Estimation of the Long-Range Dependence Parameter in Processes with Stationary Increments

This study investigates long-range dependence, or long memory, focusing on its relevance in spatial and temporal data analysis. Processes with long-range dependence have correlations that decay slower than exponentially, which is important in fields like economics and hydrology. The parameter d quantifies the persistence: d <= 0 indicates short-range dependence, 0 < d < 0.5 indicates long-range dependence, and d >= 0.5 indicates non-stationarity. Accurate estimation of d is crucial for characterizing temporal dynamics in data.

Our research focuses on estimating d within a time series with stationary increments. We use a regression technique proposed by Geweke and Porter-Hudak (1983), enhanced by the spectral density estimation method by Chen et al. (2024). Simulations demonstrate the robustness and precision of the modified GPH method in quantifying d across stationary increments without transforming the data to stationarity.

In practical applications, we apply the modified GPH method to Consumer Price Index (CPI) data, using Cressie's graphical method to determine the order of stationary increments. Exponential Smoothing effectively captures persistent correlations, making it suitable for CPI forecasting, where long-term trends are crucial for accurate predictions.

Time series

Long-range dependence

Geweke and Porter-Hudak (GPH) method

Stationary increments

Spectral density estimation 

Mid-Level

Knowledge

Women in Statistics and Data Science 2024