L1和L2规则化趋势滤波的稳健估计

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Abstract The L1 and L2 regularized trend filtering can’t extract correct trend from the series which have outliers. Thus, under the consideration of robustness, this paper substitutes least square loss function with Huber loss function to obtain a robust estimation of the L1 and L2 regularized trend filtering by convex optimization. The simulation shows that robust estimation can prevent the effect of outliers. This method can be applied to financial data which has many outliers to get a robust estimation of market trend.

Key words： L1 and L2 regularized trend filtering Huber loss function robust estimation financial data

Received: 02 May 2013 Published: 15 August 2013

PACS:

O213

Corresponding Authors: XIE Bangchang E-mail: 025674@mail.fju.edu.tw

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Cite this article:

XIE Bang-Chang,QIN Lei. Robust Estimation of L1 and L2 Regularized Trend Filtering[J]. , 2013, (8): 84-90.

URL:

http://zzs.zjgsu.edu.cn/gl/EN/ OR http://zzs.zjgsu.edu.cn/gl/EN/Y2013/V/I8/84

[1]	HODRICK R J, PRESCOTT E C. Postwar US business cycles: an empirical investigation[J]. Journal of Money, credit, and Banking, 1997: 1-16.
[2]	KIM S J, KOH K, BOYD S, et al. ?1 Trend Filtering[J]. Siam Review, 2009, 51(2): 339-360.
[3]	OSBORN D R. Moving Average Detrending and the Analysis of Business Cycles[J]. Oxford Bulletin of Economics and Statistics, 1995, 57(4): 547-558.
[4]	LUCAS R E. Two illustrations of the quantity theory of money[J]. The American Economic Review, 1980, 70(5): 1005-1014.
[5]	REINSCH C H. Smoothing by spline functions[J]. Numerische mathematik, 1967, 10(3): 177-183.
[6]	HUBER P J. Robust Statistics, Wiley, New York, 1981.
[7]	TIBSHIRANI R. Regression shrinkage and selection via the lasso[J]. Journal of the Royal Statistical Society. Series B (Methodological), 1996: 267-288.
[8]	HOERL A E, KENNARD R W. Ridge regression: Biased estimation for nonorthogonal problems[J]. Technometrics, 1970, 12(1): 55-67.
[9]	OWEN A B. A robust hybrid of lasso and ridge regression[J]. Contemporary Mathematics, 2007, 443: 59-72.
[10]	GRANT M, BOYD S, YE Y. cvx users’ guide[R]. Technical Report, 2009.
[11]	STURM J F. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones[J]. Optimization methods and software, 1999, 11(1-4): 625-653.