TY - JOUR
T1 - A Hypothesis Test Method for Detecting Multifractal Scaling, Applied to Bitcoin Prices
AU - Jiang, Chuxuan
AU - Dev, Priya
AU - Maller, Ross
PY - 2020
Y1 - 2020
N2 - Multifractal processes reproduce some of the stylised features observed in financial time
series, namely heavy tails found in asset returns distributions, and long-memory found in volatility.
Multifractal scaling cannot be assumed, it should be established; however, this is not a straightforward
task, particularly in the presence of heavy tails. We develop an empirical hypothesis test to identify
whether a time series is likely to exhibit multifractal scaling in the presence of heavy tails. The test is
constructed by comparing estimated scaling functions of financial time series to simulated scaling
functions of both an iid Student t-distributed process and a Brownian Motion in Multifractal
Time (BMMT), a multifractal processes constructed in Mandelbrot et al. (1997). Concavity measures
of the respective scaling functions are estimated, and it is observed that the concavity measures form
different distributions which allow us to construct a hypothesis test. We apply this method to test for
multifractal scaling across several financial time series including Bitcoin. We observe that multifractal
scaling cannot be ruled out for Bitcoin or the Nasdaq Composite Index, both technology driven assets.
AB - Multifractal processes reproduce some of the stylised features observed in financial time
series, namely heavy tails found in asset returns distributions, and long-memory found in volatility.
Multifractal scaling cannot be assumed, it should be established; however, this is not a straightforward
task, particularly in the presence of heavy tails. We develop an empirical hypothesis test to identify
whether a time series is likely to exhibit multifractal scaling in the presence of heavy tails. The test is
constructed by comparing estimated scaling functions of financial time series to simulated scaling
functions of both an iid Student t-distributed process and a Brownian Motion in Multifractal
Time (BMMT), a multifractal processes constructed in Mandelbrot et al. (1997). Concavity measures
of the respective scaling functions are estimated, and it is observed that the concavity measures form
different distributions which allow us to construct a hypothesis test. We apply this method to test for
multifractal scaling across several financial time series including Bitcoin. We observe that multifractal
scaling cannot be ruled out for Bitcoin or the Nasdaq Composite Index, both technology driven assets.
U2 - 10.3390/jrfm13050104
DO - 10.3390/jrfm13050104
M3 - Article
VL - 13
SP - -
JO - Journal of Risk and Financial Management
JF - Journal of Risk and Financial Management
IS - 5
ER -