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+# LSTM Time Series Prediction in R
+# Long Short-Term Memory (LSTM) Neural Network for Time Series Forecasting
+#
+# Required libraries: keras, tensorflow, (optional) tidyr or reshape2, ggplot2
+# Install with: install.packages("keras"); install.packages("tensorflow")
+# Optionally: install.packages(c("tidyr","reshape2","ggplot2"))
+# Then run: keras::install_keras()
+
+suppressPackageStartupMessages({
+  library(keras)
+  library(tensorflow)
+})
+
+#' Create sequences for LSTM training
+#' @param data: Numeric vector or matrix of time series data
+#' @param seq_length: Length of input sequences
+#' @return: List containing X (input sequences) and y (target values)
+create_sequences <- function(data, seq_length) {
+  n <- length(data)
+  
+  # Initialize lists to store sequences
+  X <- list()
+  y <- list()
+  
+  # Create sequences
+  for (i in 1:(n - seq_length)) {
+    X[[i]] <- data[i:(i + seq_length - 1)]
+    y[[i]] <- data[i + seq_length]
+  }
+  
+  # Convert lists to arrays
+  X <- array(unlist(X), dim = c(length(X), seq_length, 1))
+  y <- array(unlist(y), dim = c(length(y), 1))
+  
+  return(list(X = X, y = y))
+}
+
+#' Normalize data to [0, 1] range
+#' @param data: Numeric vector
+#' @return: List with normalized data, min, and max values
+normalize_data <- function(data) {
+  min_val <- min(data)
+  max_val <- max(data)
+  normalized <- (data - min_val) / (max_val - min_val)
+  
+  return(list(
+    data = normalized,
+    min = min_val,
+    max = max_val
+  ))
+}
+
+#' Inverse normalize data back to original scale
+#' @param data: Normalized data
+#' @param min_val: Original minimum value
+#' @param max_val: Original maximum value
+#' @return: Data in original scale
+denormalize_data <- function(data, min_val, max_val) {
+  return(data * (max_val - min_val) + min_val)
+}
+
+#' Build LSTM model for time series prediction
+#' @param seq_length: Length of input sequences
+#' @param lstm_units: Number of LSTM units (neurons)
+#' @param dropout_rate: Dropout rate for regularization (0 to 1)
+#' @param learning_rate: Learning rate for optimizer
+#' @return: Compiled Keras model
+build_lstm_model <- function(seq_length, lstm_units = 50, 
+                             dropout_rate = 0.2, learning_rate = 0.001) {
+  
+  model <- keras_model_sequential() %>%
+    layer_lstm(units = lstm_units, 
+               activation = 'tanh',
+               input_shape = c(seq_length, 1),
+               return_sequences = FALSE) %>%
+    layer_dropout(rate = dropout_rate) %>%
+    layer_dense(units = 1)  # Output layer for regression
+  
+  # Compile model
+  model %>% compile(
+    optimizer = optimizer_adam(learning_rate = learning_rate),
+    loss = 'mean_squared_error',
+    metrics = c('mae')
+  )
+  
+  return(model)
+}
+
+#' Calculate evaluation metrics
+#' @param actual: Actual values
+#' @param predicted: Predicted values
+#' @return: List of evaluation metrics
+calculate_metrics <- function(actual, predicted) {
+  mse <- mean((actual - predicted)^2)
+  rmse <- sqrt(mse)
+  mae <- mean(abs(actual - predicted))
+  
+  # R-squared
+  ss_res <- sum((actual - predicted)^2)
+  ss_tot <- sum((actual - mean(actual))^2)
+  r_squared <- 1 - (ss_res / ss_tot)
+  
+  return(list(
+    MSE = mse,
+    RMSE = rmse,
+    MAE = mae,
+    R_squared = r_squared
+  ))
+}
+
+# ========== Main Example: Sine Wave Prediction ==========
+
+cat("========== LSTM Time Series Prediction Example ==========\n\n")
+cat("Generating synthetic sine wave data...\n")
+
+# Set random seed for reproducibility
+set.seed(42)
+tensorflow::tf$random$set_seed(42)
+
+# Generate sine wave data (500 points)
+time_points <- seq(0, 20, length.out = 500)
+data <- sin(time_points)
+
+cat(sprintf("Generated %d data points\n\n", length(data)))
+
+# Normalize data
+cat("Normalizing data to [0, 1] range...\n")
+normalized <- normalize_data(data)
