Skip to Main Content
Kernel Smoothing
book

Kernel Smoothing

by Sucharita Ghosh
January 2018
Intermediate to advanced content levelIntermediate to advanced
272 pages
5h 48m
English
Wiley
Content preview from Kernel Smoothing

3 Trend Estimation

3.1 Time series replicates

Consider the trend estimation problem when the observations are serially correlated, i.e., when one has time series data. Such data are very common in many areas of applications, and examples include climate, geophysics, ecology, engineering, medicine, economics, and so on. A time series is generated when a process is monitored over time and observations are recorded. The most important feature of such data is that the observations are serially correlated. In some cases, the observed series may be treated as a time series, as, for instance, in the case of observations from deep ice cores or from a horizontal track in an ecological study.

More generally, several series may be available, as, for instance, in Figure 3.2a–c, and the problem may be to obtain an estimate of the common trend. Thus suppose that k series are available, the length of each series being n. The problem is estimation of the common mean. When one has exactly one series, then k = 1 (see, for instance, Figure 3.1). To formulate the problem, one writes down a nonparametric regression model, where the regression function is the trend function of interest. Statistical properties of the error term are decisive of the properties of the estimated trend.

image

Figure 3.1 Yearly means of daily precipitation totals (05:40 am–05:40 am following day in mm) in Arosa (1840 m asl; ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Smoothing Splines

Smoothing Splines

Yuedong Wang
Handbook of Discrete-Valued Time Series

Handbook of Discrete-Valued Time Series

Richard A. Davis, Scott H. Holan, Robert Lund, Nalini Ravishanker

Publisher Resources

ISBN: 9781118456057Purchase book