What is order flow imbalance in a public limit order book? This note defines the signed measure, shows the choice on an Apple tape, and lists the prints a researcher should refuse to sign.
A difference, not a forecast
A limit order book is a stack of prices and sizes. Trades arrive as prints. Some prints lift the displayed offer and are treated as buyer-initiated. Some hit the displayed bid and are treated as seller-initiated. Order flow imbalance is the difference between those two quantities over a window the researcher states in advance. The window can be a clock interval or a fixed count of prints. Changing the window changes the series, so the window belongs in the definition rather than in a caption added later.
The unsigned total is not the same object. A busy minute and a quiet minute can share a small difference while the busy minute contains far more shares. Teams therefore keep both the signed difference and the volume that produced it. A ratio bounded between minus one and one is useful for comparison across names. A raw share count is useful when the question is how much size actually changed hands. Publishing one without the other invites a reader to treat a thin print and a crowded print as the same event.
Order flow imbalance is the signed difference between buyer-initiated and seller-initiated volume over a window that is stated before the series is built.
How a print gets a side
Public prints do not arrive with a buy or sell label. The usual rule compares the trade price with the quote that was visible immediately before the print. A trade at the offer is called a buy. A trade at the bid is called a sell. A trade inside the spread, or a trade that matches several quotes at once, is ambiguous. On a liquid Nasdaq name such as Apple, many prints fall in that middle. Two written rules will disagree on those prints even when both rules are honest. The disagreement is a property of the tape, not a software bug.
Consider a short slice in Apple. The quote is 150.00 bid for 400 shares and 150.01 offered for 300. A print of 200 shares at 150.01 is signed as a buy. A later print of 500 shares at 150.00 is signed as a sell. Over that slice, seller-initiated volume is larger, so the imbalance is negative. If the bid size falls from 400 to 100 because of a cancel and no trade, a trade-only measure does not move, while a measure that includes quote changes does. Both series can be plotted. They answer different questions, and the chart should say which question it is.
What the series leaves out
The consolidated tape and a direct exchange feed can order the same prints differently. A trade condition can mark a print as late, as an average-price trade, or as an odd-lot that some studies drop. Leaving those conditions in the sum tilts the sign. Dropping them without a note hides a choice. Auction prints, in particular, are matched under different rules from continuous trading, so a continuous-book formula applied to the closing print mixes two mechanisms. The Apple example is continuous trading only.
Imbalance can rise before a price change, after a price change, or beside no change at all. A researcher may accept the series as a feature. Acceptance is a later decision, written down, and it is not implied by a clean chart. A thin name with a wide spread will produce a noisy sign because there are few prints and the quote rule is brittle. Apple is the example because the book is public and busy, not because the measure is special to that company or to any strategy.
A useful check is to build the Apple series twice. In one version, inside-spread prints are dropped. In the other, they are signed by a tick rule that looks only at the previous trade price. The two lines will not match, and the gap is the uncertainty of the label. A note that shows only the first line has hidden that gap. The gap is not a reason to discard the measure. It is a reason to keep the signing rule next to the chart, in the same sentence as the window, so a later reader can rebuild the number.
This piece does not claim that imbalance foretells the next price, that a model should trade the series, or that any particular window is in use on a desk. It only separates the definition from the decision to accept it.
