当我尝试在“自动”模式下调整ARMA-GARCH模型时，我遇到了问题。我尝试使用相同的信息标准选择最佳模型（我使用BIC和AIC）。 所以，我的算法“在指甲上”：
1）定义ARMA（p，q）-GARCH（e，sigma）模型的max p，max q，max e，max sigma（length）值。
2）创建（0：max p） - （0：max q） - （1：max P） - （0：max sigma）的所有组合（如1-1-2-1等）
3）针对6个主要分布的每组4个拟合ARMA-GARCH模型：norm，snorm，std，sstd，ged，sged。
4）对于p.3中的所有拟合模型，得到BIC，并在这6个模型中选择具有最小BIC的模型（针对不同的分布）。
5）对于所有四个组，使用p.3-4给出的聚合模型。
6）在第5页中选择模型组中具有最低BIC的模型
所以，当我这样做时，我有一个很大的问题 - 这个算法选择具有最大AR和MA部分的模型。并且所有ar和ma系数都很重要!!
这里是我的算法的完整列表。
主要脚本：
library(parallel);
library(fGarch);
library(broman);
maxThreads <- max(1, detectCores() - 1);
internalCluster <- makeCluster(maxThreads);
clusterEvalQ(internalCluster, { library(fGarch); library(Rsolnp); });
setwd("C:/Users/Rebelion/Desktop/Model 2.0")
GetBestGARCHModel = source("GetBestGARCHModel.R")$value;
GetEmpiricalQuantiles = source("GetEmpiricalQuantiles.R")$value;
GetGARCHFormula = source("GetGARCHFormula.R")$value;
GetGARCHQuantileValues = source("GetGARCHQuantileValues.R")$value;
GetModelFitResult = source("GetModelFitResult.R")$value;
ModelNodeCalculation = source("ModelNodeCalculation.R")$value;
CheckName = source("CheckName.R")$value;
GetGARCHBestDistribModel = source("GetGARCHBestDistribModel.R")$value;
RNGkind("L'Ecuyer-CMRG");
set.seed(round(10000*runif(1)));
(s <- .Random.seed);
N <- 200;
spec = garchSpec(model = list());
z <- garchSim(spec, n = N)
data <- z;
probabilities <- c(0.01, 0.05, 0.95, 0.99);
clusterExport(internalCluster, c("GetGARCHBestDistribModel"));
clusterExport(internalCluster, c("GetGARCHFormula"));
clusterExport(internalCluster, c("ModelNodeCalculation"));
result <- GetModelFitResult(data , probabilities, 0.95, 5, 3, internalCluster);
if (!is.null(result))
{
lowBound <- result$boundaries[[2]];
highBound <- result$boundaries[[3]];
plot(sapply(1:length(data), function(i) { data[[i]]; }), type="l");
lines(sapply(1:length(result$bestModel@fitted), function(i) { result$bestModel@fitted[[i]]; }));
lines(sapply(1:length(lowBound), function(i) { lowBound[[i]]; }), col = "red");
lines(sapply(1:length(highBound), function(i) { highBound[[i]]; }), col = "blue");
result$bestModel
} else
{
cat("Error in GARCH estimation \n");
}
stopCluster(internalCluster);
nextRNGStream(s);
nextRNGSubStream(s);
GetModelFitResult
GetModelFitResult <- function(timeSeries, boundaryProbabilities, parametersConfidence = 0.95, maxARMAPart, maxGARCHPart, cl = NULL)
{
bestModel <- GetBestGARCHModel(timeSeries, maxARMAPart, maxGARCHPart, parametersConfidence, cl);
if (!identical(bestModel$criterion, Inf))
{
print(bestModel$model)
quantilesList <- GetGARCHQuantileValues(bestModel$model, boundaryProbabilities);
print(quantilesList$quantiles);
boundaries <- lapply(quantilesList$quantiles, function(val) { bestModel$model@fitted + val*bestModel$model@sigma.t; });
names(boundaries) <- boundaryProbabilities;
result <- list(quantiles = quantilesList$quantiles, boundaries = boundaries, bestModel = bestModel$model, criterion = bestModel$criterion);
return (result);
}
else
{
result <- NULL;
}
}
GetBestGARCHModel
GetBestGARCHModel <- function(timeSeries, maxARMAModelSize, maxGARCHModelSize, confidence, cl)
{
ARParam <- MAParam <- 0:maxARMAModelSize;
sigmaParam <- 0:maxGARCHModelSize;
eParam <- 1:maxGARCHModelSize;
