Plot forecasting residuals¶

Analyzing the residuals (errors) of predictions is useful to understand the behavior of a forecaster. The function skforecast.plot.plot_residuals creates 3 plots:

• Residual values in time order

• Distribution of residuals

• Residuals autocorrelation

In [1]:

# Libraries
# ==============================================================================
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.linear_model import Ridge

from skforecast.ForecasterAutoreg import ForecasterAutoreg
from skforecast.model_selection import backtesting_forecaster
from skforecast.plot import plot_residuals

# Libraries # ============================================================================== import pandas as pd import matplotlib.pyplot as plt from sklearn.linear_model import Ridge from skforecast.ForecasterAutoreg import ForecasterAutoreg from skforecast.model_selection import backtesting_forecaster from skforecast.plot import plot_residuals

In [2]:

# Download data
# ==============================================================================
url = ('https://raw.githubusercontent.com/JoaquinAmatRodrigo/skforecast/master/data/h2o_exog.csv')
data = pd.read_csv(url, sep=',')

# Data preprocessing
# ==============================================================================
data['fecha'] = pd.to_datetime(data['fecha'], format='%Y/%m/%d')
data = data.set_index('fecha')
data = data.rename(columns={'x': 'y'})
data = data.asfreq('MS')
data = data.sort_index()

# Plot data
# ==============================================================================
fig, ax=plt.subplots(figsize=(9, 4))
data.plot(ax=ax);

# Download data # ============================================================================== url = ('https://raw.githubusercontent.com/JoaquinAmatRodrigo/skforecast/master/data/h2o_exog.csv') data = pd.read_csv(url, sep=',') # Data preprocessing # ============================================================================== data['fecha'] = pd.to_datetime(data['fecha'], format='%Y/%m/%d') data = data.set_index('fecha') data = data.rename(columns={'x': 'y'}) data = data.asfreq('MS') data = data.sort_index() # Plot data # ============================================================================== fig, ax=plt.subplots(figsize=(9, 4)) data.plot(ax=ax);

In [3]:

# Train and backtest forecaster
# ==============================================================================
n_backtest = 36*3
data_train = data[:-n_backtest]
data_test  = data[-n_backtest:]

forecaster = ForecasterAutoreg(
                 regressor = Ridge(),
                 lags      = 5 
             )

metric, predictions_backtest = backtesting_forecaster(
                                   forecaster         = forecaster,
                                   y                  = data.y,
                                   initial_train_size = len(data_train),
                                   steps              = 36,
                                   metric             = 'mean_squared_error',
                                   verbose            = True
                               )

predictions_backtest

# Train and backtest forecaster # ============================================================================== n_backtest = 36*3 data_train = data[:-n_backtest] data_test = data[-n_backtest:] forecaster = ForecasterAutoreg( regressor = Ridge(), lags = 5 ) metric, predictions_backtest = backtesting_forecaster( forecaster = forecaster, y = data.y, initial_train_size = len(data_train), steps = 36, metric = 'mean_squared_error', verbose = True ) predictions_backtest

Information of backtesting process
----------------------------------
Number of observations used for initial training: 87
Number of observations used for backtesting: 108
    Number of folds: 3
    Number of steps per fold: 36

Data partition in fold: 0
    Training:   1992-04-01 00:00:00 -- 1999-06-01 00:00:00  (n=87)
    Validation: 1999-07-01 00:00:00 -- 2002-06-01 00:00:00  (n=36)
Data partition in fold: 1
    Training:   1992-04-01 00:00:00 -- 1999-06-01 00:00:00  (n=87)
    Validation: 2002-07-01 00:00:00 -- 2005-06-01 00:00:00  (n=36)
Data partition in fold: 2
    Training:   1992-04-01 00:00:00 -- 1999-06-01 00:00:00  (n=87)
    Validation: 2005-07-01 00:00:00 -- 2008-06-01 00:00:00  (n=36)

Out[3]:

	pred
1999-07-01	0.684784
1999-08-01	0.673355
1999-09-01	0.672449
1999-10-01	0.660822
1999-11-01	0.651780
...	...
2008-02-01	0.655673
2008-03-01	0.655675
2008-04-01	0.655675
2008-05-01	0.655674
2008-06-01	0.655673

108 rows × 1 columns

The function predictions_backtest may be used with already calculated residuals or giving the predicted values and the real values of the series.

In [4]:

residuals = predictions_backtest['pred'] - data_test['y']
plot_residuals(residuals=residuals)

residuals = predictions_backtest['pred'] - data_test['y'] plot_residuals(residuals=residuals)

In [5]:

plot_residuals(y_true=data_test['y'], y_pred=predictions_backtest['pred'])

plot_residuals(y_true=data_test['y'], y_pred=predictions_backtest['pred'])

Customize plot¶

It is possible to customize the plot by passing an already created matplotlib figure or using additional keyword arguments that are passed to matplotlib.pyplot.figure().

In [6]:

fig, ax = plt.subplots(1, 1, figsize=(14, 6))
plot_residuals(residuals=residuals, fig=fig)

fig, ax = plt.subplots(1, 1, figsize=(14, 6)) plot_residuals(residuals=residuals, fig=fig)

In [7]:

plot_residuals(residuals=residuals, edgecolor="black", linewidth=15, figsize=(12, 6))

plot_residuals(residuals=residuals, edgecolor="black", linewidth=15, figsize=(12, 6))

It is also possible to customise the internal aesthetics of the plots by changing plt.rcParams.

In [8]:

plt.style.use('fivethirtyeight')
plt.rcParams['lines.linewidth'] = 1.5
dark_style = {
    'figure.facecolor'  : '#212946',
    'axes.facecolor'    : '#212946',
    'savefig.facecolor' :'#212946',
    'axes.grid'         : True,
    'axes.grid.which'   : 'both',
    'axes.spines.left'  : False,
    'axes.spines.right' : False,
    'axes.spines.top'   : False,
    'axes.spines.bottom': False,
    'grid.color'        : '#2A3459',
    'grid.linewidth'    : '1',
    'text.color'        : '0.9',
    'axes.labelcolor'   : '0.9',
    'xtick.color'       : '0.9',
    'ytick.color'       : '0.9',
    'font.size'         : 12
}
plt.rcParams.update(dark_style)

fig, ax = plt.subplots(1, 1, figsize=(14, 8))
plot_residuals(residuals=residuals, fig=fig)

plt.style.use('fivethirtyeight') plt.rcParams['lines.linewidth'] = 1.5 dark_style = { 'figure.facecolor' : '#212946', 'axes.facecolor' : '#212946', 'savefig.facecolor' :'#212946', 'axes.grid' : True, 'axes.grid.which' : 'both', 'axes.spines.left' : False, 'axes.spines.right' : False, 'axes.spines.top' : False, 'axes.spines.bottom': False, 'grid.color' : '#2A3459', 'grid.linewidth' : '1', 'text.color' : '0.9', 'axes.labelcolor' : '0.9', 'xtick.color' : '0.9', 'ytick.color' : '0.9', 'font.size' : 12 } plt.rcParams.update(dark_style) fig, ax = plt.subplots(1, 1, figsize=(14, 8)) plot_residuals(residuals=residuals, fig=fig)

In [10]:

%%html
<style>
.jupyter-wrapper .jp-CodeCell .jp-Cell-inputWrapper .jp-InputPrompt {display: none;}
</style>

%%html