models module

class models.DirectAutoRegressor(base_estimator, auto_order, exog_order, pred_step, exog_delay=None, **base_params)

Bases: fireTS.core.GeneralAutoRegressor

This model performs autoregression with exogenous inputs on the k-step ahead output directly. The model equation is written as follows.

(1)\[\begin{split}y(t + k) &=& f(y(t), ..., y(t-p+1), \\ & & x_1(t - d_1), ..., x_1(t-d_1-q_1+1), \\ & & ..., x_m(t - d_1), ..., x_m(t - d_m - q_m + 1)) + e(t)\end{split}\]

Parameters:

• base_estimator (object) – an estimator object that implements the scikit-learn API (fit, and predict). The estimator will be used to fit the function \(f\) in equation (1).
• auto_order (int) – the autoregression order \(p\) in equation (1).
• exog_order (list) – the exogenous input order, a list of integers representing the order for each exogenous input, i.e. \([q_1, q_2, ..., q_m]\) in equation (1).
• pred_step (int) – the prediction step \(k\) in equation (1). By default, it is set to 1.
• exog_delay (list) – the delays of the exogenous inputs, a list of integers representing the delay of each exogenous input, i.e. \([d_1, d_2, ..., d_m]\) in equation (1). By default, all the delays are set to 0.
• base_params (dict) – other keyword arguments for base_estimator.

predict(X, y)

Produce multi-step prediction of y. The multi-step prediction is done directly. No future X inputs are used in the prediction. The prediction equation is as follows:

\[\begin{split}\hat{y}(t + k) &=& f(y(t), ..., y(t - p + 1), \\ & & x_1(t - d_1), ..., x_1(t - d_1 - q_1 + 1) \\ & & ..., x_m(t - d_m), ..., x_m(t - d_m - q_m + 1))\end{split}\]

Parameters:

• X (array-like) – exogenous input time series, shape = (n_samples, n_exog_inputs)
• y (array-like) – target time series to predict, shape = (n_samples)
• step (int) – prediction step.

Returns:

k-step prediction time series, shape = (n_samples). The \(i\) th value of the output is the k-step prediction of the \(i\) th value of the input y. The first pred_step + max(auto_order - 1, max(exog_order + exog_delay) - 1) values of the output is np.nan.

score(X, y, method='r2', verbose=False)

Produce multi-step prediction of y, and compute the metrics against y. Nan is ignored when computing the metrics.

Parameters:

• X (array-like) – exogenous input time series, shape = (n_samples, n_exog_inputs)
• y (array-like) – target time series to predict, shape = (n_samples)
• method (string) – could be “r2” (R Square) or “mse” (Mean Square Error).

Returns:

prediction metric. Nan is ignored when computing the metrics.

class models.NARX(base_estimator, auto_order, exog_order, exog_delay=None, **base_params)

Bases: fireTS.core.GeneralAutoRegressor

NARX stands for Nonlinear AutoRegressive eXogenous model. The model equation is written as follows.

(2)\[\begin{split}y(t + 1) &=& f(y(t), ..., y(t-p+1), \\ & & x_1(t - d_1), ..., x_1(t-d_1-q_1+1), \\ & & ..., x_m(t - d_1), ..., x_m(t - d_m - q_m + 1)) + e(t)\end{split}\]

Parameters:

• base_estimator (object) – an estimator object that implements the scikit-learn API (fit, and predict). The estimator will be used to fit the function \(f\) in equation (2).
• auto_order (int) – the autoregression order \(p\) in equation (2).
• exog_order (list) – the exogenous input order, a list of integers representing the order for each exogenous input, i.e. \([q_1, q_2, ..., q_m]\) in equation (2).
• exog_delay (list) – the delays of the exogenous inputs, a list of integers representing the delay of each exogenous input, i.e. \([d_1, d_2, ..., d_m]\) in equation (2). By default, all the delays are set to 0.
• base_params (dict) – other keyword arguments for base_estimator.

forecast(X, y, step=1, X_future=None)

Forecast y multiple step ahead given the exogenous input history X, output history y and the future exogenous input X_future. X_future is assumed to be all zeros if not specified.

Parameters:

• X (array-like) – exogenous input time series, shape = (n_samples, n_exog_inputs)
• y (array-like) – target time series to predict, shape = (n_samples)
• step (int) – prediction step.
• X_futrue (array-like) – future exogenous input time series, shape = (step - 1, n_exog_inputs)

Returns:

multi-step forecasted time series, shape = (step).

predict(X, y, step=1)

Produce multi-step prediction of y. The multi-step prediction is done recursively by using the future inputs in X. The prediction equation is as follows:

\[\begin{split}\hat{y}(t + k) &=& f(\hat{y}(t + k - 1), ..., \hat{y}(t + k - p), \\ & &x_1(t + k - 1 - d_1), ..., x_1(t + k - d_1 - q_1) \\ & &..., x_m(t + k - 1 - d_m), ..., x_m(t + k - d_m - q_m))\end{split}\]

Parameters:

• X (array-like) – exogenous input time series, shape = (n_samples, n_exog_inputs)
• y (array-like) – target time series to predict, shape = (n_samples)
• step (int) – prediction step.

Returns:

k-step prediction time series, shape = (n_samples). The \(i\) th value of the output is the k-step prediction of the \(i\) th value of the input y. The first step + max(auto_order - 1, max(exog_order + exog_delay) - 1) values of the output is np.nan.

score(X, y, step=1, method='r2')

Produce multi-step prediction of y, and compute the metrics against y. Nan is ignored when computing the metrics.

Parameters:

• X (array-like) – exogenous input time series, shape = (n_samples, n_exog_inputs)
• y (array-like) – target time series to predict, shape = (n_samples)
• step (int) – prediction step.
• method (string) – could be “r2” (R Square) or “mse” (Mean Square Error).

Returns:

prediction metric. Nan is ignored when computing the metrics.