Convergent cross mapping ( CCM ) is a statistical test for a cause-and-effect relationship between two variables that, like the Granger causality test, seeks to resolve the problem that correlation does not imply causation . While Granger causality is best suited for purely stochastic systems where the influences of the causal variables are separable (independent of each other), CCM is based on the theory of dynamical systems and can be applied to systems where causal variables have synergistic effects. As such, CCM is specifically aimed to identify linkage between variables that can appear uncorrelated with each other.
21-468: [REDACTED] Look up CCM or ccm in Wiktionary, the free dictionary. CCM may refer to: Cubic centimetre ( ccm ), metric unit of volume Computing [ edit ] CCM mode , an encryption algorithm Client Configuration Manager, a component of Microsoft System Center Configuration Manager Combined Cipher Machine ,
42-585: A 2010 international treaty prohibiting cluster bombs Job titles [ edit ] Certified Case Manager , an accreditation for health care providers Certified Construction Manager, an accreditation by the Construction Management Association of America Certified Consulting Meteorologist , an accreditation of the American Meteorological Society (AMS) Command Chief Master Sergeant ,
63-453: A Canadian bicycle manufacturer CCM (ice hockey) , a Canadian sporting goods brand Central Coast Mariners FC , an Australian A-League football team Clews Competition Motorcycles , a British motorcycle manufacturer Transportation [ edit ] CCM Airlines , an airline of Corsica, France Combatant Craft Medium , a U.S. Navy patrol boat Core Cabin Module , a part of
84-400: A Canadian bicycle manufacturer CCM (ice hockey) , a Canadian sporting goods brand Central Coast Mariners FC , an Australian A-League football team Clews Competition Motorcycles , a British motorcycle manufacturer Transportation [ edit ] CCM Airlines , an airline of Corsica, France Combatant Craft Medium , a U.S. Navy patrol boat Core Cabin Module , a part of
105-641: A WWII-era cipher system Community Climate Model, predecessor of the Community Climate System Model Constrained conditional model , a machine-learning framework CORBA Component Model Customer communications management , a type of software Government [ edit ] Center for Countermeasures , a US White Sands Proving Grounds operation Chama Cha Mapinduzi , the ruling political party in Tanzania Convention on Cluster Munitions ,
126-642: A cell's cytoplasm Carbon concentrating mechanisms , a photosynthesis condition in plants Cardiac contractility modulation , a therapy for heart failure Cerebral cavernous malformation , a type of venous malformation in the brain Climate change mitigation , climate change topic Convergent cross mapping , a statistical test Places [ edit ] Cape Cod Mall , a shopping mall in Hyannis, Massachusetts Macao Cultural Centre , Macau, China Sport [ edit ] CCM (bicycle company) ,
147-536: A cell's cytoplasm Carbon concentrating mechanisms , a photosynthesis condition in plants Cardiac contractility modulation , a therapy for heart failure Cerebral cavernous malformation , a type of venous malformation in the brain Climate change mitigation , climate change topic Convergent cross mapping , a statistical test Places [ edit ] Cape Cod Mall , a shopping mall in Hyannis, Massachusetts Macao Cultural Centre , Macau, China Sport [ edit ] CCM (bicycle company) ,
168-601: A corollary to the Generalized Takens Theorem that it should be possible to cross predict or cross map between variables observed from the same system. Suppose that in some dynamical system involving variables X {\displaystyle X} and Y {\displaystyle Y} , X {\displaystyle X} causes Y {\displaystyle Y} . Since X {\displaystyle X} and Y {\displaystyle Y} belong to
189-545: A machine-learning framework CORBA Component Model Customer communications management , a type of software Government [ edit ] Center for Countermeasures , a US White Sands Proving Grounds operation Chama Cha Mapinduzi , the ruling political party in Tanzania Convention on Cluster Munitions , a 2010 international treaty prohibiting cluster bombs Job titles [ edit ] Certified Case Manager , an accreditation for health care providers Certified Construction Manager, an accreditation by
210-773: A rank and billet in the U.S. Air Force Music [ edit ] Popular music styles of Christian music : Contemporary Christian music CCM Magazine Contemporary classical music Contemporary commercial music University of Cincinnati – College-Conservatory of Music Schools and organizations [ edit ] Cardinal Courier Media , an overseeing body at St. John Fisher College City College of Manila , Philippines Council of Churches of Malaysia , an ecumenical fellowship in Malaysia County College of Morris , New Jersey, United States Science and medicine [ edit ] Calcium concentration microdomains , part of
