| Abstract [eng] |
Ordinal patterns are an effective technique introduced by C. Bandt and B. Pompe in the article about permutation entropy. The aim of this thesis is to investigate 1, 5, 10 and 30 year U.S. treasury rate and to derive two models for ordinal patterns prediction. The prediction of financial time series has not been analysed in this way so far. It was found that empirical probability distribution of ordinal patterns of different time series is close to stationary distribution of a corresponding Markov chain, measuring it by total variation metric. This means that stationary distribution of a corresponding Markov chain quite accurately describes the empirical probability distribution. Results of permutation entropy and complexity - entropy causality plane showed that none of times series is absolutely predictable, but not completely random too. The analysis also showed that there exists a strong correlation between ordinal patterns of different time series and a positive dependence that decreases with the increase in difference of bonds maturity. Two models for ordinal patterns prediction are derived in this thesis - one-dimensional and two-dimensional. The one-dimensional model is based on Markov chains and uses only historical data of modelled time series. The two-dimensional model is based on conditional probabilities and law of total probability, this model uses not only relevant time series data, but also data of some other time series, too. The prediction quality is estimated by three criteria: mean absolute percentage error, error rate lower than 5% and error rate higher than 95%. It was found that the two-dimensional prediction model can provide more accurate results than forecasting the same data with one-dimensional model. |
