Empirical Applications

In this section, two applications of TE in empirical finance are presented. In the first application, I analyze the same dataset as Dimpfl and Peter (2013) on information flows between the market for Credit Default Swaps (CDS) and bond markets. The second application focuses on the impact of the financial crisis on transatlantic information flows between stock indices, using the same dataset as Dimpfl and Peter (2014). While the TE estimates of both studies are based on a symbolic encoding, i.e., a discrete binning of the return time series, I use the quantile regression methodology presented in Section 5.1 to investigate whether TE can be identified for the entire support of the data.

Figure 5.9: Simulated Time Series for TE Estimation

The graph depicts samples of 100 observations from the systems of auto-regressive time series under consideration. On the horizontal axis is the time index and on the vertical axis the value of the time series.

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−4−202

X Y Z

(a)Independent

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−2−101

X Y Z

(b)Linear

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−50510

X Y Z

(c) Non-Linear

5.3.1 Credit Default Swaps (CDS) and Bond markets

Using discretized time series, Dimpfl and Peter (2013) employ symbolic transfer entropy to measure the information flow between CDS and bond markets. For this purpose they consider the difference between the yield of a certain bond and the currently risk free rate as mainly attributed to the credit risk, i.e, the risk that the issuer of the bond will fail to pay the outstanding commitments and default. The difference is also called the credit spread (CS). Inflation risk, liquidity risk, the risk that a holder of the bond has to reinvest because the contract is terminated somehow earlier than agreed or other risks are not considered dominant and are not controlled for.

As another measure for the default risk of a certain issuer, the authors consider the CDS premium. With CDS the credit risk associated to the bond issuer can be traded, if such CDS are available for the specific issuer. Since deviation of the CDS premium from the

Figure 5.10: Simulated Transfer Entropy

The top figure shows the kernel density estimates of 5000 simulated test statisticstT for the three time series systems in Equations (5.28) (the independent case), (5.29) (the linear case) and (5.30) (the non-linear case) are depicted. The blue line represents the kernel density of the independent case for whichT E=0 is true. The red and the green line show the densities for the linear and non-linear systems, respectively. For both,T E≠0. The coloring applies as well to the bottom graph. It shows the kernel density of the actual estimated TE values.

−6 −4 −2 0 2 4 6

0.00.10.20.30.40.5

t_T

Density

(a)Kernel Density Estimations of Test Statistic

−0.010 −0.005 0.000 0.005 0.010 0.015 0.020

050100150

TE

Density

(b)Kernel Density Estimations of TE Values

CS may present an arbitrage opportunity, CDS premium and the CS are usually modeled in the literature as co-integrated process in a Vector Error Correction Model (VECM).

Dimpfl and Peter (2013) encode the times series of changes in the CDS premium as well as the time series of changes in the CS in three discrete categories. All observations below the estimated unconditional 5%-quantile belong to the first bin and are encoded as 1 and observations between the 5%- up to the 95%-quantile belong to the second bin and are encoded with 2. All other observations above the unconditional 95%-quantile are encoded as 3 in the third bin. With these strongly coarse-grained time series, they find TE in both directions. Hence, they find that knowing in which bin the change of CS was yesterday helps to forecast the bin in which the CDS premium will be today, and vice-versa.

With the method developed in this chapter, I reanalyze the same time series Dimpfl and Peter (2013) used and explore whether their result can be generalized to the entire, continuous support of the CS and CDS premium. The results are presented in Table 5.3.

As one can see, I find that in general neither changes in the CDS premium help in predicting changes in the CS nor is today’s CS helpful in predicting tomorrows CDS. This is not in direct opposition to the results of Dimpfl and Peter (2013), since their time series was encoded. On the contrary, it rather hints to the informativeness of tail events. However, their results do not generalize to the continuous support of the underlying random variables.

5.3.2 Transatlantic Information Flows

Based on one minute intraday returns of the European, blue chip stock market indices the German DAX30, the British FTSE50 and the French CAC40, Dimpfl and Peter (2014) analyse the TE of these markets with the American S&P500 index. For the DAX, the data sample spans the years 2003 until 2010. For the FTSE and the CAC, the years 2006 until 2010 are covered. The S&P data are available for both periods. With regard to the financial crisis 2008, they subdivide their sample into a pre-crisis, crisis and post-crises period. Based on their data set I only estimate the TE for the entire sample and omit the partition of the sample with regard to the financial crisis. For all periods as well as for the entire sample, Dimpfl and Peter (2013) find significant symbolic transfer entropy. Knowing in which bin the return one minute ago was, helps to predict the current one-minute return.

In contrast to Dimpfl and Peter(2014), I not discretize the return series of the indices into three bins. I use the techniques developed in this chapter to explore whether the results for the encoded time series of Dimpfl and Peter(2014) can be generalized to the entire continuous support of the respective return series and whether TE between the markets can be detected.

Table 5.3: Results: Transfer Entropy CDS and CS

The table shows the estimated transfer entropy values in the second and fourth column. The corresponding test statistics are reported in the first and third column. The simulation study above indicates that values below -2.3 and above 1.9 are rather rare and can be considered as significant deviations from the null hypothesis.

t_{T ,CDS→CS} Tˆ_CDS→CS t_T,CS→CDS Tˆ_CS→CDS

Allianz -0.0015 -0.0004 0.0327 0.0231

BASF 0.0070 -0.0017 0.1954 -0.0062

Bayer 0.0989 0.0055 0.0028 0.0019

BMW -0.0512 0.0063 0.2204 0.0085

Carrefour -0.1443 -0.0237 0.0001 -0.0067

Deutsche Telekom 0.0002 0.0140 0.0322 0.0122

Electricit´e de France -0.0016 0.0020 -0.0000 0.0006

Enel 0.0000 0.0196 -0.0192 -0.0015

Fortum Oyi 0.0000 0.0071 0.0030 0.0088

France T´el´ecom 0.0000 0.0128 0.1419 0.0055

GDF Suez -0.0000 0.0019 -0.1117 -0.0053

Iberola 0.0636 0.0102 0.0509 0.0111

Koninklijke KPN -0.0282 0.0117 0.8598 0.0076

LVMH -0.0000 0.0076 0.3342 0.0142

Metro 0.5125 0.0099 0.1878 0.0098

ArcelorMIttal -0.0000 0.0138 -7.7769 0.0069

National Grid -0.1304 -0.0014 0.1796 0.0079

Repsol 0.0027 0.0026 0.0402 0.0012

RWE 0.0116 -0.0006 0.4038 0.0214

St. Gobain -0.0000 0.0018 -0.0110 0.0044

Solvay -0.0418 -0.0003 0.0008 -0.0078

Banco Santander Central Hispano 0.1395 0.0078 0.3026 0.0095

Telefonica 0.0186 -0.0068 0.2699 0.0165

Telecom Italia 0.0000 0.0472 0.2611 0.0098

Vattenfall -0.0000 -0.0093 -0.0198 -0.0026

Veolia -0.0000 0.0007 0.1663 -0.0077

VW -0.0000 0.0100 -0.0011 0.0043