Academic literature on the topic 'Seasonal-Trend decomposition using Loess (STL)'

Time series (TS) data is ubiquitous in various fields such as finance, economics, meteorology, and engineering. The analysis of TS data aims to understand the underlying patterns, make predictions, and inform decision-making. One of the fundamental techniques in TS analysis is decomposition, which breaks down a TS into its constituent components: trend, seasonality, and residuals. This chapter provides a comprehensive overview of TS decomposition, breaking down data into trend, seasonality, and residuals. It covers classical methods, such as additive and multiplicative models, advanced techniques like X-12-ARIMA and Seasonal-Trend decomposition using LOESS (STL), and recent approaches, including machine learning (ML) based decompositions. Practical applications in agriculture, meteorology, and economics, along with challenges like non-stationarity and nonlinear behavior, are discussed. The chapter offers guidelines for selecting appropriate methods and includes case studies for real-world insights. It is a valuable resource for researchers, data scientists, and professionals analyzing complex TS data.

<em>Abstract.</em> —The spatial and seasonal distribution of humpback whales in the Great Barrier Reef Marine Park (GBRMP) was defined using data from a systematic aerial surveillance program. The data comprised 414 pod sightings (812 individuals) recorded from July 1982 to March 1996. These sightings were supposedly of humpbacks from the east Australian Group V substock that migrates during the austral autumn from Antarctic feeding grounds to winter breeding grounds in GBR waters. Humpbacks were sighted in all months and throughout the GBRMP. However, most pods (75%) were sighted in southern GBR waters (below 19°S) and mainly during winter and spring ( July to September). Occasional sightings of humpbacks in northern GBR waters (above 16°S) in summer supports previous claims of a substock resident year-round in northern Australian tropical waters. Mother–calf sightings were rare with most recorded below 21°S and mainly in August and September. These limited sightings suggest that the main calving grounds for the east Australian Group V substock occur in the extensive southern GBR lagoonal waters defined northward by the Whitsunday Group of islands and reefs and eastward by the Pompey/Swains reef complex. An estimate of the crude birth rate was 0.072 (95% confidence interval [CI]: 0.06–0.11) with Monte Carlo estimates of the median calving rate at 0.3 calves per mature female per year (95% CI: 0.22–0.43) and the median interbirth interval at 3.4 years (95% CI: 2.3–4.5) indicating low and variable juvenile recruitment. Nonparametric time series analysis (seasonal and trend decomposition using loess, STL) of monthly humpback sightings showed that the long-term trend in sightings was increasing but that there was significant inter-annual variability in the seasonal abundance of humpbacks in the GBRMP. The STL analysis also suggested that the frequency of sightings increased earlier in winter (June) and later in the season during spring/summer (October to December). Time series regression analysis of the STL-derived trend in sightings suggested that the east Australian Group V substock increased slowly in abundance over the 14 years from 1982 to 1996 at about 3.9% per year (95% CI: 1.9% to 5.7%)—a finding consistent with an estimate of low and variable juvenile recruitment.

This study seeks to identify the most effective forecasting period and methods for predicting demand in an Accident & Emergency (A&E) department at a mid-sized hospital in England. Utilizing the National Hospital Episode Statistics (HES) dataset, that covers a 36-month period from February 2010 to January 2013, the research evaluates four commonly used forecasting methods: Autoregressive Integrated Moving Average (ARIMA), exponential smoothing, stepwise linear regression (SLR), and Seasonal and Trend decomposition using Loess (STLF). Forecast accuracy is assessed using the Mean Absolute Scaled Error (MASE). The MASE values for the best forecasting methods across different periods were 0.7834 for daily, 0.9354 for weekly, and 0.5259 for monthly estimates. The study found that the SLR model was the most effective predictive method, with monthly estimation emerging as the optimal period. Contrary to past studies that favoured daily estimates, this research indicated that daily A&E demand forecasts might not be the most accurate.