Exponential smoothing: Behavior of the ex-post sum of squares near 0 and 1

When using simple exponential smoothing on a given time series the nature of the relationship between the optimal smoothing constant and the autocorrelation structure of the series remains an unresolved question. Although numerical search routines can easily be used to find optimal values of the smoothing constant, they offer little insight into the nature of the relationship between the estimated smoothing constant and the structure of the underlying time series. We suggest that renewed investigations of the ex-post sum of squares function may prove helpful in this pursuit. Results are presented that illustrate how the optimal smoothing constant depends upon the value used to initialize the smoothing and upon the sample autocorrelation coefficients of the observed series. These results are based on a new formula for the derivative of the ex-post sum of squares function. In particular, the derivative is examined near 0 and 1, where great simplifications occur in its form, thereby facilitating investigations near these points. A necessary and sufficient condition is stated for when the ex-post sum of squares must have a positive derivative at 0 and the autocorrelation coefficients of the differenced series are shown to affect the sign of the derivative near 1. Based on these results, a general algorithm is presented as an alternative to grid search routines for minimizing the ex-post sum of squares.     

Estimation and testing of time-varying coefficient regression models in the presence of linear restrictions

A linear regression model with random walk coefficients is extended to allow for linear restrictions between the coefficients to be satisfied at each point in time. Estimation in this model is shown to be no more involved than estimation in the standard model. It is also demonstrated how, after a slight modification to the testing problem, classical test procedures may be applied to the problem of testing for such restrictions. The performance of the Lagrange Multiplier test for a variety of different restrictions is then investigated via simulation. An empirical application involving testing for homogeneity in a random walk coefficient version of the AIDS model is given.     

MeV Pb离子在非晶Si中的射程离散──离子束混合和增强扩散的影响

１．０ＭｅＶ２０８Ｐｂ离子在非晶Ｓｉ中的投影射程ＲＰ和射程偏差ΔＲＰ作为注量和温度二者的函数用背散射法进行测定．注量的变化范围为５×１０１３～７×１０１４ｃｍ－２．注入是在室温和ｔ＝－１２０℃下完成的．由由实验所确定的投影射程，射程偏差与注量或温度无关，并且分别等于２９５和７２．２ｎｍ．与ＴＲＩＭ８６的计算结果相比较，发现ＲＰ的偏离为１８％，而ΔＲＰ的偏离为３６％．ＲＰ和ΔＲＰ二者与注量及温度的无关性，排除了所观察到的与ＴＲＩＭ的矛盾是由于注入期间辐射增强扩散或离子束混合效应而引起的解释。     

MD Method in Solving Multiple Criteria Decision Problems Arising from Investment Systems

ＭＤＭｅｔｈｏｄｉｎＳｏｌｖｉｎｇＭｕｌｔｉｐｌｅＣｒｉｔｅｒｉａＤｅｃｉｓｉｏｎＰｒｏｂｌｅｍｓＡｒｉｓｉｎｇｆｒｏｍＩｎｖｅｓｔｍｅｎｔＳｙｓｔｅｍｓＤＵＷｅｎｚｈｏｎｇ;ＣＩＪｉａｎｈｕａ（ＥｃｏｎｏｍｉｃＩｎｆｏｒｍａｔｉｏｎＣｅｎｔｅｒｏｆ...     

Effect of aldosterone and methylprednisolone on cardiac NaK-ATPase

Summary Aldosterone (15 g BID) and methylprednisolone (8 mg QD) administration to female guinea-pigs augmented both the total and the specific activity of NaK-ATPase but not the activity of adenylate cyclase in the cardiac sarcolemma. The rise in NaK-ATPase was due to increase in the number of enzyme molecules; catalytic activity and ouabain-sensitivity of individual molecules did not change.Acknowledgments. This work was supported by grant 1 R01 HL16611 from the National Heart and Lung Institute of the National Institutes of Health, United States Public Health Service. I thank Mr Kooil Kang for his excellent technical assistance.     

Extraction of a weak climatic signal by an ecosystem

The complexity of ecosystems can cause subtle and chaotic responses to changes in external forcing. Although ecosystems may not normally behave chaotically, sensitivity to external influences associated with nonlinearity can lead to amplification of climatic signals. Strong correlations between an El Ni?o index and rainfall and maize yield in Zimbabwe have been demonstrated; the correlation with maize yield was stronger than that with rainfall. A second example is the 100,000-year ice-age cycle, which may arise from a weak cycle in radiation through its influence on the concentration of atmospheric CO2 (ref. 5). Such integration of a weak climatic signal has yet to be demonstrated in a realistic theoretical system. Here we use a particular climatic phenomenon-the observed association between plankton populations around the UK and the position of the Gulf Stream-as a probe to demonstrate how a detailed marine ecosystem model extracts a weak signal that is spread across different meteorological variables. Biological systems may therefore respond to climatic signals other than those that dominate the driving variables.