'Statistical Arbitrage' is explained in detail and with examples in the Trading edition of the Herold Financial Dictionary, which you can get from Amazon in Ebook or Paperback edition.
Statistical arbitrage turns out to be a scenario where a disparity in price exists between the natural price of an asset, or its inherent value, and the current market price. There are traders who specialize in arbitrage situations who will try to gain advantage from this fairly unusual situation of disparity hoping to profit from it as it naturally corrects. Some traders believe that statistical arbitrage will always yield a profit, at least on a paper trade basis. The reality is that in actual trading, unforeseen events and a limitation in investing resources could easily interfere with their capability of making money efficiently enough to be worth doing.
Statistical arbitrage is used in contrast to the generic form of arbitrage to distinguish its differences. The statistical variety relates to the actual techniques utilized in gaining advantage from the disparity that exists in two markets. With generic arbitrage, it could be that a stock price is higher in the stock market of one country than another where it is listed. In theory, traders could guarantee themselves profits simply by purchasing the stock on the cheaper exchange and simultaneously selling it on the dearer listed one. The guarantee depends on how high the transaction costs and currency conversion costs will be. There is also a considerable risk that the two divergent prices may correct themselves naturally before the traders are able to both buy and sell the security on the different exchanges.
This statistical arbitrage is a bit different from general arbitrage. In the statistical variant, such asset disparity is not simply between two or more markets. Instead it has to do with the price of an asset currently and the underlying value of the same asset. A company security proves to be a good example to contemplate. The market price will be decided by the interaction between traders in the form of supply and demand. The stock also possesses an intrinsic value which is derived from the dividends it declares to its investors and how this relates to competing investments. There may be variance in the market price because of temporary effects and external factors, as with relevant industry-specific bad or good news.
Those traders who engage in statistical arbitrage operate under the assumption that eventually the price of the asset will go back to its correct underlying value. Because of the disparity, they anticipate that the price in the future will change, and then they position accordingly to profit. In normal circumstances, these traders might consider and employ literally hundreds of different stocks at once so that they are able to effectively reduce their overall risks of an unforeseen event stopping the stock from going back up to its normal price in a fast enough time frame so that the trader makes money on the deal.
There is another meaning for statistical arbitrage. There might be a type of imbalance from the values that would typically be anticipated. Casino games like roulette are the classic example of this. Because half the spaces are red and the other half are black, players betting on red will win double their stakes should they be right. The wheel also contains a 0 that does not pay anything. This means that the chances of correctly ascertaining the color are actually just under one out of two. This house advantage is a disparity that could also be considered to be a statistical form of advantage. There is no way for the players to benefit from this, but casinos make a fortune off of it on a regular basis.