This paper presents a simple linear programme for the solution of the trend-estimation problem in time-series. We studied the trade-off between two important properties of the trend component: smoothness and fidelity (closeness to the data). The linear programming solution is a monotone sequence optimizing some (weighted) combination of both properties. A single coefficient in the objective function is user-dependent and represents the user’s preference with respect to the two properties. The method is illustrated on several empirical series.
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Acknowledgements—This work was supported in part by the Recanati Fund of The School of Business, The Hebrew University, Jerusalem. We would like to thank Ms Aliza Schachter for her very helpful suggestions, and the referees for their valuable comments.
- Linear programming
- Multiple criteria
- Time series
- Trend estimation