+data_norm <- normalized$data
+
+# Create sequences for LSTM
+seq_length <- 20
+cat(sprintf("Creating sequences with length: %d\n", seq_length))
+sequences <- create_sequences(data_norm, seq_length)
+
+X <- sequences$X
+y <- sequences$y
+
+cat(sprintf("Total sequences created: %d\n\n", dim(X)[1]))
+
+# Split into train and test sets (80-20 split)
+train_size <- floor(0.8 * dim(X)[1])
+
+# IMPORTANT: For time series, use sequential split (preserve temporal order)
+train_indices <- 1:train_size
+test_indices <- (train_size + 1):dim(X)[1]
+
+X_train <- X[train_indices, , , drop = FALSE]
+y_train <- y[train_indices, , drop = FALSE]
+X_test <- X[test_indices, , , drop = FALSE]
+y_test <- y[test_indices, , drop = FALSE]
+
+cat(sprintf("Training samples: %d\n", dim(X_train)[1]))
+cat(sprintf("Test samples: %d\n\n", dim(X_test)[1]))
+
+# Build LSTM model
+cat("Building LSTM model...\n")
+model <- build_lstm_model(
+  seq_length = seq_length,
+  lstm_units = 50,
+  dropout_rate = 0.2,
+  learning_rate = 0.001
+)
+
+cat("\nModel Architecture:\n")
+print(summary(model))
+
+# Train the model
+cat("\n========== Training LSTM Model ==========\n\n")
+
+history <- model %>% fit(
+  X_train, y_train,
+  epochs = 50,
+  batch_size = 16,
+  validation_split = 0.1,
+  verbose = 1
+)
+
+# Plot training history
+if (requireNamespace("ggplot2", quietly = TRUE)) {
+  cat("\nPlotting training history...\n")
+  plot(history)
+}
+
+# Evaluate on test data
+cat("\n========== Model Evaluation ==========\n\n")
+evaluation <- model %>% evaluate(X_test, y_test, verbose = 0)
+cat(sprintf("Test Loss (MSE): %.6f\n", evaluation[[1]]))
+cat(sprintf("Test MAE: %.6f\n\n", evaluation[[2]]))
+
+# Make predictions
+cat("Making predictions on test set...\n")
+y_pred <- model %>% predict(X_test, verbose = 0)
+
+# Denormalize predictions and actual values
+y_test_orig <- denormalize_data(y_test, normalized$min, normalized$max)
+y_pred_orig <- denormalize_data(y_pred, normalized$min, normalized$max)
+
+# Calculate metrics on original scale
+metrics <- calculate_metrics(y_test_orig, y_pred_orig)
+
+cat("\n========== Performance Metrics (Original Scale) ==========\n\n")
+cat(sprintf("Mean Squared Error (MSE): %.6f\n", metrics$MSE))
+cat(sprintf("Root Mean Squared Error (RMSE): %.6f\n", metrics$RMSE))
+cat(sprintf("Mean Absolute Error (MAE): %.6f\n", metrics$MAE))
+cat(sprintf("R-squared: %.6f\n\n", metrics$R_squared))
+
+# Display sample predictions
+cat("========== Sample Predictions ==========\n\n")
+cat(sprintf("%-15s %-15s %-15s\n", "Actual", "Predicted", "Error"))
+cat(strrep("-", 50), "\n")
+
+n_samples <- min(10, length(y_test_orig))
+for (i in 1:n_samples) {
+  error <- abs(y_test_orig[i] - y_pred_orig[i])
+  cat(sprintf("%-15.6f %-15.6f %-15.6f\n", 
+              y_test_orig[i], y_pred_orig[i], error))
+}
+
+# ========== Visualization ==========
+
+if (requireNamespace("ggplot2", quietly = TRUE)) {
+  library(ggplot2)
+  
+  cat("\n========== Creating Prediction Plot ==========\n\n")
+  
+  # Create dataframe for plotting
+  plot_data <- data.frame(
+    Index = 1:length(y_test_orig),
+    Actual = as.vector(y_test_orig),
+    Predicted = as.vector(y_pred_orig)
+  )
+  
+  # Reshape for ggplot: prefer tidyr::pivot_longer if available, fallback to reshape2::melt
+  if (requireNamespace("tidyr", quietly = TRUE)) {
+    plot_data_long <- tidyr::pivot_longer(plot_data, 
+                                          cols = -Index,
+                                          names_to = "variable",
+                                          values_to = "value")
+  } else if (requireNamespace("reshape2", quietly = TRUE)) {
+    plot_data_long <- reshape2::melt(plot_data, id.vars = "Index")
+    # Ensure consistent column names with pivot_longer
+    names(plot_data_long) <- c("Index", "variable", "value")
+  } else {
+    stop("Please install 'tidyr' or 'reshape2' to create the plot (install.packages('tidyr')).")
