Add chapter on tick rule 🔢 (#152)

Addresses #10

references/obsidian/.obsidian/graph.json

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references/obsidian/.obsidian/workspace.json

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@@ -178,7 +96,7 @@
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@@ -206,7 +124,7 @@
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@@ -237,17 +155,17 @@
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     "📑notes/🔢Hybrid rules notes.md",
+    "📑notes/🔢Basic rules notes.md",
+    "📖chapters/🔢Basic rules.md",
+    "📖chapters/🔢Quote Rule.md",
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-    "📖chapters/🔢Tick test.md",
-    "📖chapters/🔢Trade Size Rule.md",
-    "📑notes/🔢Trade Size Rule Notes.md"
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references/obsidian/IW-Queues/IW-Queue.md

@@ -10,15 +10,15 @@ interval: 1
 | [[🤖Transformer]]                               |     12.5 |       |        2 | 2022-12-15 |
 | [[👨‍🍳Tain-Test-split]]                        |       15 |       |        2 | 2022-12-15 |
 | [[🔢Trade Size Rule]]                            |     17.5 |       |        1 | 1970-01-01 |
-| [[🔢Tick test]]                                 |       20 |       |        1 | 1970-01-01 |
+| [[🔢Tick Test]]                                 |       20 |       |        1 | 1970-01-01 |
 | [[🍪Selection Of Semisupervised Approaches]] |     22.5 |       |        1 | 1970-01-01 |
 | [[🍪Selection Of Supervised Approaches]]      |       25 |       |        1 | 1970-01-01 |
 | [[🏅Robustness]]                                |     27.5 |       |        1 | 1970-01-01 |
 | [[semi-supervised]]                             |       28 |       |        1 | 1970-01-01 |
 | [[🏅Results of semi-supervised]]                |       30 |       |        1 | 1970-01-01 |
 | [[🏅Results]]                                   |     32.5 |       |        1 | 1970-01-01 |
 | [[👪Related Work]]                              |       35 |       |        1 | 1970-01-01 |
-| [[🔢Quote rule]]                                |     37.5 |       |        1 | 1970-01-01 |
+| [[🔢Quote Rule]]                                |     37.5 |       |        1 | 1970-01-01 |
 | [[💡Training and tuning]]                       |       40 |       |        1 | 1970-01-01 |
 | [[👨‍🍳Pre-Processing]]                         |       40 |       |        1 | 1970-01-01 |
 | [[💡Tuning of models (semi-supervised)]]        |       41 |       |        1 | 1970-01-01 |
@@ -36,11 +36,11 @@ interval: 1
 | [[🚏Exploratory Data Analysis]]                 |     72.5 |       |        1 | 1970-01-01 |
 | [[🧭Evaluation metric]]                         |       75 |       |        1 | 1970-01-01 |
 | [[🌏Environment]]                               |     77.5 |       |        1 | 1970-01-01 |
-| [[🔢EMO rule]]                                  |       80 |       |        1 | 1970-01-01 |
+| [[🔢EMO Rule]]                                  |       80 |       |        1 | 1970-01-01 |
 | [[🛌Token Embedding]]                           |     82.5 |       |        1 | 1970-01-01 |
 | [[🤖Pre-training of Transformers]]              |       85 |       |        1 | 1970-01-01 |
 | [[🧓Discussion]]                                |     87.5 |       |        1 | 1970-01-01 |
-| [[🔢Depth rule]]                                |       90 |       |        1 | 1970-01-01 |
-| [[🔢CLNV method]]                               |       95 |       |        1 | 1970-01-01 |
+| [[🔢Depth Rule]]                                |       90 |       |        1 | 1970-01-01 |
+| [[🔢CLNV Method]]                               |       95 |       |        1 | 1970-01-01 |
 | [[🔢Basic rules]]                               |     97.5 |       |        1 | 1970-01-01 |
 | [[🐈Gradient Boosting]]                         |        5 |       |        8 | 2023-02-07 |

references/obsidian/📑notes/🍪Selection of supervised approaches notes.md

@@ -1,9 +1,6 @@
 #gbm #transformer #supervised-learning #deep-learning 
 
 
-
-
-
 **Why probabilistic classification:**
 - Due to a unsatisfactory research situation, for trade classification (see chapter [[👪Related Work]]) we base
 - Use classification methods (*probabilistic classifier*) that can return probabilities instead of class-only for better analysis. Using probabilistic trade classification rules might have been studied in [[@easleyDiscerningInformationTrade2016]]

references/obsidian/📑notes/🔢Basic rules notes.md

@@ -5,6 +5,10 @@ Denote sells with $0$ and buys with $1$.
 “The trade indicator is a binary variable stating whether the buyer or seller of an asset has initiated the trade by submitting a market order or an immediately executed limit order.” (Frömmel et al., 2021, p. 4)
 
