Time Series and Distance Correlation

Specialeforsvar ved Niklas Sebastian Barrington Peek 

Titel:  Time Series and Distance Correlation

Abstract:  Distance correlation, introduced in the paper Székely et. al 2007, is a measure of dependence between random vectors. I show key results of existence and the asymptotics of the measure, as introduced in the literature. I use distance correlation to extend the concept of the autocorrelation function to include measurement of non-linear dependence as Zhou 2014 and Davis et. al .. Using this auto distance correlation function, or ADCF, I attempt to measure non-linear dependence in time series. I take the sample ADCF of an MA(q) process using different weight functions as proposed in Davis et. al to explore the different weight functions efficiency in measuring non-linear dependence. I find that neither of the weight functions I test are more efficient than the one proposed by Székely et. al. I simulate a Garch(1,1) because of its non-linear dependence, and attempt to see if this can be measured by the ADCF. I find that the ADCF does capture the temporal dependence of the Garch(1,1) process, though the results require a larger sample before reaching significance than the autocorrelation function under some transformation. I also take the sample ADCF of log returns of the S&P 500 and OMXC20 stock indices, and their cross distance correlation function, or CDCF. The ADCF captures the non-linear dependence of these log returns, namely lag correlation of absolute log returns and long dependence of log returns, yet still leaves open the possibility of confounding long dependence with non-stationarity

Vejleder:   Thomas V. Mikosch
Censor:     Mette M Havning