Trend Estimation
Sucharita Ghosh · 2017
This chapter considers 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, such as geophysics, ecology, engineering, and medicine. The chapter also considers the problem of nonparametric estimation of a common trend function. In order to proceed with estimation of the common trend function, smoothness conditions are imposed. There are many examples where the trend is smooth. Such trends can be deterministic or stochastic. Estimation of points of rapid change in the mean function (m(t)) in a nonparametric regression model with time series observation are of interest in palaeo climate research where changes in the past environment are of interest. The chapter addresses estimation of the time points where such changes take place and present some results when there are long memory correlations in the regression errors.