+ new backtest

Examples/run_backtesting.R

@@ -8,50 +8,71 @@ library("MSGARCH")
 data("SMI", package = "MSGARCH")
 
 ## Model specification
-models <- list(GARCH   = CreateSpec(variance.spec = list(model = c("gjrGARCH")),
-                                    distribution.spec = list(c("norm")),
-                                    switch.spec = list(K = 1)),
-               MSGARCH = CreateSpec(variance.spec = list(model = c("gjrGARCH")),
-                                    distribution.spec = list(c("norm")),
-                                    switch.spec = list(K = 2)))
-
-N_out_of_sample <- 10  # number of out-of-sample evaluation 
-N_sample        <- 2000 # fit sample size
-alpha           <- 0.05 # risk Level 
-k_update        <- 1    # frequence at which we update the model (reestimation)
+models <- list(GARCH   = MSGARCH::CreateSpec(variance.spec = list(model = c("gjrGARCH")),
+                                             distribution.spec = list(c("sstd")),
+                                             switch.spec = list(K = 1)),
+               MSGARCH = MSGARCH::CreateSpec(variance.spec = list(model = c("gjrGARCH")),
+                                             distribution.spec = list(c("sstd")),
+                                             switch.spec = list(K = 2)))
+
+n_backtest <- 1000 # number of out-of-sample evaluation 
+n_its      <- 1500 # fit sample size
+alpha      <- 0.05 # risk Level 
+k_update   <- 100   # frequence at which we update the model (reestimation)
 
 ## Initialization 
-VaR_OOS   <- matrix(NA, nrow = N_out_of_sample, ncol = length(models))
-y_OOS     <- matrix(NA, nrow = N_out_of_sample, ncol = 1)
+VaR   <- matrix(NA, nrow = n_backtest, ncol = length(models))
+y_ots <- matrix(NA, nrow = n_backtest, ncol = 1)
 model_fit <- vector(mode = "list", length = length(models))
 
 ## Backtest 
-for (i in 1:N_out_of_sample) { # iterate over out-of-sample time
-  cat("Backtest. Iteration: ", i, "\n")
-  y_fit    <- SMI[i:(N_sample + i - 1)] # training sample
-  y_OOS[i] <- SMI[N_sample + i] # store out-of-sample data
-  for (j in 1:length(models)) { # iterate over model
-    # do we update the model ?
+
+# iterate over out-of-sample time
+for (i in 1:n_backtest) { 
+  cat("Backtest - Iteration: ", i, "\n")
+  y_its    <- SMI[i:(n_its + i - 1)] # in-sample data 
+  y_ots[i] <- SMI[n_its + i]         # out-of-sample data
+
+  # iterate over models
+  for (j in 1:length(models)) { 
+
+    # do we update the model estimation
     if (k_update == 1 || i %% k_update == 1) {
-      model_fit[[j]] <- FitML(spec = models[[j]], data = y_fit) # fit the model
+      cat("Model", j, "is reestimated\n")
+      model_fit[[j]] <- MSGARCH::FitML(spec = models[[j]], data = y_its) 
     }
 
     # calculate VaR 1-step ahead
-    VaR_OOS[i,j] <- Risk(model_fit[[j]],
-                         n.ahead = 1,
-                         alpha   = alpha,
-                         do.es   = FALSE,
-                         do.its  = FALSE)$VaR
-  }
+    VaR[i,j] <- MSGARCH::Risk(model_fit[[j]]$spec, par = model_fit[[j]]$par,
+                              data = y_its,
+                              n.ahead = 1,
+                              alpha   = alpha,
+                              do.es   = FALSE,
+                              do.its  = FALSE)$VaR
+  }                                
 }
 
 ## Test the VaR
 library("GAS")
-CCtest_pvalue <- NULL
+CC_pval <- DQ_pval <- NULL
 for (j in 1:length(models)) { #iterate over model
-  test <- GAS::BacktestVaR(data  = y_OOS,
-                           VaR   = VaR_OOS[,j],
+  test <- GAS::BacktestVaR(data  = y_ots,
+                           VaR   = VaR[,j],
                            alpha = alpha)
 
-  CCtest_pvalue[j] <- test$LRcc[j] #P-Value 
+  CC_pval[j] <- test$LRcc[2]      
+  DQ_pval[j] <- test$DQ$pvalue  
 }
+names(CC_pval) <- names(DQ_pval) <- c("GARCH", "MSGARCH")
+
+print(CC_pval)
+print(DQ_pval)
+
+par(mfrow = c(1,1))
+plot(y_ots, pch = 20, las = 1, xlab = "time index", ylab = "return [%]")
+lines(VaR[,1], type = 'l', col = "red", lwd = 2)
+lines(VaR[,2], type = 'l', col = "blue", lwd = 2)
+legend("topleft", legend = c("GARCH", "MSGARCH"), col = c("red", "blue"), lwd = 2, cex = 2)
+grid()
+
+