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Nonparametric smoothing using state space techniques
Author(s) -
Brown Patrick E.,
De Jong Piet
Publication year - 2001
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316049
Subject(s) - smoothing , kalman filter , variance (accounting) , nonparametric statistics , mathematics , state space , equivalence (formal languages) , algorithm , least squares function approximation , computer science , econometrics , statistics , accounting , discrete mathematics , estimator , business
The authors examine the equivalence between penalized least squares and state space smoothing using random vectors with infinite variance. They show that despite infinite variance, many time series techniques for estimation, significance testing, and diagnostics can be used. The Kalman filter can be used to fit penalized least squares models, computing the smoothed quantities and related values. Infinite variance is equivalent to differencing to stationarity, and to adding explanatory variables. The authors examine constructs called “smoothations” which they show to be fundamental in smoothing. Applications illustrate concepts and methods.