+  }
+  
+  # Create plot (use linewidth instead of size for modern ggplot2)
+  p <- ggplot(plot_data_long, aes(x = Index, y = value, color = variable)) +
+    geom_line(linewidth = 1) +
+    geom_point(alpha = 0.5) +
+    scale_color_manual(values = c("Actual" = "blue", "Predicted" = "red")) +
+    labs(
+      title = "LSTM Time Series Predictions",
+      subtitle = sprintf("Test Set: %d samples (RMSE: %.4f)", 
+                        length(y_test_orig), metrics$RMSE),
+      x = "Sample Index",
+      y = "Value",
+      color = "Series"
+    ) +
+    theme_minimal() +
+    theme(
+      plot.title = element_text(hjust = 0.5, size = 14, face = "bold"),
+      plot.subtitle = element_text(hjust = 0.5, size = 10),
+      legend.position = "bottom"
+    )
+  
+  print(p)
+  
+  cat("Plot created successfully!\n\n")
+}
+
+# ========== Additional Example: Multi-step Prediction ==========
+
+cat("========== Multi-Step Ahead Prediction ==========\n\n")
+
+#' Make multi-step predictions
+#' @param model: Trained LSTM model
+#' @param initial_seq: Initial sequence to start prediction
+#' @param n_steps: Number of steps to predict ahead
+#' @param min_val: Min value for denormalization
+#' @param max_val: Max value for denormalization
+#' @return: Vector of predictions
+predict_multi_step <- function(model, initial_seq, n_steps, min_val, max_val) {
+  predictions <- numeric(n_steps)
+  current_seq <- initial_seq
+  
+  for (i in 1:n_steps) {
+    # Predict next value
+    pred <- model %>% predict(current_seq, verbose = 0)
+    predictions[i] <- denormalize_data(pred, min_val, max_val)
+    
+    # Update sequence: remove first value, add prediction
+    current_seq <- array(
+      c(current_seq[1, 2:seq_length, 1], pred),
+      dim = c(1, seq_length, 1)
+    )
+  }
+  
+  return(predictions)
+}
+
+# Use first test sequence for multi-step prediction
+initial_sequence <- X_test[1, , , drop = FALSE]
+n_future_steps <- 20
+
+cat(sprintf("Predicting %d steps ahead...\n", n_future_steps))
+future_predictions <- predict_multi_step(
+  model, 
+  initial_sequence, 
+  n_future_steps,
+  normalized$min,
+  normalized$max
+)
+
+cat("\nMulti-step predictions:\n")
+for (i in 1:min(10, n_future_steps)) {
+  cat(sprintf("Step %2d: %.6f\n", i, future_predictions[i]))
+}
+
+# ========== Tips and Best Practices ==========
+
+cat("\n========== LSTM Best Practices ==========\n\n")
+cat("1. Data Preprocessing:\n")
+cat("   - Normalize/standardize input data\n")
+cat("   - Handle missing values appropriately\n")
+cat("   - Consider detrending for non-stationary series\n\n")
+
+cat("2. Model Architecture:\n")
+cat("   - Start with 1-2 LSTM layers\n")
+cat("   - Use dropout for regularization (0.2-0.5)\n")
+cat("   - Consider bidirectional LSTM for complex patterns\n\n")
+
+cat("3. Training:\n")
+cat("   - Use appropriate batch size (16-128)\n")
+cat("   - Monitor validation loss to prevent overfitting\n")
+cat("   - Use early stopping and model checkpointing\n\n")
+
+cat("4. Hyperparameter Tuning:\n")
+cat("   - Sequence length: depends on temporal dependencies\n")
+cat("   - LSTM units: 32-256 typically works well\n")
+cat("   - Learning rate: 0.001-0.01 for Adam optimizer\n\n")
+
+cat("5. Evaluation:\n")
+cat("   - Use walk-forward validation for time series\n")
+cat("   - Check residuals for patterns\n")
+cat("   - Compare with baseline models (ARIMA, simple average)\n\n")
+
+cat("========== Example Complete ==========\n")
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