This paper proposes a cross-validation method for estimating the period as well as the values of multiple correlated periodic sequences when data are observed at evenly spaced time points. The period of interest is estimated conditional on the other correlated sequences. An alternative method for period estimation based on Akaike's information criterion is also discussed. The improvement of the period estimation performance is investigated both theoretically and by simulation. We apply the multivariate cross-validation method to the temperature data obtained from multiple ice cores, investigating the periodicity of the El Niño effect. Our methodology is also illustrated by estimating patients' cardiac cycle from different physiological signals, including arterial blood pressure, electrocardiography, and fingertip plethysmograph.