quantbullet.research#

Submodules#

Package Contents#

Classes#

DiscreteJumpModel

Statistical Jump Model with Discrete States
class quantbullet.research.DiscreteJumpModel[source]#

Statistical Jump Model with Discrete States

fixed_states_optimize(y, s, k=2)[source]#

Optimize the parameters of a discrete jump model with states fixed first.

Parameters:

  • y (np.ndarray) – Observed data of shape (T x n_features).

  • s (np.ndarray) – State sequence of shape (T x 1).

  • theta_guess (np.ndarray) – Initial guess for theta of shape (k x n_features).

  • k (int) – Number of states.

Returns:

  • np.ndarray: Optimized parameters of shape (k x n_features).

  • float: Optimal value of the objective function.

Return type:

tuple

generate_loss_matrix(y, theta)[source]#

Generate the loss matrix for a discrete jump model for fixed theta

Parameters:

  • y (np.ndarray) – observed data (T x n_features)

  • theta (np.ndarray) – parameters (k x n_features)

  • k (int) – number of states

Returns:

loss matrix (T x k)

Return type:

loss (np.ndarray)

fixed_theta_optimize(lossMatrix, lambda_)[source]#

Optimize the state sequence of a discrete jump model with fixed parameters

Parameters:

  • lossMatrix (np.ndarray) – loss matrix (T x k)

  • lambda (float) – regularization parameter

Returns:

optimal state sequence (T,) v (float): optimal value of the objective function

Return type:

s (np.ndarray)

initialize_kmeans_plusplus(data, k)[source]#

Initialize the centroids using the k-means++ method.

Parameters:

  • data – ndarray of shape (n_samples, n_features)

  • k – number of clusters

Returns:

ndarray of shape (k, n_features)

Return type:

centroids

classify_data_to_states(data, centroids)[source]#

Classify data points to the states based on the centroids.

Parameters:

  • data – ndarray of shape (n_samples, n_features)

  • centroids – centroids or means of the states, ndarray of shape (k, n_features)

Returns:

ndarray of shape (n_samples,), indices of the states to which each data point is assigned

Return type:

state_assignments

infer_states_stats(ts_returns, states)[source]#

Compute the mean and standard deviation of returns for each state

Parameters:

  • ts_returns (np.ndarray) – observed returns (T x 1)

  • states (np.ndarray) – state sequence (T x 1)

Returns:

mean and standard deviation of returns for each state

Return type:

state_features (dict)

remapResults(optimized_s, optimized_theta, ts_returns)[source]#

Remap the results of the optimization.

We would like the states to be in increasing order of the volatility of returns. This is because vol has smaller variance than returns, a warning is triggered if the states identified by volatility and returns are different.

cleanResults(raw_result, ts_returns, rearrange=False)[source]#

Clean the results of the optimization.

This extracts the best results from the ten trials based on the loss.

single_run(y, k, lambda_)[source]#

Run a single trial of the optimization. Each trial uses a different initialization of the centroids.

Parameters:

  • y (np.ndarray) – observed data (T x n_features)

  • k (int) – number of states

  • lambda (float) – regularization parameter

Returns:

optimal state sequence (T x 1) loss (float): optimal value of the objective function cur_theta (np.ndarray): optimal parameters (k x n_features)

Return type:

cur_s (np.ndarray)

fit(y, k=2, lambda_=100, rearrange=False, n_trials=10)[source]#

fit discrete jump model

Note

A multiprocessing implementation is used to speed up the optimization Ten trials with k means++ initialization are ran

Parameters:

  • y (np.ndarray) – observed data (T x n_features)

  • k (int) – number of states

  • lambda (float) – regularization parameter

  • rearrange (bool) – whether to rearrange the states in increasing order of volatility

Returns:

optimal state sequence (T x 1) best_loss (float): optimal value of the objective function best_theta (np.ndarray): optimal parameters (k x n_features) optimized_s (list): state sequences from all trials (10 x T) optimized_loss (list): objective function values from all trials (10 x 1) optimized_theta (list): parameters from all trials (10 x k x n_features)

Return type:

best_s (np.ndarray)

evaluate(true, pred, plot=False)[source]#

Evaluate the model using balanced accuracy score

Parameters:

  • true (np.ndarray) – true state sequence (T x 1)

  • pred (np.ndarray) – predicted state sequence (T x 1)

  • plot (bool) – whether to plot the true and predicted state sequences

Returns:

evaluation results

Return type:

res (dict)