http://landshape.org/enm/rahmstorf-et-al-2007-update/ The power of numeracy Wed, 10 Mar 2010 22:58:48 -0600 http://wordpress.org/?v=2.8.6 hourly 1 http://landshape.org/enm/rahmstorf-et-al-2007-update/comment-page-1/#comment-113534 Niche Modeling » Examples of simple smoothers Thu, 17 Apr 2008 18:31:32 +0000 http://landshape.org/enm/rahmstorf-et-al-2007-update/#comment-113534 [...] To show this I looked at three different methods with slightly varying end points. Two are causal smoothers (SSA and spline) and one is an acausal (moving average). Causal smoothers do not use future data to create a trend to the end point of the series. Acausal smoothers (such as moving averages) need past and future data, and so stop half a window short of the endpoint (see wiki) All data are global temperature data from GISS from 1973 to 2006. 1. Singular Spectrum Analysis. Below is the figure of the result of two approaches to CaterpillerSSA, with 11 year embedding period. The red curve resulted from padding the end with data reflected around the final 2006 value, the so-called ‘minimum roughness condition’. The blue one is without padding. The two different approaches differ throughout the whole length, except where the two curves meet at year 1999. The last seven points deviate quite a lot, illustrating uncertainty at the end. 2. Smooth spline The figure below is a smooth spline method of fitting and another approach to estimating uncertainty. This fits a higher order non-linear regression line to the points, with 11 degrees of freedom. In this graph, the last point 2006 has been altered to either the top or bottom of the 95% channel range. That is, the last point covers the range of random variation that might reasonably be expected. The two curves differ again, but this time they flex about the 11th point from the end. Further discussion of this method here. 3. Moving average The final figure below shows the result of running a moving average with an end point at 2006 of 0.6 and 0.3. The moving average stops 5 points short of the end of the series, and the last point varies as a result of the variation at 2006. [...] [...] To show this I looked at three different methods with slightly varying end points. Two are causal smoothers (SSA and spline) and one is an acausal (moving average). Causal smoothers do not use future data to create a trend to the end point of the series. Acausal smoothers (such as moving averages) need past and future data, and so stop half a window short of the endpoint (see wiki) All data are global temperature data from GISS from 1973 to 2006. 1. Singular Spectrum Analysis. Below is the figure of the result of two approaches to CaterpillerSSA, with 11 year embedding period. The red curve resulted from padding the end with data reflected around the final 2006 value, the so-called ‘minimum roughness condition’. The blue one is without padding. The two different approaches differ throughout the whole length, except where the two curves meet at year 1999. The last seven points deviate quite a lot, illustrating uncertainty at the end. 2. Smooth spline The figure below is a smooth spline method of fitting and another approach to estimating uncertainty. This fits a higher order non-linear regression line to the points, with 11 degrees of freedom. In this graph, the last point 2006 has been altered to either the top or bottom of the 95% channel range. That is, the last point covers the range of random variation that might reasonably be expected. The two curves differ again, but this time they flex about the 11th point from the end. Further discussion of this method here. 3. Moving average The final figure below shows the result of running a moving average with an end point at 2006 of 0.6 and 0.3. The moving average stops 5 points short of the end of the series, and the last point varies as a result of the variation at 2006. [...]

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