This paper investigates cost-sensitive online window size selection for portfolio management under changing market conditions. Specifically, we propose a two-level framework that constructs portfolios using candidate window sizes and dynamically aggregates them through online learning.

By treating candidate window sizes as "experts," we dynamically update their aggregation weights using turnover-inclusive losses. Moreover, we derive finite-horizon cost-sensitive tracking-regret bounds that account for turnover of the aggregated portfolio, with static regret as a special case.

Under bounded losses and cost rates, suitably tuned Fixed Share achieves asymptotically no tracking regret for sublinear switching budgets, with Hedge covering the static case.