# Source code for pyFTS.benchmarks.ResidualAnalysis

    #!/usr/bin/python
    # -*- coding: utf8 -*-

    """Residual Analysis methods"""

    import numpy as np
    import pandas as pd
    import matplotlib as plt
    import matplotlib.pyplot as plt
    from pyFTS.common import Transformations,Util
    from pyFTS.benchmarks import Measures
    from scipy import stats

    def residuals(targets, forecasts, order=1):
        """First order residuals"""
        return np.array(targets[order:]) - np.array(forecasts[:-1])

    def ljung_box_test(residuals, lags=[1,2,3], alpha=0.5):
        from statsmodels.stats.diagnostic import acorr_ljungbox
        from scipy.stats import chi2

        stat, pval = acorr_ljungbox(residuals, lags=lags)

        rows = []

        for ct, Q in enumerate(stat):
          lag = ct+1
          p_value = 1 - chi2.cdf(Q, df=lag)
          critical_value = chi2.ppf(1 - alpha, df=lag)
          rows.append([lag, Q, p_value, critical_value, 'H0 accepted' if Q > critical_value else 'H0 rejected'])

        return pd.DataFrame(rows, columns=['Lag','Statistic','p-Value','Critical Value', 'Result'])

    def compare_residuals(data, models, alpha=.05):
        """
        Compare residual's statistics of several models

        :param data: test data
        :param models:
        :return: a Pandas dataframe with the Box-Ljung statistic for each model
        """
        from statsmodels.stats.diagnostic import acorr_ljungbox
        rows = []
        columns = ["Model","Order","AVG","STD","Box-Ljung","p-value","Result"]
        for mfts in models:
            forecasts = mfts.predict(data)
            res = residuals(data, forecasts, mfts.order+1)
            mu = np.mean(res)
            sig = np.std(res)
            row = [mfts.shortname, mfts.order, mu, sig]
            stat, pval = acorr_ljungbox(res)
            test = 'H0 Accepted' if pval > alpha else 'H0 Rejected'
            row.extend([stat, pval, test])
            rows.append(row)
        return pd.DataFrame(rows, columns=columns)

    def plot_residuals_by_model(targets, models, tam=[8, 8], save=False, file=None):
        import scipy as sp

        fig, axes = plt.subplots(nrows=len(models), ncols=4, figsize=tam)

        for c, mfts in enumerate(models, start=0):
            if len(models) > 1:
                ax = axes[c]
            else:
                ax = axes
            forecasts = mfts.predict(targets)
            res = residuals(targets, forecasts, mfts.order)
            mu = np.mean(res)
            sig = np.std(res)

            if c == 0: ax[0].set_title("Residuals", size='large')
            ax[0].set_ylabel(mfts.shortname, size='large')
            ax[0].set_xlabel(' ')
            ax[0].plot(res)

            if c == 0: ax[1].set_title("Autocorrelation", size='large')
            ax[1].set_ylabel('ACS')
            ax[1].set_xlabel('Lag')
            ax[1].acorr(res)

            if c == 0: ax[2].set_title("Histogram", size='large')
            ax[2].set_ylabel('Freq')
            ax[2].set_xlabel('Bins')
            ax[2].hist(res)

            if c == 0: ax[3].set_title("QQ Plot", size='large')

            _, (__, ___, r) = sp.stats.probplot(res, plot=ax[3], fit=True)

        plt.tight_layout()

        Util.show_and_save_image(fig, file, save)

    def single_plot_residuals(res, order, tam=[10, 7], save=False, file=None):
        import scipy as sp

        fig, ax = plt.subplots(nrows=2, ncols=2, figsize=tam)

        ax[0][0].set_title("Residuals", size='large')
        ax[0][0].plot(res)

        ax[0][1].set_title("Autocorrelation", size='large')
        ax[0][1].set_ylabel('ACF')
        ax[0][1].set_xlabel('Lag')
        ax[0][1].acorr(res)

        ax[1][0].set_title("Histogram", size='large')
        ax[1][0].set_ylabel('Freq')
        ax[1][0].set_xlabel('Bins')
        ax[1][0].hist(res)

        _, (__, ___, r) = sp.stats.probplot(res, plot=ax[1][1], fit=True)

        plt.tight_layout()

        Util.show_and_save_image(fig, file, save)