Monday, 15 January 2007: 5:00 PM
A new method for time series filtering near endpoints
214C (Henry B. Gonzalez Convention Center)
Time series filtering can be done in the spectral domain without loss of endpoints. However, filtering is commonly performed in the time domain using convolutions, resulting in lost points near the series termini. Multiple incarnations of a least squares minimization approach are developed that retain the endpoint intervals that are normally discarded due to filtering with convolutions in the time domain. The techniques minimize the errors between the pre-determined frequency response function (FRF) of interior points with FRF's that are to be determined for each position in the endpoint zone. The least squares techniques are differentiated by their constraints: (1) unconstrained, (2) equal-mean constraint, and (3) an equal-variance constraint. The equal-mean constraint forces the new weights to sum up to the same value as the pre-determined weights. The equal-variance constraint forces the new weights to be such that, after convolution with the input values, the expected variance is identical to the expected variance of the interior points. The 3 least squares methods are each tested under three separate filtering scenarios (involving AO, MJO, and ENSO time series) and compared to each other as well as to the spectral filtering method – the standard of comparison. The results indicate that all 4 methods (including the spectral method) possess skill at determining suitable endpoints estimates. However, both the unconstrained and equal-mean schemes exhibit bias toward zero near the terminal ends due to problems with appropriating variance. The equal-variance method does not show evidence of this attribute and was never the worst performer. The equal-variance method showed great promise in the ENSO project involving a 5-month running mean filter, and performed at least on par with the other realistic methods for almost all time series positions in all three filtering scenarios. Results were also compared to the boundary constraints utilized in Mann (2004) for smoothing non-stationary time series. Although these three constraints occasionally exhibited the least RMS errors, the outputs were plagued by misappropriated variances.