Taylor Effect: It is by now well established in the financial econometrics literature that high frequency time series of financial returns are often uncorrelated but not independent because there are non-linear transformations which are positively correlated. In 1986 Taylor observed that the empirical sample autocorrelations of absolute returns, |r|, are usually larger than those of squared returns, |r|^2. A similar phenomena is observed by Ding et al. (1993) who examined daily returns of the S&P 500 index and conclude that, for this particular series, the autocorrelations of absolute returns raised to the power of θ are maximized when θ is around 1, that is, the largest autocorrelations are found in the absolute returns. Granger and Ding (1995) denote this empirical property of financial returns as Taylor Effect. Therefore, if r_t, t = 1,...T, is the series of returns and ρ_θ(k) denotes the sample autocorrelation of order k of |r_t|^θ, θ > 0, the Taylor effect can be defined as follows:

ρ₁(k) > ρ_θ(k) for any θ ≠ 1.

However, Granger and Ding (1994, 1996) analyze several series of daily exchange rates and individual stock prices, and conclude that the maximum autocorrelation is not always obtained when θ = 1 but for smaller values of θ. Nevertheless, they point out that the autocorrelations of absolute returns are always larger than the autocorrelations of squares. [1] This can also be observed when looking at USDCHF High Frequency FX rates (1996-04-01 00:00:00 to 2001-03-30 23:30:00; 62,496 observations):

teffectPlot, k = 1,...,10:

Scaling Law: Some financial time series show a selfsimilar behavior under temporal aggregation. The 'empirical scaling law' relates the average of the unconditional volatility, measured as the absolute value of the return, r(t_i), over a time interval to the size of the time interval:

where the drift exponent 1/E is an estimated constant that Müller et al. (1990) find to be similar across different currencies and ΔT is a time constant that depends on the currency [2]. The Wiener process, a continuous Gaussian random walk, exhibits a scaling law with a drift exponent of 0.5 (slope of green line). The estimated drift component for the USDCHF series is 0.52, which is actually not statistically different from 0.5:

For more information see Fractals and Intrinsic Time - A Challenge to Econometricians.

Here is the official Rmetrics site.

[1]: see Stochastic Volatility Models and the Taylor Effect, Alberto Mora-Galán and Ana Pérez and Esther Ruiz
[2] see The Impact of News on Foreign Exchange Rates: Evidence from High Frequency Data, Dirk Eddelbuettel and Thomas H. McCurdy