The role 'complementary' is a landmark role, meaning users of assistive technologies can use the keyboard to navigate between different landmarks on the page. So effectively it facilitates browsing. The Paciello Group Blog explains ARIA landmarks clearly.
In contrast the role 'log' is a widget role, which according to the WAI-ARIA specification means assistive technologies should switch from browsing mode to application mode, and pass keyboard events through to the web application.
So the roles have different functions; 'complementary' facilitates finding the ticker, and 'log' facilitates interacting with it. Both should enhance the accessibility of the page, so both should be used.
So the roles you have chosen are correct, and nesting them as you have done, is the best solution.
To get the ticker to announce updates other ARIA properties and states are required. Gez Lemon has a good primer on those attributes related to live regions.