DQtest-methods function

A regression-based test to backtest VaR models proposed by Engle and Manganelli (2004)

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 $\alpha = 1-VaR$. The conditional expectation should also be zero meaning that $Hit_t(\alpha)$ 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 $DQ = Hit^T X(X^T X)^{-1} X^T Hit/ \alpha(1-\alpha)$

where $X$ is the matrix of explanatory variables (e.g., raw and squared past returns) and $Hit$ the vector collecting $Hit_t(\alpha)$. Under the null hypothesis, Engle and Manganelli (2004) show that the proposed statistic $DQ$ follows a $\chi^2_q$ where $q = rank(X)$. methods

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.

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)

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.