Trend

Trend#

class chainladder.Trend(trends=0.0, dates=None, axis='origin')[source]#

Estimator to create and apply trend factors to a Triangle object. Allows for compound trends as well as storage of the trend matrix to be used in other estimators, such as CapeCod.

Parameters:
trends: list-like

The list containing the annual trends expressed as a decimal. For example, 5% decrease should be stated as -0.05

dates: list of date-likes

A list-like of (start, end) dates to correspond to the trend list.

axis: str (options: [‘origin’, ‘valuation’])

The axis on which to apply the trend

Attributes:
trend_:

A triangle representation of the trend factors

Examples

The same annual decimal trend is applied along origin or valuation axes, producing different factor surfaces.

tri = cl.load_sample("raa")
origin = cl.Trend(0.05, axis="origin").fit(tri)
val = cl.Trend(0.05, axis="valuation").fit(tri)
print(np.round(origin.trend_, 4))

         12      24      36      48      60      72      84      96      108     120
1981  1.5513  1.5513  1.5513  1.5513  1.5513  1.5513  1.5513  1.5513  1.5513  1.5513
1982  1.4775  1.4775  1.4775  1.4775  1.4775  1.4775  1.4775  1.4775  1.4775     NaN
1983  1.4071  1.4071  1.4071  1.4071  1.4071  1.4071  1.4071  1.4071     NaN     NaN
1984  1.3401  1.3401  1.3401  1.3401  1.3401  1.3401  1.3401     NaN     NaN     NaN
1985  1.2763  1.2763  1.2763  1.2763  1.2763  1.2763     NaN     NaN     NaN     NaN
1986  1.2155  1.2155  1.2155  1.2155  1.2155     NaN     NaN     NaN     NaN     NaN
1987  1.1576  1.1576  1.1576  1.1576     NaN     NaN     NaN     NaN     NaN     NaN
1988  1.1025  1.1025  1.1025     NaN     NaN     NaN     NaN     NaN     NaN     NaN
1989  1.0500  1.0500     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN
1990  1.0000     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN

print(np.round(val.trend_, 4))

         12      24      36      48      60      72      84      96    108  120
1981  1.5513  1.4775  1.4071  1.3401  1.2763  1.2155  1.1576  1.1025  1.05  1.0
1982  1.4775  1.4071  1.3401  1.2763  1.2155  1.1576  1.1025  1.0500  1.00  NaN
1983  1.4071  1.3401  1.2763  1.2155  1.1576  1.1025  1.0500  1.0000   NaN  NaN
1984  1.3401  1.2763  1.2155  1.1576  1.1025  1.0500  1.0000     NaN   NaN  NaN
1985  1.2763  1.2155  1.1576  1.1025  1.0500  1.0000     NaN     NaN   NaN  NaN
1986  1.2155  1.1576  1.1025  1.0500  1.0000     NaN     NaN     NaN   NaN  NaN
1987  1.1576  1.1025  1.0500  1.0000     NaN     NaN     NaN     NaN   NaN  NaN
1988  1.1025  1.0500  1.0000     NaN     NaN     NaN     NaN     NaN   NaN  NaN
1989  1.0500  1.0000     NaN     NaN     NaN     NaN     NaN     NaN   NaN  NaN
1990  1.0000     NaN     NaN     NaN     NaN     NaN     NaN     NaN   NaN  NaN

Multiple trends with paired dates apply a different annual trend to each window, producing a surface that matches neither single flat trend. Each tuple runs from the recent anchor back to the older bound, so here a 10% trend covers the recent origins (1985 and later) and a 5% trend the earlier ones.

tri = cl.load_sample("raa")
piece = cl.Trend(
    trends=[0.10, 0.05],
    dates=[(None, "1985"), ("1985", None)],
    axis="origin",
).fit(tri)
print(np.round(piece.trend_, 4))

