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This paper studies techniques for fitting parsimonious periodic time series models to periodic data. Large sample standard errors for the parameter estimates in a periodic autoregressive moving-average time series model under parametric constraints are derived. Likelihood ratio statistics for hypothesis testing are examined. The techniques are applied in modeling daily temperatures at Griffin, Georgia, USA.

Tail estimates are developed for power law probability distributions with exponential tempering, using a conditional maximum likelihood approach based on the upperorder statistics. Tempered power law distributions are intermediate between heavy power-law tails and Laplace or exponential tails, and are sometimes called "semiheavy" tailed distributions. The estimation method is demonstrated on simulateddata from a tempered stable distribution, and for several data sets from geophysics and finance that show a power law probability tail with some tempering.

This paper studies correlation and partial autocorrelation properties of periodic autoregressive moving-average (PARMA) time series models. An efficient algorithm to compute PARMA autocovariances is first derived. An innovations based algorithm to compute partial autocorrelations for a general periodic series is then developed. Finally, periodic moving averages and autoregressions are characterized as periodically stationary series whose autocovariances and partial autocorrelations, respectively, are zero at all lags that exceed some periodically varying threshold.

The article considers the Yule-Walker estimator of the autoregressive coefficient based on the observed time series that contains an unknown trend function and an autoregressive error term. The trend function is estimated by means of B-splines and then subtracted from the observations. The Yule-Walker estimator is obtained from the residual sequence. Asymptotic properties of this estimator are derived. The performance of the estimator is illustrated by simulation studies and real data analysis.

A robust estimation procedure for periodic autoregressive (PAR) time series is introduced. The asymptotic properties and the asymptotic relative efficiency are discussed by the estimating equation approach. The performance of the robust estimators for PAR time-series models with order one is illustrated by a simulation study. The technique is applied to a real data analysis. Copyright 2007 The Author

The rapid rise in the incidence of obesity has emerged as one of the most pressing global public health issues in recent years. The underlying etiological causes of obesity, whether behavioral, environmental, genetic, or a combination of several of them, have not been completely elucidated. The obesity epidemic has been attributed to the ready availability, abundance, and overconsumption of high-energy content food. We determined here by Pearson's correlation the relationship between food type consumption and rising obesity using the loss-adjusted food availability data from the United States Department of Agriculture (USDA) Economic Research Services (ERS) as well as the obesity prevalence data from the Behavioral Risk Factor Surveillance System (BRFSS) and the National Health and Nutrition Examination Survey (NHANES) at the Centers for Disease Control and Prevention (CDC). Our analysis showed that total calorie intake and consumption of high fructose corn syrup (HFCS) did not correlate with rising obesity trends. Intake of other major food types, including chicken, dairy fats, salad and cooking oils, and cheese also did not correlate with obesity trends. However, our results surprisingly revealed that consumption of corn products correlated with rising obesity and was independent of gender and race/ethnicity among population dynamics in the U.S. Therefore, we were able to demonstrate a novel link between the consumption of corn products and rising obesity trends that has not been previously attributed to the obesity epidemic. This correlation coincides with the introduction of bioengineered corns into the human food chain, thus raising a new hypothesis that should be tested in molecular and animal models of obesity.

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