Modelling and quantifying the underlying characteristics of the cryptocurrency market has drawn increasing attention since Bitcoin went online in 2009. This study proposes a two-stage decomposition and composition method (2SDC) that begins with a Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) for better interpreting cryptocurrency formations. This study involves daily closing price data from six cryptocurrencies (i.e., Bitcoin, Ethereum, Bitcoin Cash, Litecoin, Monero and Dash) from July 23rd, 2017 to July 23rd, 2019. In the first stage, six time series are jointly decomposed into 10 independent intrinsic mode functions (IMF) from high to low frequency plus one residual. In the second stage, the IMFs for each cryptocurrency are composed into three components based on Wilcoxon signed-rank test, including high and low frequency components and a long-term trend. These three multi-scale components can be interpreted as short-term fluctuations caused by investor sentiment and micro-structure, the effect of significant events and fundamental values. Furthermore, we demonstrated that the low and high frequency compositions are determining factors of cryptocurrency prices, which supports for the existing evidence (e.g. Bouoiyour, Selmi, Tiwari, & Olayeni, 2016; Ji, Bouri, Lau, & Roubaud, 2019).