         12      24      36      48      60      72      84      96      108     120
1981  2.0429  2.0429  2.0429  2.0429  2.0429  2.0429  2.0429  2.0429  2.0429  2.0429
1982  1.9456  1.9456  1.9456  1.9456  1.9456  1.9456  1.9456  1.9456  1.9456     NaN
1983  1.8529  1.8529  1.8529  1.8529  1.8529  1.8529  1.8529  1.8529     NaN     NaN
1984  1.7647  1.7647  1.7647  1.7647  1.7647  1.7647  1.7647     NaN     NaN     NaN
1985  1.6105  1.6105  1.6105  1.6105  1.6105  1.6105     NaN     NaN     NaN     NaN
1986  1.4641  1.4641  1.4641  1.4641  1.4641     NaN     NaN     NaN     NaN     NaN
1987  1.3310  1.3310  1.3310  1.3310     NaN     NaN     NaN     NaN     NaN     NaN
1988  1.2100  1.2100  1.2100     NaN     NaN     NaN     NaN     NaN     NaN     NaN
1989  1.1000  1.1000     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN
1990  1.0000     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN

The recent origins (1985-1990) follow the 10% path exactly, matching a single flat 10% trend, while the earlier origins compound the extra 5% on top and rise above a flat 5% surface, so the staged factors track neither flat trend alone.

Because trend_ is a stored factor surface, transform can pre-level a triangle so a downstream CapeCod reflects staged annual assumptions that a single scalar trend could not express. Leveling the losses lifts the a-priori for the older years, so total IBNR rises against an unleveled fit (29.3M versus 26.4M):

tr = cl.load_sample("clrd")[["CumPaidLoss", "EarnedPremDIR"]].sum()
sample_weight = tr["EarnedPremDIR"].latest_diagonal
t_step = cl.Trend(
    trends=[0.04, 0.02],
    dates=[(None, "1995"), ("1995", None)],
    axis="origin",
).fit(tr["CumPaidLoss"])
paid_leveled = t_step.transform(tr["CumPaidLoss"])
leveled = cl.CapeCod(trend=0).fit(paid_leveled, sample_weight=sample_weight)
unleveled = cl.CapeCod(trend=0).fit(tr["CumPaidLoss"], sample_weight=sample_weight)
print(np.round(t_step.trend_, 4))
print(int(round(float(np.nansum(leveled.ibnr_.values)), 0)))
print(int(round(float(np.nansum(unleveled.ibnr_.values)), 0)))

         12      24      36      48      60      72      84      96      108     120
1988  1.2647  1.2647  1.2647  1.2647  1.2647  1.2647  1.2647  1.2647  1.2647  1.2647
1989  1.2399  1.2399  1.2399  1.2399  1.2399  1.2399  1.2399  1.2399  1.2399     NaN
1990  1.2156  1.2156  1.2156  1.2156  1.2156  1.2156  1.2156  1.2156     NaN     NaN
1991  1.1918  1.1918  1.1918  1.1918  1.1918  1.1918  1.1918     NaN     NaN     NaN
1992  1.1684  1.1684  1.1684  1.1684  1.1684  1.1684     NaN     NaN     NaN     NaN
1993  1.1455  1.1455  1.1455  1.1455  1.1455     NaN     NaN     NaN     NaN     NaN
1994  1.1230  1.1230  1.1230  1.1230     NaN     NaN     NaN     NaN     NaN     NaN
1995  1.0816  1.0816  1.0816     NaN     NaN     NaN     NaN     NaN     NaN     NaN
1996  1.0400  1.0400     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN
1997  1.0000     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN     NaN
29278236
26370689
fit(X, y=None, sample_weight=None)[source]#

Fit the model with X.

Parameters:
X: Triangle-like

Data to which the model will be applied.

y: Ignored
sample_weight: Ignored
Returns:
self: object

Returns the instance itself.

transform(X, y=None, sample_weight=None)[source]#

If X and self are of different shapes, align self to X, else return self.

Parameters:
X: Triangle

The triangle to be transformed

Returns:
X_new: New triangle with transformed attributes.

Inherited Methods

Trend.fit_transform

Fit to data, then transform it.

Trend.get_metadata_routing

Get metadata routing of this object.

Trend.get_params

Get parameters for this estimator.

Trend.set_output

Set output container.

Trend.set_params

Set the parameters of this estimator.

Trend.to_json

Serializes triangle object to json format

Trend.to_pickle

Serializes triangle object to pickle.