Table 1 Definition of Within-window variables with illustration of the feature extraction to predict the mid-price movement of the i-th window, \(i=3,\dots , N/k\), where \(P^{mid}_{i,\cdot }\) indicates the mid-price sequence within the i-th window, \((P^{mid}_{i,1},\dots , P^{mid}_{i,k})\). Each window contains k=5 events
From: Novel modelling strategies for high-frequency stock trading data
Definition | Description |
|---|---|
\(V_1=(P_{i-1,k}^{bid}-P_{i-1,1}^{bid})/P_{i-1,1}^{bid}\) | best bid price difference return |
\(V_2=(P_{i-1,k}^{ask}-P_{i-1,1}^{ask})/P_{i-1,1}^{ask}\) | best ask price difference return |
\(V_3=(P_{i-1,k}^{bid}-P_{i-1,1}^{ask})/P_{i-1,1}^{ask}\) | bid-ask spread crossing return |
\(V_4=\sum _{j=1}^{k}P_{i-1,j}^{ask}/k\) | mean best ask price |
\(V_5=\sum _{j=1}^{k}P_{i-1,j}^{bid}/k\) | mean best bid price |
\(V_6=\sum _{j=1}^{k}P^{mid}_{i-1,j}/k\) | mean mid-price |
\(V_7=\sum _{j=1}^{k}V^{ask}_{i-1,j}\) | best ask price market depth |
\(V_8=\sum _{j=1}^{k}V^{bid}_{i-1,j}\) | best bid price market depth |
\(V_9= \sqrt{Var(P^{mid}_{i-2,\cdot }, P^{mid}_{i-1,\cdot })}\) | within-window volatility of two previous windows |
\(V_{10}=1/(t_{i-1,k}-t_{i-1,1})\) | trade intensity |