Introduction With the vast amount of time series data being generated across the globe, from financial markets and cryptocurrencies to climate and environmental sciences, effective modeling has become essential. Time series models play a crucial role in identifying future patterns, forecasting values, and uncovering the factors that influence these dynamic processes. While modern machine learning and deep learning models are increasingly applied in time series analysis, their lack of interpretability often limits their practical use. As a result, classical time series models such as AR, MA, ARIMA, and SARIMA remain widely used due to their transparency and ease of interpretability. However, these traditional models typically fail to capture long-term dependencies in the data, that is, relationships between observations that are far apart in time. This is where long memory time series models become valuable. Among them, Autoregressive Fracti...
Introduction to Spatiotemporal Kriging: A Powerful Tool for Space-Time Data Imputation In many real-world applications, data are collected across both space and time, think of rainfall measurements across a network of weather stations over several months, or air pollution levels recorded hourly at various urban locations. Analyzing such data requires methods that can account for both spatial and temporal dependencies. This is where spatiotemporal kriging comes in, a geostatistical technique designed to interpolate or predict missing values in datasets that vary across space and time. In this article, I will guide you step by step through the process of performing spatio-temporal kriging for imputing missing values. Consider a spatiotemporal process denoted as: { Z ( s , t ) : ( s , t ) ∈ D ⊆ R d × R } Here, s ∈ R d \mathbf{s} \in \mathbb{R}^d , with d = 2 d = 2 , represents the spatial location (typically latitude and longitude), and t ∈ R denotes time. This formulatio...