The microstructure noise is, roughly speaking, the small-scale noise introduced into the market as a result of the way the market is designed.
For example, suppose that there is an asset and the "real" price for this, is 126.6. That is, if we magically knew everyone's honest, perfect maximum buy and minimum sell prices and could match them off and arrive at the equilibrium price, then it would be 126.6.
However, imagine that the market only quotes in whole numbers. That means you can either buy at 127 or sell at 126, but it is physically impossible to trade at 126.6. Intuitively we expect to see a sequence of trades switching between 126 and 127. This is called "bid ask bounce" and is perhaps the simplest example of microstructure.
Even with such a trivial example, we can start to do interesting things. For example, since the price is closer to 127 than 126, we might expect to see more 127s than 126s. We could use a simple logit function or something to select the probability the next tick is on the near or far side. Also we can "what-if" the market has a different tick size? Clearly we expect in our model the bid ask bounce to reduce.
In our example the latent price is a constant, but that is not very realistic. For a better model one would usually assume some dynamic model for this hidden price process. Perhaps Brownian motion, for example. Now you can see how with our model from above, we will see trade prices bouncing either side of our hidden price. As the price gets closer to a whole number, more trades are done on that, until it crosses and then we start seeing trades on the next tick along.
As you can imagine, you can continue to play this game, making the latent price process more complex, and adding more complex microstructure models to generate the trades around that price. And all along we have assumed independence of latent price and microstructure noise. That is to say, our microstructure process does not impact the latent price, and the microstructure process stays the same, regardless of what the price is doing.
This is a useful assumption to make, since it separates the problem out - without it you probably wouldn't be able to solve much and the usefulness may be limited. That said, it is easy enough to think up possible models that would break this:
- Modelling effect of limit orders in the order book when price breaks new ground
- Market maker inventory changes during long price runs in one direction.
- Psychological anchors set by previously traded prices impacting latent price.