In order for organisations to remain competitive in times of ambiguity and uncertainty, there is a need to detect and anticipate unknown unknowns, also called `black swans'. When these are ignored they may lead to competitive struggles. In this paper, we build on this view and suggest that big data analytics can provide necessary insights to help change strategy making. Research suggests that ambidextrous organisations should focus on developing and maintaining their dynamic capabilities. Following on from this, we take a dynamic capabilities perspective and propose a theoretical framework to explain the intricacies of big data analytics. This framework explains the ability of organisations to detect, anticipate and respond strategically in ambiguous and uncertain business environments. For a meta-synthesis of 101 cases of big data analytics, we employ a multi-method approach that incorporates Natural Language Processing, semantic analysis and case analysis, allowing extraction and analysis of structured information from unstructured data. Overall, we find evidence of big data analytics helping to detect, anticipate and respond to industry disruption. We offer six propositions about the relationships between the levels of data analytics capabilities and strategic dynamic capabilities. We find that descriptive data analytics improves the capability of an organisation to understand the business context (sensing) and that predictive data analytics aids in the realisation of business opportunities (seizing). This study contributes to an understanding of big data analytics as a dynamic organisational capability that supports strategic decision-making in times of ambiguity and uncertainty. We conclude by suggesting areas for further investigation, particularly in regard to the strategic application of prescriptive data analytics.