R语言时间序列 滚动窗口预测

Question

给定时间序列csv文件data1：https://pan.baidu.com/s/1NE2Hm17Knid4uaBBkEjw8g
提取码：us7d
因变量y为文件中的VIX，独立变量x的第一列和第二列为截点项和VIX滞后(x_0=0)，进行提前一步的滚动窗口练习。
需要将窗口长度设置为3000，并对下一个期间y_t+1进行预测；从头开始，一直滚到最后；对于每次滚动，使用lasso和ridge进行预测，λ=1。
请问一下这个问题应该怎么解决？

Answer 1

下面是一个可能的 R 代码实现：

# Load required libraries
library(glmnet)

# Load data
data <- read.csv("file.csv")

# Define parameters
window_size <- 3000
lambda <- 1

# Split data into X and y
y <- data$VIX
X <- data.frame(Intercept = rep(1, length(y)), Lag = c(0, head(y, -1)))

# Loop through the data using a rolling window
for (i in 1:(length(y) - window_size)) {
  y_train <- y[i:(i + window_size - 1)]
  X_train <- X[i:(i + window_size - 1), ]
  
  # Fit Lasso and Ridge models
  fit_lasso <- glmnet(as.matrix(X_train), y_train, alpha = 1, lambda = lambda)
  fit_ridge <- glmnet(as.matrix(X_train), y_train, alpha = 0, lambda = lambda)
  
  # Predict next step
  y_lasso_pred <- predict(fit_lasso, newx = as.matrix(X[i + window_size, ]))
  y_ridge_pred <- predict(fit_ridge, newx = as.matrix(X[i + window_size, ]))
  
  # Do something with the predictions (e.g. store them, compare them, etc.)
}

对于每次滚动，您可以存储 Lasso 和 Ridge 模型的预测结果，然后可以使用这些预测结果进行评估。具体而言，您可以计算预测值与实际值的误差，并计算误差的平均值、方差、中位数等。此外，您还可以使用图形和散点图来可视化预测结果。

例如，下面是存储预测结果和评估预测误差的代码示例：

# Load required libraries
library(glmnet)
library(ggplot2)

# Load data
data <- read.csv("file.csv")

# Define parameters
window_size <- 3000
lambda <- 1

# Split data into X and y
y <- data$VIX
X <- data.frame(Intercept = rep(1, length(y)), Lag = c(0, head(y, -1)))

# Initialize vectors to store predictions
y_lasso_preds <- numeric(length(y) - window_size)
y_ridge_preds <- numeric(length(y) - window_size)

# Loop through the data using a rolling window
for (i in 1:(length(y) - window_size)) {
  y_train <- y[i:(i + window_size - 1)]
  X_train <- X[i:(i + window_size - 1), ]
  
  # Fit Lasso and Ridge models
  fit_lasso <- glmnet(as.matrix(X_train), y_train, alpha = 1, lambda = lambda)
  fit_ridge <- glmnet(as.matrix(X_train), y_train, alpha = 0, lambda = lambda)
  
  # Predict next step
  y_lasso_preds[i] <- predict(fit_lasso, newx = as.matrix(X[i + window_size, ]))
  y_ridge_preds[i] <- predict(fit_ridge, newx = as.matrix(X[i + window_size, ]))
}

# Calculate prediction errors
errors_lasso <- y[(window_size + 1):length(y)] - y_lasso_preds
errors_ridge <- y[(window_size + 1):length(y)] - y_ridge_preds

# Plot prediction errors
ggplot(data.frame(error = errors_lasso, model = "Lasso"), aes(x = error)) + 
  geom_histogram

以及

ggplot(data.frame(error = errors_ridge, model = "Ridge"), aes(x = error)) + 
  geom_histogram + 
  ggtitle("Histogram of Prediction Errors") + 
  xlab("Error") + 
  ylab("Frequency") + 
  facet_wrap(~ model)

您可以使用上面的代码示例作为起点，并根据您的需求进行修改。