Person identification based on touch screen gestures is a well-known method of authentication in mobile devices. Usually it is only checked if the user entered the correct pattern. Taking into account other biometric data based on the speed and shape of finger movements can provide higher security while the convenience of this authorisation method is not impacted. In this work the application of Sequential Joint Functional Principal Analysis (FPCA) as a dimensionality reduction method for gesture data is explored. Performance of the classifier is measured using 5-fold stratified cross-validation on a set of gestures collected from 12 people. The effects of sampling rate on classification performance is also measured. It is shown that the Support Vector Machine classifier reaches the accuracy of 79% using features obtained using the Sequential Joint FPCA, compared to 70% in the case of Euclidean PCA.