By Baldev Raj (auth.), Baldev Raj (eds.)

During 1985-86, the purchase editor for the arts and social sciences department of Kluwer educational Publishers within the Netherlands visited the collage of Horida (where i used to be additionally traveling whereas on sabbatical depart from Wilfrid Laurier collage because the McKethan-Matherly Senior study Fellow) to debate publishing plans of the school. He expressed a willing curiosity in publishing the lawsuits of the convention of the Canadian Econometric examine team (CESG) that used to be to be held the subsequent 12 months at WLU. This quantity is the top made from his curiosity, patience, and endurance. yet for his endurance i'd have given up on th~ undertaking lots of the papers (though now not all) incorporated during this quantity are in keeping with shows at CESG meetings. often times students have been invited to give a contribution to this quantity the place their learn complimented these awarded at those meetings although they weren't convention members. seeing that papers chosen for presentation on the CESG meetings are mostly the completed manufactured from scholarly learn and sometimes less than submission to refereed journals, it used to be impossible to submit the convention lawsuits of their entirety. for this reason it was once made up our minds, in session with the writer, to ask a pick out checklist of authors to put up major extensions of the papers they offered on the CESG meetings for inclusion during this quantity. The editor needs to precise gratitude to all these authors who submitted their papers for assessment by way of nameless referees and for making revisions to comply to our editorial process.

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19. For an application to aggregate output dynamics, see Diebold and Rudebusch (1988a). RANDOM WALKS VS. FRACTIONAL INTEGRATION 43 Appendix: Details of Numerical Procedure The simulation for each of the test statistics is executed as follows. Consider first Rl(k) , the scalar test statistic for the no-drift case. A sample of T N(O, 1) deviates is generated by IMSL subroutine GGNML; these are the values of Alx,. A distributional assumption is of course necessary for finite-sample tabulation. In some economic contexts the nonnality assumption may be inappropriate, but judicious choice of sampling frequency will usually enable its approximate satisfaction.

Ak, respectively. Then, under the random walk null hypothesis, we have: a~ = 2ar a~ = 3ar ak=Kar, or: 2ay 3ar K ar - = - = .. , the variance-time function grows linearly. Conversely, if a time series is white noise, then the variance-time function is horizontal at 2a2. , ARMA) processes have variance-time functions which become flat. These facts have been exploited at least since Working (1949) in attempts to determine the nature of asset price fluctuations. More recently, authors such as Campbell and Mankiw (1987), Cochrane (1988), Fama and French (1988), Huizinga (1986), Lo and MacKinlay (1988), and Poterba and Summers (1987) have used the variance-time function or closely related constructs to 30 FRANCIS X.

2 near the origin. Note, however, the wider range of spectral behavior near the origin that becomes possible when the 'integer d' restriction is relaxed, which gives the ARFIMA class the potential to provide superior approximations to low-frequency dynamics. In the time domain, fractional integration imparts 'long memory,' which is associated with significant dependence between observations widely separated in time. s The usual ARMA process is a short-memory process, and the autocorrelations decline exponentially: Px(t) - r" , 0 < r < 1, t ~ 00.