This paper investigates the multifractal behavior of the probability of default (PD) of real sector firms and Turkey sovereign credit default swap (CDS). Moreover, we emphasize the co-movements of Hölder exponents during the financial crisis periods. For this reason, first, it is necessary to figure out the default probabilities of real sector firms. The default probability is evaluated weekly by the methodology of Moody’s Analytics, which is a commonly used approach, in which the market value of a firm is a call option written on its total assets. Multifractal detrended fluctuation analysis (MF-DFA), multifractal detrended cross-correlation analysis (MF-DCCA) and multifractal detrended moving average cross-correlation analysis (MF-X-DMA) techniques are applied to identify the multifractal behavior of the large-scale fluctuations of PDs and CDSs. In this way, we can evaluate the local Hurst exponents. Besides, the oscillation method is employed to estimate the pointwise and local Hölder exponents. In the period between January 2001 and March 2018, the structure of dynamic co-movements of Hölder exponents is determined by applying wavelet coherency methodology and the relations in crisis period are revealed. The selected period covers the crises with structural differences: Turkey banking crisis, the US sub-prime mortgage crisis and the European sovereign debt crisis that occurred in 2001, 2008 and 2009, respectively. Besides, during the periods of financial crises, among the local Hölder exponents, severely correlated large scales show multifractal features, and hence vector fractionally autoregressive integrated moving average (VFARIMA) forecasting provides better results than scalar models.

中文翻译：

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土耳其金融危机多重分形性质的痕迹：Hölder 指数的联动与大规模预测

本文研究了实体部门公司违约概率 (PD) 和土耳其主权信用违约互换 (CDS) 的多重分形行为。此外，我们强调金融危机期间 Hölder 指数的联动。出于这个原因，首先，有必要弄清楚实体部门公司的违约概率。违约概率每周通过穆迪分析的方法进行评估，这是一种常用的方法，其中公司的市场价值是写在其总资产上的看涨期权。应用多重分形去趋势波动分析（MF-DFA）、多重分形去趋势互相关分析（MF-DCCA）和多重分形去趋势移动平均互相关分析（MF-X-DMA）技术来识别大尺度的多重分形行为。 PDs 和 CDSs 的波动。通过这种方式，我们可以评估局部 Hurst 指数。此外，采用振荡方法估计逐点和局部 Hölder 指数。在 2001 年 1 月至 2018 年 3 月期间，应用小波相干方法确定了 Hölder 指数的动态联动结构，并揭示了危机时期的关系。所选时期涵盖了具有结构性差异的危机：土耳其银行业危机、美国次贷危机和欧洲主权债务危机，分别发生在 2001 年、2008 年和 2009 年。此外，在金融危机期间，在局部 Hölder 指数中，严重相关的大尺度表现出多重分形特征，