Dưới đây là một cuộc điều tra tỉ lệ hay kiên trì dài hạn (LTP) trong chuỗi thời gian bao gồm lượng mưa, nhiệt độ và vòng proxy cây. Việc công nhận, định lượng và tác động đối với phân tích được rút ra chủ yếu từ Koutsoyiannis Kou02]. Chúng được đặc trưng bằng nhiều cách, có bộ nhớ lâu dài, tự giống nhau trong phân phối, 'dài' hoặc 'béo' đuôi trong việc phân phối hoặc các tài sản khác. Có những khác biệt quan trọng để thực hiện giữa kiên trì ngắn hạn (STP), và các hiện tượng LTP | Chapter 10 Long term persistence Below is an investigation of scaling or long term persistence LTP in time series including temperature precipitation and tree-ring proxies. The recognition quantification and implications for analysis are drawn largely from Koutsoyiannis Kou02 . They are characterized in many ways as having long memory self similarity in distribution long or fat tails in the distribution or other properties. There are important distinctions to make between short term persistence STP and LTP phenomena. STP occurs for example in Markov or AR 1 process where each value depends only on the previous step. As shown previously the autocorrelations in an STP series decay much more rapidly than LTP. In addition LTP are related to a number of properties that are interesting in themselves. These properties may not all be present in a particular situation and definitions of LTP also vary between authors. Some of the properties are KMF04 Defn. I Persistent autocorrelation at long lags Where p k is the autocorrelation function ACF with lag k then a series Xt is LTP if there is a real number a E 0 1 and a constant cp 0 such that limt_ p fc 1 llmfc r L a J- Cp rv In other words the definition states that the ACF decays to zero with a hyperbolic rate of approximately k a. In contrast the ACF of a STP process decays exponentially. Defn. II Infinite ACF sum As a consequence of the hyperbolic rate of decay the ACF of a LTP is usually non-summable Efc p k Defn. III High standard errors for large samples The standard error or variances of the sample mean of a LTP process decay more slowly than the reciprocal of the sample size. 157 2007 by Taylor and Francis Group LLC 158 Niche Modeling V AR Xm a2m a as m x where a 1 Here m refers to the size of the aggregated process . the sequential sum of m terms of X. Due to this property classical statistical tests are incorrect and confidence intervals underestimated. Defn. IV Infinite power at zero wavelength The spectral .
