Functional Outlier Time Series Detection

A comprehensive R implementation for detecting outliers in functional time series data using various depth-based and bootstrap methods.

Overview

This repository provides multiple approaches for outlier detection in functional time series, based on and extending methods from the literature, and is the official research code repository for:

A Hybrid Nonparametric Framework for Outlier Detection in Functional Time Series

Available Methods

1. Original Proposal

Bootstrap-based outlier detection methods following Raña et al. (2015):

• SmBoD: Standard smoothed bootstrap on data
• MBBo: Moving block bootstrap (for temporal dependence)
• StBo: Stationary bootstrap

2. Multivariate Process

Multivariate extension using derivative information:

• Uses original process, first derivative, and second derivative
• Combines information across variables with weighted depth

⚠️ Note: May mask magnitude outliers. Use when you expect shape but not magnitude outliers.

3. DirOut Methods

Directional outlyingness-based detection:

• Two-component outlyingness (average and variance)
• Captures both magnitude and shape outliers

4. Sliding Window

Local outlier detection using sliding windows:

• Window-based functional depth and boxplot detection
• Aggregates outlier flags across multiple windows

Quick Start

Installation

# Required packages
library(fda)
library(roahd)
library(fda.usc)
library(mrfDepth)
library(fdaoutlier)  # For DirOut methods

Basic Example

# Source required files
source("R/utils.R")
source("R/depths.R")

# Prepare your functional data
data_matrix <- matrix(rnorm(100*50), nrow = 100, ncol = 50)
fdataobj <- fdata(data_matrix)

# Method 1: Original proposal (MBBo)
source("R/original_proposal/bootstrap-procedures.R")
source("R/original_proposal/outlier-detection-procedures.R")

result <- outlier_bootstrap(
    fdataobj = fdataobj,
    boot = MBBo,
    dfunc = MBD
)

print(result$outliers)

Documentation

Each method has detailed documentation with:

• Complete function signatures and parameter descriptions
• Working code examples
• Parameter tuning guidelines
• Troubleshooting tips

See the README files in each directory:

• R/original_proposal/README.md
• R/multivariate_process/README.md
• R/dirout/README.md
• R/sliding_window/README.md

Repository Structure

R/
├── original_proposal/     # Original bootstrap methods
├── multivariate_process/  # Multivariate extension with derivatives
├── dirout/                # Directional outlyingness methods
├── sliding_window/        # Sliding window approach
├── real_data/            # Real data examples
├── depths.R              # Depth function implementations
├── utils.R               # Utility functions
└── simulated-models.R    # Simulation models for testing

Reference

If you use this code, please cite:

A Hybrid Nonparametric Framework for Outlier Detection in Functional Time Series
CC BY-NC-ND 4.0

https://onlinelibrary.wiley.com/doi/10.1002/env.70099