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We propose a microscopic model to describe the dynamics of the fundamentalevents in the limit order book (LOB): order arrivals and cancellations. It isbased on an operator algebra for individual orders and describes their effecton the LOB. The model inputs are arrival and cancellation rate distributionsthat emerge from individual behavior of traders, and we show how prices andliquidity arise from the LOB dynamics. In a simulation study we illustrate howthe model works and highlight its sensitivity with respect to assumptionsregarding the collective behavior of market participants. Empirically, we testthe model on a LOB snapshot of XETRA, estimate several linearized modelspecifications, and conduct in- and out-of-sample forecasts.The in-sampleresults based on contemporaneous information suggest that our model describesreturns very well, resulting in an adjusted $R^2$ of roughly 80%. In the morerealistic setting where only past information enters the model, we observe anadjusted $R^2$ around 15%. The direction of the next return can be predicted(out-of-sample) with an accuracy above 75% for time horizons below 10 minutes.On average, we obtain an RMSPE that is 10 times lower than values documented inthe literature.

From orders to prices: A stochastic description of the limit order book to forecast intraday returns