gridVal <- expand.grid(ARParam, MAParam, eParam, sigmaParam);
parametersList <- lapply(length(gridVal[,1]):1, function(i)
{
return (sapply(1:4, function(j, k = i) { return (gridVal[k,][[j]]); }));
});
if (!is.null(cl))
{
bestLocalModels <- parLapplyLB(cl, parametersList, GetGARCHBestDistribModel, data = timeSeries, criterionType = "BIC");
}
else
{
bestLocalModels <- lapply(parametersList, GetGARCHBestDistribModel, data = timeSeries, criterionType = "BIC");
}
criterionList <- sapply(bestLocalModels, function(mod) { return(mod$criterion); } );
bestModelIndex <- which.min(criterionList);
if (!identical(criterionList[bestModelIndex], Inf)) { bestModel <- bestLocalModels[[bestModelIndex]]$model; }
else { bestModel <- NULL; }
result <- list(model = bestModel, criterion = bestLocalModels[[bestModelIndex]]$criterion);
return(result);
}
GetGARCHBestDistribModel
GetGARCHBestDistribModel <- function(data, modelParams, criterionType, confidence = 0.95)
{
garchFormula <- GetGARCHFormula(c(modelParams[1], modelParams[2]), c(modelParams[3], modelParams[4]));
distribs <- c("norm", "snorm", "std", "sstd", "ged", "sged");
fittedModels <- lapply(distribs, ModelNodeCalculation, data = data, garchFormula = garchFormula);
names(fittedModels) <- distribs;
fittedModelIC <- sapply(fittedModels, function(model)
{
if (!is.null(model)) { result <- model@fit$ics[[criterionType]]; }
else { result <- Inf; }
return(result);
});
bestModelIndex <- which.min(fittedModelIC);
bestModelIC <- min(fittedModelIC);
if (!identical(bestModelIC, Inf))
{
bestModel <- fittedModels[[bestModelIndex]];
pValues <- bestModel@fit$matcoef[, "Pr(>|t|)"];
includeMean <- !is.na(pValues[["mu"]]) & (pValues[["mu"]] < 1 - confidence);
includeLeverage <- !is.na(pValues[["gamma1"]]) & (pValues[["gamma1"]] < 1 - confidence);
#includeDelta <- !is.na(pValues[["delta"]]) & (pValues[["delta"]] < 1 - confidence);
model <- try(garchFit(garchFormula, data, cond.dist=bestModel@fit$params$cond.dist, trace=FALSE,
include.mean = includeMean, leverage = includeLeverage), silent = TRUE);
if (inherits(model, "try-error")) { model <- bestModel; }
else { bestModelIC <- model@fit$ics[[criterionType]]; }
result <- list(model = model, criterion = bestModelIC);
}
else
{
result <- list(model = NULL, criterion = Inf);
}
return(result);
}
ModelNodeCalculation
ModelNodeCalculation <- function(distrib, data, garchFormula)
{
model <- try(garchFit(garchFormula, data, cond.dist=distrib, trace=FALSE, leverage = TRUE), silent = TRUE);
if (inherits(model, "try-error")) { model <- NULL; }
return(model);
}
GetGARCHQuantileValues
GetGARCHQuantileValues <- function(model, probabilities, sd = 1)
{
xi <- nu <- distrib <- NA;
mu <- 0;
coef <- model@fit$matcoef[,1];
isSkewed <- CheckName(coef, "skew");
isShaped <- CheckName(coef, "shape");
isMeaned <- CheckName(coef, "mu");
distrib <- model@fit$params$cond.dist;
xi <- switch(1 + as.numeric(any(isSkewed)), 0, coef[["skew"]]);
nu <- switch(1 + as.numeric(any(isShaped)), 0, coef[["shape"]]);
mu <- switch(1 + as.numeric(any(isMeaned)), 0, coef[["mu"]]);
#quantiles <- switch(distrib, norm = qnorm(probabilities, mean = mu, sd = sd), snorm = qsnorm(probabilities, xi = xi, mean = mu, sd = sd),