 
+<mark style="background: #FFB86CA6;">“Methods of inferring trade direction can be classified as: tick tests, which use changes in trade prices; the quote method, which compares trade prices to quotes;” (Finucane, 2000, p. 557)
+</mark>
+
+
 **Synonyms**
 1. Broader term is **trade site classification** = assign the side to a to a transaction and differentiate between buyer- and seller-initiated transactions
 2. It's also sometimes called trade sign classification

references/obsidian/📑notes/🔢CLNV method notes.md

@@ -1,5 +1,21 @@
 Tags: #trade-classification #CLVN 
 
+Long form:
+$$
+  \begin{equation}
+
+    \text{Trade}_{i,t}=
+    \begin{cases}
+      \operatorname{tick}(), & \text{if}\ P_{i, t} \in \left(A_{i, t}, \infty\right) \\
+      1, & \text{if}\ P_{i, t} \in \left[\frac{3}{10} B_{i,t} + \frac{7}{10} A_{i,t}, A_{i, t}\right] \\
+      \operatorname{tick}(), & \text{if}\ P_{i, t} \in \left(\frac{7}{10} B_{i,t} + \frac{3}{10} A_{i,t}, \frac{3}{10} B_{i,t} + \frac{7}{10} A_{i,t}\right) \\
+      0, & \text{if} P_{i, t} \in \left[ B_{i,t}, \frac{7}{10} B_{i,t} + \frac{3}{10} A_{i,t}\right] \\
+	  \operatorname{tick}(), & \text{if} \ P_{i, t} \in \left(-\infty, B_{i, t}\right) \\
+    \end{cases}
+  \end{equation}
+$$
+
+
 - “We compare the accuracy rates of various algorithms in classifying ECN trades. We divide trades according to their price distribution relative to quotes. We expect the classification rules to perform better when trades occur at the ask or bid. When trades receive price improvement, buys and sells will execute at prices inside the quotes. In these instances, not only does the quote rule meet with some challenge, the tick rule will also be more difficult as buys (sells) will more likely occur on downticks (upticks).” (Chakrabarty et al., 2007, p. 3811)
 
 - “We find that ECN trades are difficult to classify as the overall success rates of the LR, EMO, and tick rules are 74.42%, 75.80%, and 75.40%, respectively. Our algorithm modestly outperforms these three, with an overall success rate of 76.52%, but we show that our algorithm substantially outperforms the others for trades inside the quotes. For trades inside 1 Our primary sample is from the INET ECN. We use ArcaEx data to confirm the robustness of our results across another ECN. Table 3 reports results using the ArcaEx data. All other tables use the INET sample. B. Chakrabarty et al. / Journal of Banking & Finance 31 (2007) 3806–3821 380” (Chakrabarty et al., 2007, p. 3807) “the quotes our success rate is 76.32% compared to 71.85% for the LR rule and 71.35% for both the tick and EMO rules. We also find that a significant proportion of trades execute outside the quotes. This phenomenon, called a ‘‘trade-through’’, is prevalent for NASDAQ markets due to the absence of the trade-through rule in our study period.2” (Chakrabarty et al., 2007, p. 3808)

references/obsidian/📑notes/🔢Hybrid rules notes.md

@@ -1,20 +1,5 @@
 Tags: #trade-classification 
 
-Long form:
-$$
-  \begin{equation}
-
-    \text{Trade}_{i,t}=
-    \begin{cases}
-      \operatorname{tick}(), & \text{if}\ P_{i, t} \in \left(A_{i, t}, \infty\right) \\
-      1, & \text{if}\ P_{i, t} \in \left[\frac{3}{10} B_{i,t} + \frac{7}{10} A_{i,t}, A_{i, t}\right] \\
-      \operatorname{tick}(), & \text{if}\ P_{i, t} \in \left(\frac{7}{10} B_{i,t} + \frac{3}{10} A_{i,t}, \frac{3}{10} B_{i,t} + \frac{7}{10} A_{i,t}\right) \\
-      0, & \text{if} P_{i, t} \in \left[ B_{i,t}, \frac{7}{10} B_{i,t} + \frac{3}{10} A_{i,t}\right] \\
-	  \operatorname{tick}(), & \text{if} \ P_{i, t} \in \left(-\infty, B_{i, t}\right) \\
-    \end{cases}
-  \end{equation}
-$$
-
 
 - Why is there a need for hybrid classification rules? What are the problems of the tick and quote rule?
 - The previous trade classification rules are applicable to certain trades or come with their own drawbacks e. g., they perform poorly for a greater distance to quotes. To mitigate the disadvantages, rules are combined to hybrids through ensembeling. In certain cases through stacking.