Jaechoul Lee

Trends in Extreme U.S. Temperatures

This paper develops trend estimation techniques for monthly maximum and minimum temperature time series observed in the 48 conterminous United States over the last century. While most scientists concur that this region has warmed on aggregate, there is no a priori reason to believe that temporal trends in extremes andaverageswillexhibitthesamepatterns.Indeed,underminorregularityconditions, thesamplepartialsum and maximum of stationary time series are asymptotically independent (statistically). Previous authors have suggested that minimum temperatures are warming faster than maximum temperatures in the United States; such an aspect can be investigated via the methods discussed in this study. Here, statistical models with extreme value and changepoint features are used to estimate trends and their standard errors. A spatial smoothing is then done to extract general structure. The results show that monthly maximum temperatures are not often greatly changing—perhaps surprisingly, there are many stations that show some cooling. In contrast,theminimumtemperaturesshowsignificantwarming. Overall,thesoutheasternUnitedStatesshows the least warming (even some cooling), and the western United States, northern Midwest, and New England have experienced the most warming.

Equivalent sample sizes in time series regressions

This article studies confidence intervals for regression parameters in time series settings. An equivalent sample size method is proposed that retains the simple interval structure inherent with white noise model errors, but modifies the sample size to account for the serial autocorrelations present in the errors. This makes the interval perform akin to weighted least squares intervals. The accuracy of the approach is demonstrated in three common regression problems. A noteworthy by-product of the work identifies explicit variances of several classical regression statistics in time series settings.

Prescribed Fire Effects on Activity and Movement of Cattle in Mesic Sagebrush Steppe

ABSTRACT Prescribed fire has long been used worldwide for livestock and wildlife management. Prescribed fire effects on activity budgets and movement path characteristics of grazing animals, however, remain largely unknown. We evaluated whether prescribed-fire treatments in mesic sagebrush steppe affect cattle behaviors, which could influence foraging efficiency and, ultimately, impact animal productivity.Mature, lactating beef cows grazing within two study areas located in the Owyhee Mountains of southwestern Idaho, United States were tracked with Global Positioning System collars for 2 yr before and 5 yr after fall prescribed fire. Tracking data were then classified into stationary, foraging, and traveling activity types on the basis of movement distance and velocity thresholds. After fire, cattle in burned sites tended to increase their foraging activity budgets, bout durations, bout counts, and path lengths relative to prefire and cattle in unburned sites. Fire did not affect steepness of cattle foraging paths. Prescribed fire in mesic sagebrush steppe can be used to create opportunities for cattle to improve foraging efficiency by altering their activity budgets and movement path characteristics. Any consequent improvements in foraging efficiency could, in turn, promote increased rates of weight gain, better body condition, enhanced reproductive success, and ultimately, more pounds of beef for market.

A Reformulation of Weighted Least Squares Estimators

This article studies weighted, generalized, least squares estimators in simple linear regression with serially correlated errors. Closed-form expressions of weighted least squares estimators and variances are presented under some common stationary autocorrelation settings, a first-order autoregression and a first-order moving-average. These explicit expressions also have appealing applications, including an efficient weighted least squares computation method and a new sufficient and necessary condition on the equality of weighted least squares estimators and ordinary least squares estimators.

An efficient generalized least squares algorithm for periodic trended regression with autoregressive errors

Time series data with periodic trends like daily temperatures or sales of seasonal products can be seen in periods fluctuating between highs and lows throughout the year. Generalized least squares estimators are often computed for such time series data as these estimators have minimum variance among all linear unbiased estimators. However, the generalized least squares solution can require extremely demanding computation when the data is large. This paper studies an efficient algorithm for generalized least squares estimation in periodic trended regression with autoregressive errors. We develop an algorithm that can substantially simplify generalized least squares computation by manipulating large sets of data into smaller sets. This is accomplished by coining a structured matrix for dimension reduction. Simulations show that the new computation methods using our algorithm can drastically reduce computing time. Our algorithm can be easily adapted to big data that show periodic trends often pertinent to economics, environmental studies, and engineering practices.

A New Test for Short Memory in Long Memory Time Series

This article considers short memory characteristics in a long memory process. We derive new asymptotic results for the sample autocorrelation difference ratios. We used these results to develop a new portmanteau test that determines if short memory parameters are statistically significant. In simulations, the new test can detect short memory components more often than the Ljung-Box test when these short memory components are in fact within a long memory process. Interestingly, our test finds short memory autocorrelations in U.S. inflation rate data, whereas the Ljung-Box test fails to find these autocorrelations. Modeling these short memory autocorrelations of the inflation rate data leads to improved model accuracy and more precise prediction.

A refined efficiency rate for ordinary least squares and generalized least squares estimators for a linear trend with autoregressive errors

When a straight line is fitted to time series data, generalized least squares (GLS) estimators of the trend slope and intercept are attractive as they are unbiased and of minimum variance. However, computing GLS estimators is laborious as their form depends on the autocovariances of the regression errors. On the other hand, ordinary least squares (OLS) estimators are easy to compute and do not involve the error autocovariance structure. It has been known for 50 years that OLS and GLS estimators have the same asymptotic variance when the errors are second‐order stationary. Hence, little precision is gained by using GLS estimators in stationary error settings. This article revisits this classical issue, deriving explicit expressions for the GLS estimators and their variances when the regression errors are drawn from an autoregressive process. These expressions are used to show that OLS methods are even more efficient than previously thought. Specifically, we show that the convergence rate of variance differences is one polynomial degree higher than that of least squares estimator variances. We also refine Grenanders (1954) variance ratio. An example is presented where our new rates cannot be improved upon. Simulations show that the results change little when the autoregressive parameters are estimated.