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Computational finance: correlation, volatility, and markets

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Financial data by nature are inter‐related and should be analyzed using multivariate methods. Many models exist for the joint analysis of multiple financial instruments. Early models often assumed some type of constant behavior between the instruments over the time period of analysis. But today, time‐varying covariance models are a key component of financial time series analysis leading to a deeper understanding of changing market conditions. Models for covolatility of financial data quickly grow in their complexity and parameters, and 20 years of research offers a variety of solutions to this complexity. After a short introduction of univariate volatility models, this article begins with the basic multivariate formulation for time series covariance modeling and moves to leading time series tools that address this complexity. Coupling these models with regime switching via a Markov process extends the features that can be understood from market behavior. We ground this review in an example of modeling the covariance of securities within sectors and sectors within markets, with dynamics that allow for two different market regimes. Specifically, we simultaneously model individual daily stock data that belong to one of three market sectors and examine the behavior of the market as a whole as well as the behavior of the market sectors over time. A motivation for this characterization concerns portfolio diversification and stock anomalies, and we capture the changing comovement of stocks within and between sectors as market conditions change. For example, some of these market conditions include market crashes or collapses and common external influences. WIREs Comput Stat 2014, 6:326–340. doi: 10.1002/wics.1323 This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Daily stock returns of 63 series spanning three sectors.
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Biplot for covariance matrix of June 2, 2000.
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Biplot for covariance matrix of October 4, 2001.
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One step ahead forecasts for average correlations between sectors. The scale for each plot is 0 to 0.8.
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Daily stock returns of 63 series spanning three sectors. High‐ and low‐correlation regimes are depicted. The estimated regime probabilities, rounded to 1 decimal place, are given at the top of each graph.
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Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
Applications of Computational Statistics > Computational Finance

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