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In this article we consider the large-sample behavior of estimates of autocorrelations and autoregressive moving average (ARMA) coefficients, as well as their distributions, under weak conditions. Specifically, the usual text book formulas for variances of these estimates are based on strong assumptions and should not be routinely applied without careful consideration. Such is the case when the time series follows an ARMA process with uncorrelated innovations that may not be assumed to be independent and identically distributed. As a specific case, it is well known that if the process is independent and identically distributed, then the sample autocorrelation estimates, scaled by the square root of the sample size, are asymptotically standard normal. This result is used extensively as a diagnostic check on the residuals of a fitted model, or as an initial test on the observed time series to determine whether further model fitting is warranted. In this article we show that this result can be quite misleading. Specifically, if the underlying process is assumed to be uncorrelated rather than independent, then the asymptotic distribution is not necessarily standard normal. Although this distinction may appear superficial, the implications for making valid inference in time series modeling are broad. Usual procedures in time series analysis model correlation structure by fitting models whose estimated errors mimic an uncorrelated sequence. Therefore, testing for the presence of zero autocorrelation using a result that assumes independence may lead to incorrect conclusions. Furthermore, there exist stationary time series that have zero autocorrelation at all lags but yet are not independent, and so it is important to have valid procedures under general dependence structures. Here we present general asymptotic theory for the estimated autocorrelation function and discuss testing for lack of correlation without the further assumption of independence. We propose appropriate resampling methods that can be used to approximate the sampling distribution of the autocorrelation estimates under weak assumptions.

Sex differences exist in the relationship between impairment (muscle strength and contraction velocity) and function. Older men and women may employ different strategies to achieve success on different functional tasks. These findings may have important implications for clinicians practicing geriatric rehabilitation.

Background: Pimobendan is a positive inotrope and vasodilator that may be useful in the treatment of pulmonary hypertension (PHT) secondary to degenerative mitral valve disease.Hypothesis: Pimobendan decreases the severity of PHT measured echocardiographically and improves quality-of-life scores. Changes in N-terminal probrain natriuretic peptide (NT-proBNP) concentrations will reflect improvement in severity of PHT.Animals: Ten client-owned dogs with peak tricuspid regurgitant flow velocity (TRFV) !3.5 m/s. Methods: Prospective short-term, double-blinded, crossover design, with a long-term, open-label component. Short term, dogs were randomly allocated to receive either placebo or pimobendan (0.18-0.3 mg/kg PO q12 h) for 14 days. After a 1-week washout, they received the alternative treatment for 14 days, followed by pimobendan open-label for 8 weeks.Results: Short-term comparison: peak TRFV decreased in all dogs on pimobendan compared with placebo from a median of 4.40 (range, 3.2-5.6) to 3.75 (range, 2.4-4.8) m/s (P o .0001). NT-proBNP concentration decreased after treatment with pimobendan from a median of 2,143 (range, 450-3,981) to 1,329 (range, 123-2,411) pmol/L (P 5 .0009). All dogs improved their quality-of-life score (P 5 .006). In the long-term comparisons, peak TRFV decreased in all dogs from a median of 4.28 (range, 3.5-5.7) to 3.52 (range, 2.4-5.0) m/s (P o .0001). No significant changes in NT-proBNP or quality-of-life scores were detected.Conclusions and Clinical Importance: Pimobendan lowered severity of measurable PHT, improved quality-of-life scores, and decreased NT-proBNP concentrations short-term. Long term, only the reduction in TRFV was maintained.

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