Define Sampling below the Nyquist Rate?
A further reduction of the sampling frequency will reason one sample to be taken each period. The Case 3 plot depicts the effect of this in both frequency and time domains. In the time domain, the inferred signal does not be like our original signal. In the frequency domain, an alias of our real signal spectrum appears near the frequency of our original. We are now in a situation the same to that of the share prices. It is not probable to reconstruct the original signal from our samples. This effect is known as aliasing in signal processing.
It must be noted that aliasing a signal is not all the time a problem and can, actually be advantageous in some cases where exact reconstruction of the signal is not needed. Since you may have already gathered, the minimum sampling rate should be twice that of the highest frequency component of the signal. This frequency is known as the Nyquist Limit. The theory behind this originated from Nyquist's Sampling Theorem. Shannon's Sampling Theorem as well states the same fact. We cannot again construct the original signal if it was sampled at a rate below the Nyquist limit.