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Time series factor models

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Abstract In today's data‐driven age observing a large number of variables over time for purposes of understanding the dynamics of a system is commonplace. The number of variables grows as our ability to measure, store, and retrieve data grows. Time series factor models and dynamic factor models combine data reduction and time series forecasting strategies to extract the critical information useful in forecasting a singular or small number of series from a large number of explanatory variables. Since the 1990s, these methodologies have proven a useful analytical tool in many areas of applied statistics, but most notably econometrics and finance. Furthermore, recent results in random matrix theory, which examines dimension reduction strategies as the number of variables and observations both go to infinity, have direct applicability in the area of time series factor models. This article reviews the recent history of time series factor models and demonstrates the applicability of these tools, while providing some cautionary issues through an example in the equities market. WIREs Comput Stat 2013, 5:97–104. doi: 10.1002/wics.1245 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

Daily quantiles of the 140 return series from the NYSE rescaled by a rolling robust estimate of scale. Series included were continually traded during the time window. The 1st and 99th quantiles are plotted in red, 5th and 95th in black, 25th and 75th in blue, and the median is plotted in green.

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Time series factor model estimate of sector behavior from 2008 through March of 2009 for sector 25 and sector 50 depicted in blue; observed sector means are shown in green. The TSFM is constructed from historical data starting in 1995 and ending in 2007.

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Weights given to each sector in the first two principal components. Dark blue corresponds to the first principal component; light blue the second.

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Correlation across sector means; the red line depicts the loess curve.

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Correlation for each return series and the 20‐factor TSFM estimate computed from the 140 return series. Correlations range between 0.233 and 0.998 and individual series are indicated by their respective ticker symbol.

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Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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