while
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- Robinson (1995a)
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- proves consistency and asymptotic normality forin the case of Gaussian ARMA innovations in (1). Ooms and Hassler (1997) show that the spectral regression will contain singularities due to prior deseasonalization of the series through standard seasonal adjustment techniques (utilizing seasonal dummy variables).

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- Robinson, Peter. 1995b. Gaussian semiparametric estimation of long range dependence.. 23:1630-1661.

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- to 9 non o 2 ()ln() () TT gT TT T gT 1 !1!1!1 0 0 (0 0 5) 2 () I2 -s ==0 -;- ;:::; s;s seasonal frequencies when estimating the log-periodogram regression in : (2) We refer to this method, which yields more stable and reliable estimates than those generated by the standard spectral regression approach, as the adjusted spectral regression method. The Gaussian Semiparametric Method
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- Robinson (1995b)
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- proposes a Gaussian semiparametric estimator, GS hereH f f - G-;H;H dHdH after, of the self-similarity parameter , which is not defined in closed form. It is assumed that the spectral density of the time series, denoted by, behaves as as () ()0 (0)(0 1) =+ ()=ln () (21) 1 ln H 12+ -! 21 2 for Gand.

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- Sowell, Fallaw. 1992. Maximum likelihood estimation of stationary univariate fractionally-integrated time-series models. . 53:165-188.

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- Prefix
- Cheung and Diebold (1994) suggest that the frequency-domain approximate ML estimator compares favorably, in terms of its finite-sample properties, to the much more computationally arduous time-domain exact ML estimator proposed by
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- Sowell (1992)
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- in the case that the mean of the process is unknown. ()( ) I-f-;\r \r -11 3. Data and Empirical Estimates Data We perform the analysis on CPI-based inflation rates for 27 countries and WPI-based inflation rates for 22 countries.

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- Tsay, Wen-Jen. 1995. Spurious effects concerned with fractional processes. Ph.D. dissertation, Michigan State University, East Lansing, MI.

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- Prefix
- Care must be exercised in estimating any regression in which two or more fractionally integrated processes appear, as they would in virtually any model containing two or more of the series studied here. If their orders of integration sum to greater than 0.5, ëspurious regressioní effects might appear
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- (Tsay 1995).
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- 9 4. Conclusions and Implications This paper tests for the existence of long memory, or persistence, in international inflation rates for a number of industrial and developing countries using semiparametric and maximum likelihood estimation methods.

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