Financial technologies, stemming from the application of artificial intelligence to big data in finance, are continuously expanding, across different markets and financial services. While financial technologies bring many opportunities, such as reduced costs and extended inclusion, they also bring risks, among which cyber risks, which are constantly increasing and are difficult to measure. Among the difficulties in measurement lies the existence of interdependence among different cyber risks. The study of interdependence and possible contagion channels between cyber attacks to different institutions and economic sectors is indeed increasingly important to ensure economic and financial sustainability. Against this backdrop, this paper proposes a multivariate model for count time series of cyber risk events, in which the time-varying intensity parameter determining the probability that a cyber attack occurs evolves according to general autoregressive score models, taking both time and sectorial dependence into account. The model is particularly suitable for studying how the behaviors of different markets or sectors are interconnected and it constitutes a new approach to the multivariate analysis of count time series of cyber loss events.