Abstract
In this paper, we study the problem of extracting trends from time series data involving missing values. In particular, we investigate a general class of procedures that impute the missing data and then extract trends using seasonal-trend decomposition based on loess (STL), where loess stands for locally weighted smoothing, a popular tool for describing the regression relationship between two variables by a smooth curve. We refer to them as the imputation-STL procedures. Two results are obtained in this paper. First, we settle a theoretical issue, namely the connection between imputation error and the overall error from estimating the trend. Specifically, we derive the bounds for the overall error in terms of the imputation error. This subsequently facilitates the error analysis of any imputation-STL procedure and justifies its use in practice. Second, we investigate loess-STL, a particular imputation-STL procedure with the imputation also being performed using loess. Through both theoretical arguments and simulation results, we show that loess-STL has the capacity of handling a high proportion of missing data and providing reliable trend estimates if the underlying trend is smooth and the missing data are dispersed over the time series. In addition to mathematical derivations and simulation study, we apply our loess-STL procedure to profile radiosonde records of upper air temperature at 22 Antarctic research stations covering the past 50 years. For purpose of illustration, we present in this paper only the results for Novolazaravskaja station which has temperature records with more than 8.4% dispersed missing values at 8 pressure levels from October/1969 to March/2011.
Subject
Atmospheric Science,Environmental Science (miscellaneous)
Reference46 articles.
1. Note on graduation by adjusted average;Henderson;Trans. Actuar. Soc. Am.,1916
2. STL: A seasonal-trend decomposition procedure based on loess;Cleveland;J. Off. Stat.,1990
3. Postwar US business cycles: An empirical investigation;Hodrick;J. Money Credit. Bank.,1997
4. New capabilities and methods of the X-12-ARIMA seasonal-adjustment program;Findley;J. Bus. Econ. Stat.,1998
5. A generalization of median filtering using linear combinations of order statistics;Bovik;IEEE Trans. Acoust. Speech Signal Process.,1983
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献