
[{"active"=>true, "defaultValue"=>false, "label"=>"Prospecting", "validFor"=>nil, "value"=>"Prospecting"},
{"active"=>true, "defaultValue"=>false, "label"=>"Qualification", "validFor"=>nil, "value"=>"Qualification"},
{"active"=>true, "defaultValue"=>false, "label"=>"Needs Analysis", "validFor"=>nil, "value"=>"Needs Analysis"},
{"active"=>true, "defaultValue"=>false, "label"=>"Value Proposition", "validFor"=>nil, "value"=>"Value Proposition"},
{"active"=>true, "defaultValue"=>false, "label"=>"Id. Decision Makers", "validFor"=>nil, "value"=>"Id. Decision Makers"},
{"active"=>true, "defaultValue"=>false, "label"=>"Perception Analysis", "validFor"=>nil, "value"=>"Perception Analysis"},
{"active"=>true, "defaultValue"=>false, "label"=>"Proposal/Price Quote", "validFor"=>nil, "value"=>"Proposal/Price Quote"},
{"active"=>true, "defaultValue"=>false, "label"=>"Negotiation/Review", "validFor"=>nil, "value"=>"Negotiation/Review"},
{"active"=>true, "defaultValue"=>false, "label"=>"Closed Won", "validFor"=>nil, "value"=>"Closed Won"},
{"active"=>true, "defaultValue"=>false, "label"=>"Closed Lost", "validFor"=>nil, "value"=>"Closed Lost"}]
But I can't seem to find a way to retrieve the "Type" metadata associated with each picklist value that you can see with the web interface:
_img alt="Screenshot" src="https://www.dropbox.com/s/h1u6t16dr5vm1vh/Screenshot%202016-10-31%2017.30.02.png?dl=1" /_
Is there any way to get that "Type" metadata using the REST API?

Type information is saved in ForecastingType and ForecastingTypeToCategory system object, see below SOQL-
select CanDisplayQuotas, CreatedById, CreatedDate, DeveloperName, Id, IsActive, IsAmount, IsDeleted, IsQuantity, Language, LastModifiedById, LastModifiedDate, MasterLabel, SystemModstamp from ForecastingType
select CreatedById, CreatedDate, DisplayPosition, ForecastingItemCategory, ForecastingTypeId, Id, IsAdjustable, IsDeleted, IsOwnerAdjustable, LastModifiedById, LastModifiedDate, SystemModstamp from ForecastingTypeToCategory
You can reference this information by doing API calls to the two objects-
https://developer.salesforce.com/docs/atlas.en-us.api.meta/api/sforce_api_objects_forecastingtype.htm