BacktestVaR function

Backtest Value at Risk (VaR)

This function implements several backtesting procedures for the Value at Risk (VaR). These are: (i) The statistical tests of Kupiec (1995), Christoffesen (1998) and Engle and Manganelli (2004), (ii) The tick loss function detailed in Gonzalez-Rivera et al. (2004), the mean and max absolute loss used by McAleer and Da Veiga (2008) and the actual over expected exceedance ratio.

BacktestVaR(data, VaR, alpha, Lags = 4)

Arguments

• data: numeric Vector of observations.

• VaR: numeric Vector containing the VaR series.

• alpha: numeric The VaR confidence level.

• Lags: numeric Lags used in the Dynamic Quantile test of Engle and Manganelli (2004).

Details

This function implements several backtesting procedure for the Value at Risk. The implemented statistical tests are:

• LRuc The unconditional coverage test of Kupiec (1995).
• LRcc The conditional coverage test of Christoffesen (1998).
• DQ The Dynamic Quantile test of Engle and Manganelli (2004).

The implemented VaR backtesting quantities are:

• AD mean and maximum absolute deviation between the observations and the quantiles as in McAleer and Da Veiga (2008).
• Loss Average quantile loss and quantile loss series as in Gonzalez-Rivera et al. (2004).
• AE Actual over Expected exceedance ratio.

Returns

A list with elements: LRuc, LRcc, DQ, AD, AE.

Author(s)

Leopoldo Catania

References

Christoffersen PF (1998). "Evaluating Interval Rorecasts." International Economic Review, 39(4), 841-862.

Engle RF and Manganelli S. (2004). "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles." Journal of Business & Economic Statistics, 22(4), 367-381. tools:::Rd_expr_doi("10.1198/073500104000000370") .

Gonzalez-Rivera G, Lee TH, and Mishra, S (2004). "Forecasting Volatility: A Reality Check Based on Option Pricing, Utility Function, Value-at-Risk, and Predictive Likelihood." International Journal of Forecasting, 20(4), 629-645. tools:::Rd_expr_doi("10.1016/j.ijforecast.2003.10.003") .

Kupiec PH (1995). "Techniques for Verifying the Accuracy of Risk Measurement Models." The Journal of Derivatives, 3(2), 73-84. tools:::Rd_expr_doi("10.3905/jod.1995.407942")

McAleer M and Da Veiga B (2008). "Forecasting Value-at-Risk with a Parsimonious Portfolio Spillover GARCH (PS-GARCH) Model." Journal of Forecasting, 27(1), 1-19. tools:::Rd_expr_doi("10.1002/for.1049") .

Examples

data("StockIndices")

GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
                     GASPar = list(location = FALSE, scale = TRUE,
                                   shape = FALSE))

FTSEMIB = StockIndices[, "FTSEMIB"]

InSampleData  = FTSEMIB[1:1500]
OutSampleData = FTSEMIB[1501:2404]

Fit = UniGASFit(GASSpec, InSampleData)

Forecast = UniGASFor(Fit, Roll = TRUE, out = OutSampleData)

alpha = 0.05

VaR = quantile(Forecast, alpha)

BackTest = BacktestVaR(OutSampleData, VaR, alpha)