Lecture-on time series analysis

Lecture-on time series analysis - 1 Fast Calculations of...

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Unformatted text preview: 1 Fast Calculations of Simple Primitives in Time Series Dennis Shasha Department of Computer Science Courant Institute of Mathematical Sciences New York university Joint work with Richard Cole, Xiaojian Zhao (correlation), Zhihua Wang (humming), Yunyue Zhu (both), and Tyler Neylon (svds, trajectories) 2 Roadmap Section 1 : Motivation Section 2 : Statstream: A Fast Sliding Window based Correction Detector Problem Statement Cooperative and Uncooperative Time Series Algorithmic Framework DFT based Scheme and Random Projection Combinatorial Design and Bootstrapping Empirical Study Section 3 : Elastic Burst Detection Problem Statement Challenge Shifted Binary Tree Astrophysical Application 3 Overall Motivation Financial time series streams are watched closely by millions of traders. What exactly do they look for and how can we help them do it faster? Typical query:“W hich pairs of stocks had highly correlated returns over hich pairs of stocks had highly correlated returns over the last three hours the last three hours ?” Physicists study the time series emerging from their sensors. Typical query:“ Do there exist bursts of gamma rays in windows of any size Do there exist bursts of gamma rays in windows of any size from 8 milliseconds to 4 hours from 8 milliseconds to 4 hours ?” Musicians produce time series. Typical query: “Even though I can’t hum well, please find this song. I want the CD.” 4 Why Speed Is Important As processors speed up, algorithmic efficiency no longer matters … one might think. True if problem sizes stay same but they don’t. As processors speed up, sensors improve --satellites spewing out a terabyte a day, magnetic resonance imagers give higher resolution images, etc. Desire for real time response to queries. /86 5 Surprise, surprise More data, real-time response, increasing importance of correlation IMPLIES Efficient algorithms and data management more important than ever! /86 6 Section 2: Statstream: A Fast Sliding Window based Correction Detector 7 Scenario Stock prices streams The New York Stock Exchange (NYSE) 50,000 securities (streams); 100,000 ticks (trade and quote) Pairs Trading, a.k.a. Correlation Trading Query:“which pairs of stocks were correlated with a value of over 0.9 for the last three hours?” XYZ and ABC have been correlated with a correlation of 0.95 for the last three hours. Now XYZ and ABC become less correlated as XYZ goes up and ABC goes down. They should converge back later. I will sell XYZ and buy ABC … 8 Motivation: Online Detection of High Correlation Correlated!...
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Lecture-on time series analysis - 1 Fast Calculations of...

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