Content Delivery Networks (CDNs) are faced with an increasing and time varying demand of video contents. Their ability to promptly react to this demand is a success factor. Caching helps, but the question is: which contents to cache? Considering that the most popular contents should be cached, this paper focuses on how to predict the popularity of video contents. With real traces extracted from YouTube, we show that Auto-Regressive and Moving Average (ARMA) models can provide accurate predictions. We propose an original solution combining the predictions of several ARMA models. This solution achieves a better Hit Ratio and a smaller Update Ratio than the classical Least Frequently Used (LFU) caching technique.