Are Hurst exponents estimated from short or irregular time series meaningful?

We show that several time series analysis methods that are often used for detecting self-affine fractal scaling and determining Hurst exponents in data sets may lead to spurious results when applied to short discretized data series. We show that irregularities in the series, such as jumps or spikes (as are often found in geophysical data) may lead to spurious scaling and consequently to an incorrect determination of the Hurst exponent. We also illustrate the statistical error in measuring Hurst exponent in series where self-affine fractal scaling does exist. Users should be aware of these caveats when interpreting the results of short time series analysis.