Let’s understand how the Gini Index works by looking at this simple example.
Let’s start by calculating the Gini Index for ‘Past Trend’.
P(Past Trend=Positive): 6/10
P(Past Trend=Negative): 4/10
If (Past Trend = Positive & Return = Up), probability = 4/6
If (Past Trend = Positive & Return = Down), probability = 2/6
Gini index = 1 – ((4/6)^2 + (2/6)^2) = 0.45
If (Past Trend = Negative & Return = Up), probability = 0
If (Past Trend = Negative & Return = Down), probability = 4/4
Gini index = 1 – ((0)^2 + (4/4)^2) = 0
Weighted sum of the Gini Indices can be calculated as follows:
Gini Index for Past Trend = (6/10)*0.45 + (4/10)*0 = 0.27
Calculation of Gini Index for Open Interest
P(Open Interest=High): 4/10
P(Open Interest=Low): 6/10
If (Open Interest = High & Return = Up), probability = 2/4
If (Open Interest = High & Return = Down), probability = 2/4
Gini index = 1 – ((2/4)^2 + (2/4)^2) = 0.5
If (Open Interest = Low & Return = Up), probability = 2/6
If (Open Interest = Low & Return = Down), probability = 4/6
Gini index = 1 – ((2/6)^2 + (4/6)^2) = 0.45
Weighted sum of the Gini Indices can be calculated as follows:
Gini Index for Open Interest = (4/10)*0.5 + (6/10)*0.45 = 0.47
Calculation of Gini Index for Trading Volume
P(Trading Volume=High): 7/10
P(Trading Volume=Low): 3/10
If (Trading Volume = High & Return = Up), probability = 4/7
If (Trading Volume = High & Return = Down), probability = 3/7
Gini index = 1 – ((4/7)^2 + (3/7)^2) = 0.49
If (Trading Volume = Low & Return = Up), probability = 0
If (Trading Volume = Low & Return = Down), probability = 3/3
Gini index = 1 – ((0)^2 + (1)^2) = 0
Weighted sum of the Gini Indices can be calculated as follows:
Gini Index for Trading Volume = (7/10)*0.49 + (3/10)*0 = 0.34
From the above table, we observe that ‘Past Trend’ has the lowest Gini Index and hence it will be chosen as the root node for the decision tree.
We will repeat the same procedure to determine the sub-nodes or branches of the decision tree.
We will calculate the Gini Index for the ‘Positive’ branch of Past Trend as follows:
Stay tuned for the next installment in this series, in which Shagufta will continue discussing Calculations of Gini Index for Trading Volume!
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