Over-the-top adaptive video streaming services are frequently impacted by fluctuating network conditions that can lead to rebuffering events (stalling events) and sudden bitrate changes. These events visually impact video consumers' quality of experience (QoE) and can lead to consumer churn. The development of models that can accurately predict viewers' instantaneous subjective QoE under such volatile network conditions could potentially enable the more efficient design of quality-control protocols for media-driven services, such as YouTube, Amazon, Netflix, and so on. However, most existing models only predict a single overall QoE score on a given video and are based on simple global video features, without accounting for relevant aspects of human perception and behavior. We have created a QoE evaluator, called the time-varying QoE Indexer, that accounts for interactions between stalling events, analyzes the spatial and temporal content of a video, predicts the perceptual video quality, models the state of the client-side data buffer, and consequently predicts continuous-time quality scores that agree quite well with human opinion scores. The new QoE predictor also embeds the impact of relevant human cognitive factors, such as memory and recency, and their complex interactions with the video content being viewed. We evaluated the proposed model on three different video databases and attained standout QoE prediction performance.