231-889: The Construction Management Association of America Certified Consulting Meteorologist , an accreditation of the American Meteorological Society (AMS) Command Chief Master Sergeant , a rank and billet in the U.S. Air Force Music [ edit ] Popular music styles of Christian music : Contemporary Christian music CCM Magazine Contemporary classical music Contemporary commercial music University of Cincinnati – College-Conservatory of Music Schools and organizations [ edit ] Cardinal Courier Media , an overseeing body at St. John Fisher College City College of Manila , Philippines Council of Churches of Malaysia , an ecumenical fellowship in Malaysia County College of Morris , New Jersey, United States Science and medicine [ edit ] Calcium concentration microdomains , part of
SECTION 10
#1732781026968252-552: The state space of a dynamical system can be reconstructed from a single observed time series of the system, X {\displaystyle X} . This reconstructed or shadow manifold M X {\displaystyle M_{X}} is diffeomorphic to the true manifold, M {\displaystyle M} , preserving instrinsic state space properties of M {\displaystyle M} in M X {\displaystyle M_{X}} . Convergent Cross Mapping (CCM) leverages
273-480: The Chinese space station Other uses [ edit ] Catherine Cortez Masto (born 1964), United States Senator from Nevada Caja Castilla-La Mancha (CCM) , a former Spanish savings bank Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title CCM . If an internal link led you here, you may wish to change the link to point directly to
294-425: The Chinese space station Other uses [ edit ] Catherine Cortez Masto (born 1964), United States Senator from Nevada Caja Castilla-La Mancha (CCM) , a former Spanish savings bank Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title CCM . If an internal link led you here, you may wish to change the link to point directly to
315-443: The free dictionary. CCM may refer to: Cubic centimetre ( ccm ), metric unit of volume Computing [ edit ] CCM mode , an encryption algorithm Client Configuration Manager, a component of Microsoft System Center Configuration Manager Combined Cipher Machine , a WWII-era cipher system Community Climate Model, predecessor of the Community Climate System Model Constrained conditional model ,
336-424: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=CCM&oldid=1235404585 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages CCM [REDACTED] Look up CCM or ccm in Wiktionary,
357-500: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=CCM&oldid=1235404585 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Convergent cross mapping In the event one has access to system variables as time series observations, Takens' embedding theorem can be applied. Takens' theorem generically proves that
378-652: The prediction skill of X {\displaystyle X} increases and saturates as the entire M Y {\displaystyle M_{Y}} is used, this provides evidence that X {\displaystyle X} is causally influencing Y {\displaystyle Y} . Cross mapping is generally asymmetric. If X {\displaystyle X} forces Y {\displaystyle Y} unidirectionally, variable Y {\displaystyle Y} will contain information about X {\displaystyle X} , but not vice versa. Consequently,
399-591: The reconstructed states based on Y {\displaystyle Y} can be used to cross predict values of X {\displaystyle X} . CCM leverages this property to infer causality by predicting X {\displaystyle X} using the M Y {\displaystyle M_{Y}} library of points (or vice-versa for the other direction of causality), while assessing improvements in cross map predictability as larger and larger random samplings of M Y {\displaystyle M_{Y}} are used. If
420-400: The same dynamical system, their reconstructions via embeddings M X {\displaystyle M_{X}} and M Y {\displaystyle M_{Y}} , also map to the same system. The causal variable X {\displaystyle X} leaves a signature on the affected variable Y {\displaystyle Y} , and consequently,
441-524: The state of X {\displaystyle X} can be predicted from M Y {\displaystyle M_{Y}} , but Y {\displaystyle Y} will not be predictable from M X {\displaystyle M_{X}} . The basic steps of convergent cross mapping for a variable X {\displaystyle X} of length N {\displaystyle N} against variable Y {\displaystyle Y} are: CCM
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