en>TakuyaMurata: stable homotopy group

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stable homotopy group

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'''Skill''' in [[forecasting]] (or '''skill score''',<ref>[http://amsglossary.allenpress.com/glossary/search?id=skill1 Glossary of Meteorology, American Meteorological Society]</ref> '''forecast skill''', '''prediction skill''') is a scaled representation of [[forecast error]] that relates the forecast accuracy of a particular forecast model to some reference model.

{| class=wikitable
|[[Mean squared error]] (MSE)
|<math>\ \mathit{MSE} = \frac{\sum_{t=1}^N {E_t^2}}{N} </math>
|-
|Forecast skill (SS)
|<math>\ \mathit{SS} = 1- \frac{\mathit{MSE}_\text{forecast}}{\mathit{MSE}_\text{ref}} </math>
|}

A perfect forecast results in a forecast skill of 1.0, a forecast with similar skill to the reference forecast would have a skill of 0.0, and a forecast which is less skillful than the reference forecast would have negative skill values.<ref name="Roebber">{{Citation
|last = Roebber
|first = Paul J.
|year = 1998
|title = The Regime Dependence of Degree Day Forecast Technique, Skill, and Value
|publisher = Allen Press
|journal = American Meteorological Society -- Weather and Forecasting
|volume = 13
|issue = 3
|pages = 783–794
|url = http://ams.allenpress.com/perlserv/?request=get-document&doi=10.1175%2F1520-0434(1998)013%3C0783%3ATRDODD%3E2.0.CO%3B2
|accessdate = 2009-01-19
|doi = 10.1175/1520-0434(1998)013<0783:TRDODD>2.0.CO;2
|bibcode = 1998WtFor..13..783R }}</ref><ref name="Murphy">{{Citation
|last = Murphy
|first = Allen H.
|year = 1988
|title = Skill Scores Based on the Mean Square Error and Their Relationships to the Correlation Coefficient
|publisher = Allen Press
|journal = American Meteorological Society -- Monthly Weather Review
|volume = 116
|issue = 12
|pages = 2417–2424
|doi = 10.1175/1520-0493(1988)116<2417:SSBOTM>2.0.CO;2
|url = http://ams.allenpress.com/perlserv/?request=get-abstract&doi=10.1175%2F1520-0493(1988)116%3C2417%3ASSBOTM%3E2.0.CO%3B2
|accessdate = 2009-01-19
|bibcode = 1988MWRv..116.2417M }}</ref>

== References ==
{{reflist}}

[[Category:Statistical forecasting]]
[[Category:Climate and weather statistics]]
[[Category:Weather forecasting]]

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en>TakuyaMurata: stable homotopy group