clone() was designed with several mistakes (see this question), so it's best to avoid it.
From Effective Java 2nd Edition, Item 11: Override clone judiciously
Given all of the problems associated with Cloneable, it’s safe to say that other interfaces should not extend it, and that classes designed for inheritance (Item 17) should not implement it. Because of its many shortcomings, some expert programmers simply choose never to override the clone method and never to invoke it except, perhaps, to copy arrays. If you design a class for inheritance, be aware that if you choose not to provide a well-behaved protected clone method, it will be impossible for subclasses to implement Cloneable.
This book also describes the many advantages copy constructors have over Cloneable/clone.
All standard collections have copy constructors. Use them.
List<Double> original = // some list
List<Double> copy = new ArrayList<Double>(original);