Cognitive Radio (CR) is a wireless advanced technology which can utilize an unlicensed as well as a licensed spectrum without a harmful interference to the primary users. An unbiased consistent spectrum estimator is required for the primary user’s detection (sensing) for distinguishing the narrow band signals in a noisy environment. Cognitive radio’s hardware solutions available in a commercial market are frequency band constrained at RF Front-End. In multi-dimensional radio spectrum space any of the dimension: time, frequency, code or space can be used as a transmission opportunity. The spectrum hole time opportunistic prediction is a promising solution to determine the free time slots for transmission within a frequency band. This paper presents classical and parametric statistical spectrum estimators for primary user’s detection. It also presents statistical auto-regressive and moving average predictive modeling for grey-hole spectrum opportunities prediction in a time domain for cognitive radios where frequency, code and space (geographical location) are operational constraints. A prototype system for a cognitive radio is built on top of the software-defined radio in a MATLAB/-Simulink and interfaced with an USRP2 main-board and RFX2400 daughter-board from Ettus Research LLC. © 2011 IEEE.