ELRF Residuals

import chainladder as cl
import pandas as pd

This example replicates the diagnostic residuals from Barnett and Zehnwirth’s “Best Estimates for Reserves” paper in which they describe the Extended Link Ratio Family (ELRF) model. This Development estimator is based on the ELRF model.

The weighted standardized residuals are contained in the std_residuals_ property of the fitted estimator. Using these, we can replicate Figure 2.6 from the paper.

raa = cl.load_sample('raa')
model = cl.Development().fit(raa)

plot1a = model.std_residuals_.T
plot1b = model.std_residuals_.mean('origin').T
plot2a = model.std_residuals_
plot2b = model.std_residuals_.mean('development')
plot3a = model.std_residuals_.dev_to_val().T
plot3b = model.std_residuals_.dev_to_val().mean('origin').T
plot4 = pd.concat((
    (raa[raa.valuation < raa.valuation_date] * 
     model.ldf_.values).unstack().rename('Fitted Values'),
    model.std_residuals_.unstack().rename('Residual')), axis=1).dropna()

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import matplotlib.pyplot as plt
plt.style.use('ggplot')
%config InlineBackend.figure_format = 'retina'

fig, ((ax00, ax01), (ax10, ax11)) = plt.subplots(ncols=2, nrows=2, figsize=(13,10))
fig.suptitle("Barnett Zehnwirth\nStandardized residuals of the Extended Link Ratio Family (ELRF)\n(Fig 2.6)");


plot1a.plot(
    style='.', color='gray', legend=False, ax=ax00,
    xlabel='Development Month', ylabel='Weighted Standardized Residuals')
plot1b.plot(
    color='red', legend=False, ax=ax00)
plot2a.plot(
    style='.', color='gray', legend=False, ax=ax01, xlabel='Origin Period')
plot2b.plot(
    color='red', legend=False, ax=ax01)
plot3a.plot(
    style='.', color='gray', legend=False, ax=ax10,
    xlabel='Valuation Date', ylabel='Weighted Standardized Residuals')
plot3b.plot(color='red', legend=False, grid=True, ax=ax10)
plot4.plot(kind='scatter', marker='o', color='gray', 
           x='Fitted Values', y='Residual', ax=ax11, sharey=True);