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Given that we are a market taker (removing liquidity from the limit order book through market orders), what should we be trying to forecast?

It seems like the most pertinent thing for us to forecast is the execution prices of our buy or sell orders of a certain size so that we can determine if our current entry and future exit would be profitable, e.g. the mid price and spread for sufficiently small orders, but then what are constructions such as the weighted mid price $(\frac{p_\text{bid}q_\text{offer} + p_\text{offer}q_\text{bid}}{q_\text{offer} + q_\text{bid}})$ used for? Are they meant to be predictive of future mid prices/potentially spreads?

I saw that this answer describes how features such as the last traded price (or perhaps the log returns of the last traded price) can be used to predict log returns of the mid price which is also described by that answer as being relevant for market taking, but wanted to confirm if this is what we're usually trying to predict in a market taking context.

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    $\begingroup$ Your post is a bit clearer now but it still has too broad and multiple questions. It needs to focus on something narrower while also avoiding the XY Problem $\endgroup$
    – Alper
    Sep 9, 2023 at 8:52
  • $\begingroup$ Noted @Alper , thank you for the reasoning, I will attempt to modify it based on those points. $\endgroup$
    – QMath
    Sep 9, 2023 at 9:18

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What you need depend on what you are trying to do (note that the rest of the explanation is very simplified).

If your target is to execute a big order, you can use a short term mid price prediction to time your actions (why buy at $P_{T}$ when you can buy at $P_{T+\Delta t}$, where $P_{T} > P_{T+\Delta t}$).

If you are doing a naive HFT on a single exchange - you are interested in a bid/ask price crossing between $T$ and $T+\Delta t$. Here you are interested in predicted exit price with respect to a slippage on enter.

If you are trying to arbitrage between exchanges - you may try to predict ToB (top of the book) prices on both of them and try to cross them.

If you are doing structural arbitrage on multiple exchanges - you are very interested in slippage.

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  • $\begingroup$ Thank you for the variety of examples/succinct explanations! :) In your second example, when you mention "bid/ask price crossing" are you referring to something like, after accounting for market frictions/slippage/etc., going short (respectively long) when the current execution bid (ask) price is higher (lower) than the predicted future execution ask (bid) price? $\endgroup$
    – QMath
    Sep 2, 2023 at 3:25
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    $\begingroup$ @QMath Yes. But you can make this model more complex or sophisticated. Or just be the fastest. Or the greediest (PFOF). $\endgroup$
    – Alex D
    Sep 2, 2023 at 16:58

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