TVGEV: Check Return Levels • NSGEV

The check function

The Non-Stationary Return Level (NSRL) of Parey et al is implemented for Time-Varying GEV models in the predictUncond function of the NSGEV package. The package has a function named check_predictUncond that can be used to check the results of NSGEV::predictUncond. For now, the check does not check the computation of the confidence limits, but only the value of the RL as given by the Quant column in the data frame returned by predictUncond. Since the NSRL is given by an equation with no explicit solution, it is worth checking that the returned value is consistent with the definition of the NSRL.

The check relies on the simulate method for the "TVGEV" class. Firstly, an unconditional prediction is obtained for each period in a set of periods of interest. All these periods share the same beginning date, say $t_0$ . The period with number $j$ contains $B_j$ blocks where $B_j$ is the maximal horizon chosen via period (or set by default if period is not given). Remind that predictUncond generally computes the results for several periods with the same origin $t_0$ as required here. Secondly, a large number, say $m$ , of paths $Y^{[i]}(t)$ is generated from the model. For each predicted period $j$ and each path $i$ , we compute the number $N^{[i]}(u_j)$ of exceedances over the quantile $u_j$ corresponding to the period. We eventually take the average of the $m$ values $N^{[i]}(u_j)$ for $i= 1$ to $m$ and compare it to the expectation. If $m$ is large, then the average should be close to the expectation.

Example: annual maxima of TX in Dijon

The example run with example(TVGEV) defines a TVGEV model for the annual maxima of daily maximum temperature (TX) at Dijon (Fr) in an object named res2.

Consider as period of interest the period starting at year 2020. The following code computes the NSRL for several periods of time.

pu <- predictUncond(res2, newdateFrom = "2020-01-01", confintMethod = "proflik")
kable(pu, digits = 2)

Date	Period	Level	Quant	L	U
2020-01-01	5	95%	37.15	35.97	38.38
2020-01-01	10	95%	38.23	36.95	39.62
2020-01-01	20	95%	39.31	37.82	41.00
2020-01-01	30	95%	40.04	38.33	42.01
2020-01-01	40	95%	40.65	38.71	42.89
2020-01-01	50	95%	41.22	39.03	43.72
2020-01-01	70	95%	42.30	39.57	45.36
2020-01-01	100	95%	43.90	40.29	47.85

plot(pu)

## Warning in plot.predict.TVGEV(pu): Inasmuch the plot is actually a 'ggplot', it
## is better to use the 'autoplot' method for consistency

For instance, for the period of $B_j = 40$ years beginning at the date "2020-01-01", the level $u_j =40.65$ Celsius is expected to be exceeded once (in average) across a large number of paths.

set.seed(12345)
check_predictUncond(res2, newdateFrom = "2020-01-01")

##         5        10        20        30        40        50        70       100 
## 1.0175000 1.0113333 0.9903333 0.9911667 1.0005000 0.9916667 1.0031667 1.0260000

We use the default number of paths $m = 5000$ , but only the 100 first paths are displayed on the plot. The results are in good accordance with the definition.

Findings

This test shows that the NSRL computed by predictUncond is in good accordance with the definition.