# ged = qged(probabilities, nu = nu, mean = mu, sd = sd), sged = qsged(probabilities, nu = nu, xi = xi, mean = mu, sd = sd),
# std = qstd(probabilities, nu = nu, mean = mu, sd = sd), sstd = qsged(probabilities, nu = nu, xi = xi, mean = mu, sd = sd));
empiricalQuantiles <- GetEmpiricalQuantiles(probabilities, distrib, mean = mu, xi = xi, nu = nu, sd = sd);
GetGARCHQuantileValues <- list(quantiles = empiricalQuantiles, distrib = distrib, distribParams = c(xi, nu, mu));
return(GetGARCHQuantileValues);
}
GetEmpiricalQuantiles
GetEmpiricalQuantiles <- function(probabilities, distrib, mean = 0, sd = 1, xi, nu, count = 1000000)
{
sampleGeneration <- switch(distrib, norm = rnorm(count, mean = mean, sd = sd),
snorm = rsnorm(count, mean = mean, sd = sd, xi = xi),
ged = rged(count, mean = mean, sd = sd, nu = nu),
sged = rsged(count, mean = mean, sd = sd, xi = xi, nu = nu),
std = rged(count, mean = mean, sd = sd, nu = nu),
sstd = rsged(count, mean = mean, sd = sd, xi = xi, nu = nu));
sampleQuantiles <- quantileSE(sampleGeneration, p = probabilities, na.rm = TRUE, names = FALSE);
return (sampleQuantiles["quantile",]);
}
GetGARCHFormula
GetGARCHFormula <- function(armaOrder, garchOrder)
{
garchFormulaString <- "~ ";
garchFormulaString <- paste(garchFormulaString, "arma(", armaOrder[1], ", ", armaOrder[2], ") + ", sep = "");
garchFormulaString <- paste(garchFormulaString, "garch(", garchOrder[1], ", ", garchOrder[2], ")", sep = "");
garchFormula <- as.formula(garchFormulaString);
return(garchFormula);
}
检查名
CheckName <- function(inputList, name)
{
listNames <- names(inputList);
result <- any(sapply(1:length(listNames), function(i) { name == listNames[i]; }));
return (result);
}
因此，例如，一个模拟结果：
> result$bestModel
Title:
GARCH Modelling
Call:
garchFit(formula = garchFormula, data = data, cond.dist = bestModel@fit$params$cond.dist,
include.mean = includeMean, leverage = includeLeverage, trace = FALSE)
Mean and Variance Equation:
data ~ arma(5, 5) + garch(2, 0)
<environment: 0x00000000082bf868>
[data = data]
Conditional Distribution:
ged
Coefficient(s):
mu ar1 ar2 ar3 ar4 ar5 ma1 ma2 ma3 ma4 ma5 omega alpha1 alpha2 shape
5.2245e-04 7.6557e-01 -3.0486e-01 3.6348e-01 2.4784e-01 -7.1259e-01 -9.3906e-01 4.5539e-01 -7.4762e-01 -1.5968e-01 9.8356e-01 4.7787e-06 2.8803e-01 1.0000e-08 2.6449e+00
Std. Errors:
based on Hessian
Error Analysis:
Estimate Std. Error t value Pr(>|t|)
mu 5.225e-04 1.218e-07 4288.015 < 2e-16 ***
ar1 7.656e-01 2.913e-05 26285.263 < 2e-16 ***
ar2 -3.049e-01 2.918e-05 -10447.691 < 2e-16 ***
ar3 3.635e-01 2.915e-05 12471.080 < 2e-16 ***
ar4 2.478e-01 2.902e-05 8541.232 < 2e-16 ***
ar5 -7.126e-01 2.878e-05 -24762.254 < 2e-16 ***
ma1 -9.391e-01 2.839e-05 -33074.580 < 2e-16 ***
ma2 4.554e-01 2.781e-05 16377.493 < 2e-16 ***
ma3 -7.476e-01 2.693e-05 -27764.536 < 2e-16 ***
ma4 -1.597e-01 2.561e-05 -6235.408 < 2e-16 ***
ma5 9.836e-01 2.359e-05 41695.273 < 2e-16 ***
omega 4.779e-06 NA NA NA
alpha1 2.880e-01 9.373e-02 3.073 0.00212 **
alpha2 1.000e-08 5.983e-02 0.000 1.00000
shape 2.645e+00 6.135e-02 43.115 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log Likelihood:
913.7433 normalized: 4.568717
我无法理解它是如何可能的？这个问题可以保存我尝试的所有型号。高斯噪声，ARMA-GARCH模型，纯GARCH模型等
有什么问题？它是在主算法还是代码实现中？
谢谢。