linear = linear_model.LinearModel(features, labels, terms)
linear.inference()

"""
Explanation: Linear Model(for compare)

$\hat{c}{t,i} = \sum{k=1}^6 w_{k,i} c_{t-k, i}$
End of explanation
"""


#PYTEST_VALIDATE_IGNORE_OUTPUT
linear.plot_direction_accuracy()

"""
Explanation: accuracy
$a_{t,i} \leftarrow 1 \hspace{5mm} \text{if} \hspace{5mm}\hat{c}{t.i} * c{t,i} > 0$<br>
$\hspace{12mm} 0 \hspace{5mm} \text{otherwise}$ 

histgram: $\left{ E_t[a_{t,i}] \right}_i$ distribution
whole accuracy: $ E_{t,i}[a_{t,i}]$
End of explanation
"""


#PYTEST_VALIDATE_IGNORE_OUTPUT
linear.plot_profit()

"""
Explanation: profit

${\large p_t \leftarrow p_{t-1} * E_i \left[\left(\frac{x_{t,i}}{x_{t-1,i}}\right)^{\operatorname{sgn}(\hat{c}_{t,i})}\right]}
\hspace{1cm} (p_0=1)$
whole accuracy: ${\large \sqrt[#{t}]{\prod_t p_t}}$
End of explanation
"""


