DQtest {segMGarch} | R Documentation |
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).
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)
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. |
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.
#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)