Advanced Features in WaveQTE

Advanced Wavelet Analysis

Different Wavelet Filters

library(WaveQTE)

# Get data
data <- get_stock_data("AAPL", "2019-01-01", "2023-12-31")

# Compare different wavelet filters
filters <- c("la8", "d4", "c6")
wave_results <- lapply(filters, function(wf) {
  wavelet_decompose(data[,1], wf = wf)
})

# Compare variance decompositions
var_results <- lapply(wave_results, analyze_wavelet_variance)

# Print results
for(i in seq_along(filters)) {
  cat("\nFilter:", filters[i], "\n")
  print(var_results[[i]]$percentage)
}

Bootstrap Analysis

# Perform bootstrap analysis
x <- as.numeric(data[,1])
y <- lag(x, 1)  # Create lagged series

boot_results <- bootstrap_qte(
  x, y,
  tau = 0.5,
  B = 1000,
  block_size = 20
)

# Analyze results
hist(boot_results$boot_samples,
     main = "Bootstrap Distribution of QTE",
     breaks = 50)

cat("95% Confidence Interval:", 
    paste(round(boot_results$ci, 4), collapse = " to "))

Network Analysis Options

Community Detection

# Create network
net <- create_qte_network(data, wave_results, scale = 1)
metrics <- calculate_network_metrics(net)

# Analyze communities
communities <- metrics$communities
print(communities)

# Plot with community structure
plot_enhanced_network(net, scale = 1, tau = 0.5) +
  aes(color = factor(membership(communities)))

Network Dynamics

# Calculate time-varying networks
window_size <- 252
n_windows <- nrow(data) - window_size + 1

network_evolution <- lapply(1:n_windows, function(i) {
  window_data <- data[i:(i+window_size-1),]
  window_wave <- lapply(1:ncol(window_data), function(j) {
    wavelet_decompose(window_data[,j])
  })
  create_qte_network(window_data, window_wave, scale = 1)
})

# Analyze network metrics over time
density_evolution <- sapply(network_evolution, function(net) {
  calculate_network_metrics(net)$density
})

plot(density_evolution, type = "l",
     main = "Network Density Evolution",
     xlab = "Time", ylab = "Density")

Customizing Visualizations

Enhanced Network Plots

# Create custom network visualization
plot_enhanced_network(net, scale = 1, tau = 0.5) +
  theme_minimal() +
  scale_color_brewer(palette = "Set3") +
  ggtitle("Custom Network Visualization") +
  theme(
    plot.title = element_text(hjust = 0.5, size = 14),
    legend.position = "bottom"
  )

Custom Heatmaps

# Calculate QTE matrix
qte_results <- calculate_multiscale_qte(
  wave_results[[1]], 
  wave_results[[2]], 
  tau_levels = seq(0.1, 0.9, by = 0.1)
)

# Create custom heatmap
plot_qte_heatmap(qte_results) +
  scale_fill_viridis_c(option = "magma") +
  theme_minimal() +
  theme(
    axis.text.x = element_text(angle = 45, hjust = 1),
    plot.title = element_text(hjust = 0.5, size = 14)
  )

Advanced Parameter Settings

Optimal Wavelet Level Selection

# Function to evaluate decomposition levels
evaluate_levels <- function(data, max_level = 8) {
  results <- lapply(1:max_level, function(level) {
    wave <- wavelet_decompose(data, n.levels = level)
    var_analysis <- analyze_wavelet_variance(wave)
    list(
      level = level,
      variance = var_analysis$variance,
      percentage = var_analysis$percentage
    )
  })
  
  # Find optimal level based on variance explained
  var_explained <- sapply(results, function(r) {
    sum(unlist(r$percentage[1:length(r$percentage)-1]))
  })
  
  optimal_level <- which.max(diff(var_explained))
  return(list(
    optimal_level = optimal_level,
    var_explained = var_explained
  ))
}

# Apply to data
level_analysis <- evaluate_levels(as.numeric(data[,1]))
cat("Optimal decomposition level:", level_analysis$optimal_level)

Performance Optimization

Parallel Processing

library(parallel)
library(doParallel)

# Setup parallel backend
n_cores <- detectCores() - 1
cl <- makeCluster(n_cores)
registerDoParallel(cl)

# Parallel QTE calculation
parallel_qte <- function(returns, wave_decomp, tau_levels) {
  foreach(tau = tau_levels, .combine = rbind) %dopar% {
    sapply(1:length(wave_decomp[[1]]$details), function(scale) {
      calculate_qte(
        wave_decomp[[1]]$details[[scale]],
        wave_decomp[[2]]$details[[scale]],
        tau = tau
      )
    })
  }
}

# Use parallel implementation
system.time({
  results_parallel <- parallel_qte(
    data,
    wave_results,
    seq(0.1, 0.9, by = 0.1)
  )
})

stopCluster(cl)