The recent low and prolonged minimum of the solar cycle, along with the slow growth in activity of the new cycle, has led to suggestions that the Sun is entering a Grand Solar Minimum (GSMi), potentially as deep as the Maunder Minimum (MM). This raises questions about the persistence and predictability of solar activity. We study the autocorrelation functions and predictability R2L(t) of solar indices, particularly group sunspot number RG and heliospheric modulation potential Φ for which we have data during the descent into the MM. For RG and Φ, R2L(t) > 0.5 for times into the future of t ≈ 4 and ≈ 3 solar cycles, respectively: sufficient to allow prediction of a GSMi onset. The lower predictability of sunspot number RZ is discussed. The current declines in peak and mean RG are the largest since the onset of the MM and exceed those around 1800 which failed to initiate a GSMi.