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Stylized Facts

SEWELL, Martin, 2011. Characterization of financial time series. Research Note RN/11/01, University College London, London.

What are stylized facts?

A stylized fact is a term used in economics to refer to empirical findings that are so consistent (for example, across a wide range of instruments, markets and time periods) that they are accepted as truth. Due to their generality, they are often qualitative.
Sewell (2006)

"In social sciences, especially economics, a stylized fact is a simplified presentation of an empirical finding. While results in statistics can only be shown to be highly probable, in a stylized fact, they are presented as true. They are a means to represent complicated statistical findings in an easy way. A stylized fact is often a broad generalisation, which although essentially true may have inaccuracies in the detail."
Wikipedia (2006)

"Definition: Stylized facts are observations that have been made in so many contexts that they are widely understood to be empirical truths, to which theories must fit. Used especially in macroeconomic theory. Considered unhelpful in economic history where context is central. " (2006)

"Nevertheless, the result of more than half a century of empirical studies on financial time series indicates that this is the case if one examines their properties from a statistical point of view: the seemingly random variations of asset prices do share some quite nontrivial statistical properties. Such properties, common across a wide range of instruments, markets and time periods are called stylized empirical facts.
Stylized facts are thus obtained by taking a common denominator among the properties observed in studies of different markets and instruments. Obviously by doing so one gains in generality but tends to lose in precision of the statements one can make about asset returns. Indeed, stylized facts are usually formulated in terms of qualitative properties of asset returns and may not be precise enough to distinguish among different parametric models. Nevertheless, we will see that, albeit qualitative, these stylized facts are so constraining that it is not easy to exhibit even an (ad hoc) stochastic process which possesses the same set of properties and one has to go to great lengths to reproduce them with a model."
Cont (2001)

"An important part of the research is the analysis of financial data [1-3], which has led to the characterization of some empirical statistical regularities, known as “stylized facts”."
Challet, Marsili and Zhang (2001)

[daily returns] "General properties that are expected to be present in any set of returns are called stylized facts."
Taylor (2005), page 51

"The one common observation across these dimensions is that “market activity” is strongly correlated with price variability. Trading volume, return volatility, and bid-ask spreads are highest around the open and close of trading; return variability per unit of time is higher over trading than nontrading periods; trading volume and spreads are particularly high on days with large return innovations; and public information releases—which theoretically may induce price jumps without any trading—are typically associated with extrememely heavy volume."
Andersen and Bollerslev (1998)

[The predictability of asset returns: recent empirical evidence] "However, we would be remiss if we did not cite the rich empirical tradition on which the recent literature is built, which includes: Alexander (1961, 1964), Cootner (1964), Cowles (1960), Cowles and Jones (1937), Fama (1965), Fama and Blume (1966) Kendall (1953), Granger and Morgenstern (1963), Mandelbrot (1963), Osborne (1959, 1962), Roberts (1959), and Working (1960). Campbell, Lo and MacKinlay (1997)











Relationships between stylized facts

Cont (2001) is good
Guillaume, et al. (1997) is good for FX