Appendix B

Elements of Statistics and Time Series Analysis

Statistics, “that gray area which is not quite a branch of mathematics—and just as surely not quite a branch of science” (Press et al., 2002), is primarily concerned with the description, study, and categorization of observed data sets and with relating these sets to theories regarding the data-generating processes. The statistical method typically consists in stating a hypothesis (e.g., “the correlation between two time series is zero”) and then assessing its plausibility given observations. Statistics can neither prove nor disprove a hypothesis but can, through a statistical significance test, produce a quantitative measure of the likelihood that the hypothesis is true.

A reader requiring the knowledge of statistics, its methods, and its specializations, such as time series analysis, should consult any of the numerous texts available. Here we only present a selection of results relevant to this book.

Asset Volatility

In the context of financial economics asset volatility usually means the standard deviation of this asset's logarithmic returns. Let be a time series of an asset's total return levels (in addition to price changes, they may incorporate the effects of distributions, such as dividends or coupon payments). Then a corresponding time series of logarithmic returns is defined by , .

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