The 25-year decline in nonperforated appendicitis and the recent increase in appendectomies coincident with more frequent use of CT imaging and laparoscopic appendectomies did not result in expected decreases in perforation rates. Similarly, time series analysis did not find a significant negative relationship between negative appendectomy and perforation rates. This disconnection of trends suggests that perforated and nonperforated appendicitis may have different pathophysiologies and that nonoperative management with antibiotic therapy may be appropriate for some initially nonperforated cases. Further efforts should be directed at identifying preoperative characteristics associated with nonperforating appendicitis that may eventually allow surgeons to defer operation for those cases of nonperforating appendicitis that have a low perforation risk.

No abstract

A class of stationary long-memory processes is proposed which is an extension of the fractional autoregressive moving-average (FARMA) model. The FARMA model is limited by the fact that it does not allow data with persistent cyclic (or seasonal) behavior to be considered. Our extension, which includes the FARMA model as a special case, makes use of the properties of the generating function of the Gegenbauer polynomials, and we refer to these models as Gegenbauer autoregressive moving-average (GARMA) models. While the FARMA model has a peak in the spectrum at f = 0, the GARMA process can model long-term periodic behavior for any frequency 0 < f < 0.5.Properties of the GARMA process are examined and techniques for generation of realizations, model identification and parameter estimation are proposed. The use of the GARMA model is illustrated through simulated examples as well as with classical sunspot data.

No abstract

Long-memory models have been used by several authors to model data with persistent autocorrelations. The fractional and fractional autoregressive movingaverage (FARMA) models describe long-memory behavior associated with an in®nite peak in the spectrum at f 0. The Gegenbauer and Gegenbauer ARMA (GARMA) processes of Gray, Zhang and Woodward (On generalized fractional processes. J. Time Ser. Anal. 10 (1989), 233±57) can model long-term periodic behavior for any frequency 0 < f < 0X5. In this paper we introduce a k-factor extension of the Gegenbauer and GARMA models that allows for long-memory behavior to be associated with each of k frequencies in [0, 0X5]. We prove stationarity conditions for the k-factor model and discuss issues such as parameter estimation, model identi®cation, realization generation and forecasting. A two-factor GARMA model is then applied to the Mauna Loa atmospheric CO 2 data. It is shown that this model provides a reasonable ®t to the CO 2 data and produces excellent forecasts.