1. General Analysis

Correlation

Correlation is a statistical measure that captures the strength and direction of the linear relationship between two variables. It's a normalized version of covariance, ranging from -1 to 1.

Properties:

• Positive correlation (0 < r <= 1): As one variable increases, the other tends to increase as well (strong positive correlation at r close to 1, weak positive correlation closer to 0).
• Negative correlation (-1 <= r < 0): As one variable increases, the other tends to decrease (strong negative correlation at r close to -1, weak negative correlation closer to 0).
• Zero correlation (r = 0): There's no linear relationship between the variables.
• Correlation is generally preferred over covariance because it's scale-independent, making it easier to interpret the strength of the relationship between variables measured in different units.

Formula:

corr(X, Y) = cov(X, Y) / (std(X) * std(Y))

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1.1 Default Attributes

1.1.1 Correlation

• Linear Relationships 1 : Open price , High Price , Low price , Close Price , Mean price .
• Linear Relationships 2 : Volume , Assets' Volumes , Number of Trades .
• Idea : Mix the attributes

1.2 Mixing with Volume per Number of Trades

• Volume per number of Trades has close to 0 correlation with attributes that volume had 0 correlation before .

• Now volume has increased correlation with attributes that had 0 before .

• Idea : Mix with asset volume analogy , how much it is bought while it is sold .

1.3 Mixing with Asset Volume Analogy

• The analogy seem to have a strong linear dependence with attributes that hadn't seem for volume to correlate .

• Idea : Multiply MVA with volume per number of trades .

1.4 Mixing More

df["VAPT"] = (df['Taker buy base asset volume']-df['Taker buy quote asset volume'])/(2*df["Number of trades"])

df["VAPV"] = (df['Taker buy base asset volume']-df['Taker buy quote asset volume'])/(2*df["Volume"])

• The use of mixing volume and number of trades with buying and selling rate , makes attributes linearly dependent .

1.5 Correlation in Time

10 mins time series

• There is a linear dependence between next mean price and all attributes .

45 mins time series

55 minutes time series

60 minutes time series

Results

• 45 min length seems to be OK !

2. Attempts

2.1 Keras - TensorFlow

2.1.1 Model that is Valid of Working for XRP

# create model
model = Sequential()
model.add(Input(shape=input_shape))

model.add(LSTM(input_shape[0],activation='tanh',return_sequences=True,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(Bidirectional(LSTM(input_shape[1]**2,activation='tanh',return_sequences=True,return_state=False,recurrent_activation='sigmoid',go_backwards=False)))

model.add(LSTM(input_shape[0],activation='tanh',return_sequences=False,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(Dense(1, activation='linear'))

Architecture

• 4 Layer Model
• 1st Layer has number of nodes equal to the length of Time Series .
• 2nd Layer is Bidirectional and has number of nodes equal to the multiplication of Time Series' length with number of features of each Time Series .
• 3rd Layer is as 1st .
• Output Layer has 1 node and linear activation function as activation function .
• Input and Hidden Layers have LSTM nodes with tanh as activation function and sigmoid as recurrent activation function .
• The model is trained using SGD as optimizer and MSE as loss function .

Hyperparameters

• Learning Rate equals 0.05 .
• Momentum equals 0.8 .
• Batch Size equals 10 .
• Time Series length equals 30 minutes .

Comments

• Now always working .

2.1.2 Same model with MAE as loss function , no Bidirectional Layer

model = Sequential()

model.add(Input(shape=input_shape))

model.add(LSTM(input_shape[0],activation='tanh',return_sequences=True,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(LSTM(input_shape[0] * input_shape[1],activation='tanh',return_sequences=True,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(LSTM(input_shape[0],activation='tanh',return_sequences=False,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(Dense(1, activation='linear'))

• Learning Rate : 0.001
• Momentum : 0.8

Comments

• Better performance than before .
• It has been trained for 12 epochs .
• We need less training time .
• Change the hyperparameters .

2.1.2 Same Model with One More Layer

model = Sequential()

model.add(Input(shape=input_shape))

model.add(LSTM(input_shape[0],activation='tanh',return_sequences=True,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(LSTM(input_shape[0] * input_shape[1],activation='tanh',return_sequences=True,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(LSTM(input_shape[0] * input_shape[1],activation='tanh',return_sequences=True,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(LSTM(input_shape[0],activation='tanh',return_sequences=False,return_state=False,recurrent_activation='sigmoid',go_backwards=False))

model.add(Dense(1, activation='linear'))

• Learning Rate : 0.01
• Momentum : 0.7

• Learning Rate : 0.01
• Momentum : 0.8

• Learning Rate : 0.01
• Momentum : 0.9

• Learning Rate : 0.01
• Momentum : 0.65

• Learning Rate : 0.01
• Momentum : 0.95

• Learning Rate : 0.05
• Momentum : 0.7

• Learning Rate : 0.05
• Momentum : 0.8

• Learning Rate : 0.05
• Momentum : 0.9

• Learning Rate : 0.05
• Momentum : 0.65

• Learning Rate : 0.05
• Momentum : 0.95