Time-scale and memory in financial time series: a data mining approach

摘要

Financial time series analysis is a highly empirical discipline concerned with the evolutionudof the price of an asset. The key feature that distinguishes financial time seriesudfrom time series of other scientific domains is the element of uncertainty that they contain.udThe recent financial crisis has tested the capabilities of several existing modelsudand evidenced the need for methods able to deal with the high complexity and theudnon-stationary characteristics of the data observed in financial markets. The objectiveudof this thesis is to provide a better understanding of financial time series, to enhance theudabilities of existing methods, especially their predictive performance but also to developudnovel methods which aim to provide inferences in the presence of non-stationarities andudreduce the complexity of high dimensional tasks. To this end, the memory in the magnitudeudand the memory in the sign of logarithmic returns is studied and a novel modeludis constructed whose fit suggests that long memory might be present in the volatilityudprocess and that when memory in the sign increases so does the memory in the magnitude.udAdditionally, wavelets are employed for that they operate in both the time andudfrequency domains. Thus, classic time series models and other methods extensively usedudin the time domain are deployed across different frequency bands to combine knowledgeudfrom both domains and provide information that might not be accessible otherwise. Inudparticular, the volatility process is modeled in the time domain after some of the noisyudbehavior that exists in high frequencies, which might also contain outliers, is neglected.udMoreover, the volatility process is modeled directly in the wavelet domain in a scale-by-udscale manner in an effort to improve the forecasting performance. Furthermore, weudattempt to detect changes in the autocorrelation function of a process, which resultudin changes in the spectral density function, by monitoring the wavelet variance acrossuddifferent multiresolution scales.