lpha <- runif(1)
beta <- runif(1)
while (alpha + beta >= up_limit)
{
alpha <- runif(1)
beta <- runif(1)
}
return(
list(omega = omega, alpha = alpha, beta = beta))
}
train_length <- 3000
val_length <- 1000
test_length <- 1000
train_m1 <- numeric(train_length)
train_m2 <- numeric(train_length)
train_m1_5 <- numeric(train_length)
train_omega <- numeric(train_length)
train_alpha <- numeric(train_length)
train_beta <- numeric(train_length)
val_m1 <- numeric(val_length)
val_m2 <- numeric(val_length)
val_m1_5 <- numeric(val_length)
val_omega <- numeric(val_length)
val_alpha <- numeric(val_length)
val_beta <- numeric(val_length)
test_m1 <- numeric(test_length)
test_m2 <- numeric(test_length)
test_m1_5 <- numeric(test_length)
生成训练数据。
# Train Data ----
for (i in 1:train_length)
{
garch_coef <- GarchCoefGenerator()
garch_sample <- garchSim(
garchSpec(
model = garch_coef),
n.start = 1000, n = 1000)
train_m1[i] <- M1(garch_sample)
train_m2[i] <- M2(garch_sample)
train_m1_5[i] <- M1_5(garch_sample)
train_omega[i] <- garch_coef$omega
train_alpha[i] <- garch_coef$alpha
train_beta[i] <- garch_coef$beta
}
trainX <- data.frame(
m1 = train_m1,
m2 = train_m2,
m1_5 = train_m1_5) %>%
as.matrix()
trainY <- data.frame(
omega = train_omega,
alpha = train_alpha,
beta = train_beta) %>%
as.matrix()
生成验证数据。
# Val Data ----
for (i in 1:val_length)
{
garch_coef <- GarchCoefGenerator()
garch_sample <- garchSim(
garchSpec(
model = garch_coef),
n.start = 1000, n = 1000)
val_m1[i] <- M1(garch_sample)
val_m2[i] <- M2(garch_sample)
val_m1_5[i] <- M1_5(garch_sample)
val_omega[i] <- garch_coef$omega
val_alpha[i] <- garch_coef$alpha
val_beta[i] <- garch_coef$beta
}
valX <- data.frame(
m1 = val_m1,
m2 = val_m2,
m1_5 = val_m1_5) %>%
as.matrix()
valY <- data.frame(
omega = val_omega,
alpha = val_alpha,
beta = val_beta) %>%
as.matrix()
用 keras 构建神经网络。
# Model Training ----
model <- keras_model_sequential()
model %>%
layer_dense(
units = 9,
input_shape = c(3),
activation = 'sigmoid') %>%
layer_dense(
units = 3,
activation = 'sigmoid') %>%
compile(
loss = 'mae',
optimizer = 'adam')
summary(model)
实验采用了结构非常简单的神经网络结构，一个两层的多元感知机，超参数、激活函数和优化方法没有调优。
__________________________________________________________________________
Layer (type) Output Shape Param #
==========================================================================
dense_1 (Dense) (None, 9) 36
__________________________________________________________________________
dense_2 (Dense) (None, 3) 30
==========================================================================
Total params: 66
Trainable params: 66
Non-trainable params: 0
__________________________________________________________________________
训练。
history <- model %>%
fit(
trainX,
trainY,
validation_data = list(
valX, valY),
batch_size = 50,
epochs = 1000)
plot(history)
训练结果非常理想，训练集和验证集上的 loss 基本上同步衰减到 0.11 左右，并且从趋势上看大约已经接近了极限水平。
延续前面两篇博文的主题，将 \(\text{GARCH}(1,1)\) 的模型参数限定为 \((0.2,0.2,0.2)\)，生成测试数据，后面要测试估计值的稳定性，以及是否有偏。
# Test ----
for (i in 1:test_length)
{
garch_coef <- list(
omega = 0.2, alpha = 0.2, beta = 0.2)