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A range of applications in cognitive radio networks, from adaptive spectrum sensing to predictive spectrum mobility and dynamic spectrum access, depend on our ability to foresee the state evolution of radio spectrum, raising a fundamental question: To what degree is radio spectrum state (RSS) predictable? In this article we explore the fundamental limits of predictability in RSS dynamics by studying the RSS evolution patterns in spectrum bands of several popular services, including TV bands, ISM bands, cellular bands, and so on. From an information theory perspective, we introduce a methodology of using statistical entropy measures and Fano inequality to quantify the degree of predictability underlying real-world spectrum measurements. Despite the apparent randomness, we find a remarkable predictability, as large as 90 percent, in real-world RSS dynamics over a number of spectrum bands for all popular …