I'm going to Taiwan on 9 to 16 of December and wondering is there a high possibility of typhoon?

Also most of my plan is to stay in Taipei and surrounding suburbs (Beitou,Damsui,Jiufen,Yeh liu,Yangmingsan) but also I want to visit one of these places :Taroko national park, Sun moon lake, ALishan ,do u think the weather will allow me to do so? I'm not worried about the transportation, only the weather is my concern.

Thank you in advance for ur help