Time series analysis

Acycle: Acycle是一个用于研究和教育的时间序列分析软件，提供强大的分析工具和用户友好的界面，适合学术研究和教学使用。

This Chaos Time Series Toolbox includes a variety of MATLAB programs for analyzing chaotic time series. The toolbox features methods for calculating delay time, embedding dimension, and various prediction techniques. The provided code is fully functional and ready to run, ensuring an effective and reliable approach to chaotic data analysis.

This MATLAB code imports time-series data related to riverbank and water depth coordinates in XY format, sampled every 10 minutes. The code calculates the cross-sectional area for each water depth and writes the following data to an Excel file: Date/Time, Water Depth, and the cross-sectional area for each water depth.

Time Series Database (TSDB) is a database system specifically designed for efficiently storing, managing, and processing time series data. This type of data typically involves numerical values associated with specific timestamps, commonly found in monitoring, IoT, financial transactions, and operational analytics. This article explores several key NoSQL time series databases, including InfluxDB, ScyllaDB, CrateDB, and Riak TS, as well as Apache Druid, highlighting their characteristics and application scenarios. 1. InfluxDB InfluxDB, developed by InfluxData, is an open-source time series database designed for real-time analysis and big data. It features high write performance and low-latency query capabilities, supporting complex time series data queries. InfluxDB is particularly suited for handling data from sensors, logs, metrics, and is widely used in monitoring systems, IoT applications, and real-time analysis scenarios. 2. ScyllaDB ScyllaDB is a high-performance distributed database based on Apache Cassandra. It offers higher throughput and lower latency than native Cassandra. Its optimized time series data processing capabilities make it ideal for real-time applications such as monitoring and log analysis. ScyllaDB supports multi-data center deployments to ensure high availability and consistency of data. 3. CrateDB CrateDB is a column-oriented distributed SQL database that can handle large-scale time series data. It provides a SQL interface, making time series data operations more familiar to traditional database users. CrateDB is suitable for projects that require rapid analysis of large amounts of time series data and prefer using SQL for querying. 4. Riak TS Developed by Basho Technologies, Riak TS is a NoSQL solution focused on time series data. It inherits the core features of Riak, such as high availability and scalability. Riak TS is suitable for applications that need to store and retrieve time series data in a distributed environment, such as recording equipment status in the telecommunications or energy industries. 5. Apache Druid Although Druid is not a traditional NoSQL database, it is a columnar data store designed for real-time analytics. Druid is renowned for its excellent Online Analytical Processing (OLAP) performance and low-latency query capabilities, making it suitable for big data real-time analysis and business intelligence applications. These databases each have their strengths. InfluxDB and Druid excel in real-time analytics, ScyllaDB and CrateDB offer powerful distributed processing capabilities, while Riak TS specializes in distributed storage and retrieval. Developers should consider data scale, performance requirements, query complexity, SQL support, and team expertise when choosing a solution.

该代码有助于填补时间序列数据中的空白。为此，它需要一个缺少日期和时间的 DateTime 数组以及具有相应缺失值的 测量数组。它将检查日期数组中缺少的日期，并为测量数组中的相应日期填充 NaN，这将有助于获取连续的时间序列数据。

Periods是一个函数，其目的是找到时间序列数据的主要谐波分量。该函数获取时间序列中主要谐波分量的周期、幅度和滞后相位。它基于循环下降的周期性回归方法，包括统计显著性检验。上述功能非常易于使用，并不需要用户完全理解时间序列理论或大量输入，但足够灵活以承担更复杂的任务，例如预测。此外，根据先前的知识，可以轻松地包括或排除特定时期。González-Rodríguez, E.等人提供了有关如何使用该功能的参考资料和更详细的信息；（2015）时间序列中周期的提取和建模的计算方法。开放统计杂志，5, 604-617。http://dx.doi.org/10.4236/ojs.2015.56062。Periods在MATLAB 2013a版本及后续版本上进行了测试。任何问题/意见都可以通过电子邮件发送至egonzale@cice

给定时间序列，该算法生成随机变体，其中原始值都被保留（但它们的位置是随机的），但逐点Holder结构是固定的。这对于各种形式的假设检验很有用。参考文献：Keylock, CJ 2017. 保留逐点的多重分形代理数据生成算法Hölder规律结构，初步应用于湍流，Physical Review E 95, 032123，https://doi.org/10.1103/PhysRevE.95.032123。

在本论文中，我们将时间序列数据挖掘的方法应用到中日证券市场的比较问题中，并在聚类分析中定义新的函数以判别最优的分类数。我们发现：在指数收盘价时间序列比较方面，中日两个证券市场的确存在一定的相似性，但中国市场的短期波动要大于日本市场。因此，如果将日本证券市场的发展历史作为中国证券市场的事件库，不足以描述和预测中国证券市场的走势。同时，在中国证券市场上，深证成指比上证综指的短期波动幅度更大，具有更多的高频噪声。

信号与系统：时域频域分析及MATLAB软件的应用 在信号与系统的研究中，时域和频域分析是两种基本的分析方法。时域分析关注信号随时间变化的特性，而频域分析则分析信号在不同频率上的分布。MATLAB软件作为一种强大的计算工具，可以有效地实现时域和频域分析，提供丰富的函数库来处理各种信号和系统。 时域分析 时域分析通常通过图形表示信号随时间的变化。例如，正弦波、方波等信号可以通过MATLAB的内置函数绘制。时域分析对于理解信号的瞬时特性、周期性等非常重要。 频域分析 频域分析则通过傅里叶变换等技术将信号从时域转换到频域，揭示信号在不同频率上的组成成分。MATLAB提供了FFT（快速傅里叶变换）等函数，可以快速进行频域分析，帮助研究人员理解信号的频谱特性。 MATLAB的应用 在MATLAB中，信号与系统的分析方法可以通过编程实现，包括滤波器设计、系统响应分析等。MATLAB不仅能够处理简单的时频分析任务，还支持复杂的信号处理和系统建模。 通过结合时域和频域分析，结合MATLAB软件的强大功能，用户可以深入理解信号与系统的行为，并设计出高效的信号处理方案。

Independent Component Analysis (ICA) stands as a pivotal advancement across diverse fields such as neural networks, advanced statistics, and signal processing. This resource furnishes a thorough introduction to ICA, encompassing the foundational mathematical principles, critical solutions, algorithms, and comprehensive exploration of novel applications in domains like image processing, telecommunications, and audio signal processing. The text meticulously dissects ICA into four core segments:* Fundamental Mathematical Concepts: This section lays the groundwork for understanding the mathematical underpinnings of ICA.* The Basic ICA Model and Solution: A detailed examination of the core ICA model and its associated solution strategies.* Extensions of the Basic ICA Model: Exploration of various extensions to the fundamental ICA model, enhancing its adaptability and applicability.* Real-World Applications of ICA Models: Delving into practical implementations of ICA models across diverse disciplines. The authors, renowned for their contributions to ICA development, provide a comprehensive treatise on relevant theories, cutting-edge algorithms, and real-world implementations, making this an indispensable resource for students and practitioners alike.