DQtest-methods: A regression-based test to backtest VaR models proposed by...

In segMGarch: Multiple Change-Point Detection for High-Dimensional GARCH Processes

Description

Typical VaR tests cannot control for the dependence of violations, i.e., violations may cluster while the overall (unconditional) average of violations is not significantly different from α = 1-VaR. The conditional expectation should also be zero meaning that Hit_t(α) is uncorrelated with its own past and other lagged variables (such as r_t, r_t^2 or the one-step ahead forecast VaR). To test this assumption, the dynamic conditional quantile (DQ) test is used which involves the following statistic DQ = Hit^T X(X^T X)^{-1} X^T Hit/ α(1-α) where X is the matrix of explanatory variables (e.g., raw and squared past returns) and Hit the vector collecting Hit_t(α). Under the null hypothesis, Engle and Manganelli (2004) show that the proposed statistic DQ follows a χ^2_q where q = rank(X).

Usage

DQtest(y, VaR, VaR_level, lag = 1, lag_hit = 1, lag_var = 1)

## S4 method for signature 'ANY'
DQtest(y, VaR, VaR_level, lag = 1, lag_hit = 1,
  lag_var = 1)

Arguments

y	The time series to apply a VaR model (a single asset rerurn or portfolio return).
VaR	The forecast VaR.
VaR_level	The VaR level, typically 95% or 99%.
lag	The chosen lag for y.Default is 1.
lag_hit	The chosen lag for hit. Default is 1.
lag_var	The chosen lag for VaR forecasts. Default is 1.

References

Engle, Robert F., and Simone Manganelli. "CAViaR: Conditional autoregressive value at risk by regression quantiles." Journal of Business & Economic Statistics 22, no. 4 (2004): 367-381.

Examples

#VaR_level=0.95
#y=rnorm(1000,0,4)
#VaR=rep(quantile(y,1-VaR_level),length(y))
#y[c(17,18,19,20,100,101,102,103,104)]=-8
#lag=5
#DQtest(y,VaR,VaR_level,lag)

Example output

segMGarch documentation built on May 2, 2019, 7:23 a.m.