Universal behavior of the interoccurrence times between losses in financial markets: independence of the time resolution.
Universal behavior of the interoccurrence times between losses in financial markets: independence of the time resolution.
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DOI：
10.1103/physreve.90.062809
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发表时间：
2014-11
期刊：
影响因子：
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通讯作者：
J. Ludescher;A. Bunde
中科院分区：
文献类型：
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作者：
J. Ludescher;A. Bunde
我们考虑了在一分钟到一天的时间尺度上的代表性财务记录（股票和指数），以及历史月度数据集，并表明在低于负阈值-Q的损失之间的互现时间r的分布P(Q)(r)可以用相同的Q指数在所有时间尺度上描述，P(Q)(r)∝1/{[1+(Q -1)βr](1/(Q -1))}。我们提出，P(Q)(r)的资产和时间尺度无关的分析形式可以被视为金融市场的附加风格化事实，并代表了对市场模型的非平凡检验。我们分析了三种市场模型(i)乘法随机级联，（ii）多重分形随机漫步和（iii）广义自回归条件异方差[GARCH(1,1)]模型的相互发生时间的分布P(Q)(r)以及自相关C(Q)(s)。我们发现，在考虑的模型中，只有多重分形随机游走模型近似地再现了P(Q)(r)的Q指数形式和C(Q)(s)的幂律衰减。
We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution P(Q)(r) of the interoccurrence times r between losses below a negative threshold -Q, for fixed mean interoccurrence times R(Q) in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, P(Q)(r)∝1/{[1+(q-1)βr](1/(q-1))}. We propose that the asset- and time-scale-independent analytic form of P(Q)(r) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution P(Q)(r) as well as the autocorrelation C(Q)(s) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q-exponential form of P(Q)(r) and the power-law decay of C(Q)(s).