Browsing by Author "Du Toit, Cornel"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Non-parametric volatility measurements and volatility forecasting models
    (Stellenbosch : Stellenbosch University, 2005-03) Du Toit, Cornel; Conradie, W. J.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH ABSTRACT: Volatilty was originally seen to be constant and deterministic, but it was later realised that return series are non-stationary. Owing to this non-stationarity nature of returns, there were no reliable ex-post volatility measurements. Subsequently, researchers focussed on ex-ante volatility models. It was only then realised that before good volatility models can be created, reliable ex-post volatility measuremetns need to be defined. In this study we examine non-parametric ex-post volatility measurements in order to obtain approximations of the variances of non-stationary return series. A detailed mathematical derivation and discussion of the already developed volatility measurements, in particular the realised volatility- and DST measurements, are given In theory, the higher the sample frequency of returns is, the more accurate the measurements are. These volatility measurements referred to above, however, all have short-comings in that the realised volatility fails if the sample frequency becomes to high owing to microstructure effects. On the other hand, the DST measurement cannot handle changing instantaneous volatility. In this study we introduce a new volatility measurement, termed microstructure realised volatility, that overcomes these shortcomings. This measurement, as with realised volatility, is based on quadratic variation theory, but the underlying return model is more realistic.
  • Thumbnail Image
    Item
    Probabilistic graphical modelling of seismic data processing in mining
    (Stellenbosch : Stellenbosch University., 2020-04) Du Toit, Cornel; Eggers, H. C.; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT: Mining has long been characterised by deep shafts and dangerous conditions. Accurate monitoring and prediction of seismic activity and rockfalls are matters of life and death. The Institute of Mine Seismology (IMS) is the world’s largest independent organisation that provides worldwide mine seismic data processing using human data processors. Approximately 35000 seismic events are processed per day by a team of 65 data processors (24 hours a day, 365 days a year) in order to provide rapid data assessments to the mine, typically within minutes of the event being recorded by the seismic network. This aim is achievable only with the assistance of automatic, computer-based, data processing. While automatic processing is common in natural earthquake seismology, in mining-induced seismology the problem is more complex, and an automatic processor is yet to be developed. In mine seismology, classification of the recorded data is essential as there are many sources of noise in mines. Furthermore, with dense seismic sensor arrays in seismically active mines, multiple signals associated with both seismic events and noise sources may be conflated into a single seismogram. The matching of a Pressure (P)- and Shear (S)-wave for a specific seismic event in the presence of multiple sensors is not a simple task, even when analysed by an experienced seismologist. In this dissertation, an automatic method based on probabilistic graphical models for both the event classification (seismic event, blast or rejected event) and the determination of the phase arrival times (P- and S-wave) is investigated. This machine learning approach has lead to higher reliability, faster availability of results, more satisfied clients, less organisational load as well as a financial advantage to IMS and its clients. By using Hidden Markov Models (HMM) as classification tool, different characteristics of the wave can be analysed for classification. By identifying the most likely hidden states (P-wave and S-wave) using the Viterbi algorithm combined with standard short-term average (STA) and long-term average (LTA) analysis, the candidate phase arrivals for each sensor are determined. The probability of each candidate phase arrival being the true arrival is seen as a parameter, expressed as a mixing weight, through the introduction of latent variables. The latent variables, together with the seismic event location parameters (3D multi-sensor and origin time), are written as a probabilistic graphical model (PGM) which turns out to be a hierarchical Bayesian network. In most cases, the maximum a posterior (MAP) estimates of the latent variables are the true phase arrivals. In cases where the optimisation technique failed to deliver the MAP estimates e.g. got stuck in local maxima, outlier detection techniques are used to identify spurious events. Of a total of 80 mines, the automatic processor which forms the subject of this dissertation is currently being tested on the 25 most seismically active ones. Of an average 35000 daily events (based on all 80 mines), 60% can be successfully processed. The average quality control score of the automatic processor is slightly higher than the average human quality score at a fraction of cost.