This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with...

This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with...

Recent results on so-called SEMIFAR models introduced by Beran (1997) are discussed. The nonparametric deterministic trend is estimated by a kernel method. The differencing and fractional differencing parameters as well as the autoregressive coefficients are estimated by an approximate maximum...

Mostly used estimators of Hurst exponent for detection of long-range dependence are biased by presence of short-range dependence in the underlying time series. We present confidence intervals estimates for rescaled range and modified rescaled range. We show that the difference in expected values...

In the paper, we research on the presence of long-range dependence in returns and volatility of BUX, PX and WIG between years 1997 and 2009 with use of classical and modified rescaled range. Moving block bootstrap with pre-whitening and postblackening is used for the construction of confidence...

The problem of predicting 0-1-events is considered under general conditions, including stationary processes with short and long memory as well as processes with changing distribution patterns. Nonparametric estimates of the probability function and prediction intervals are obtained.

In this paper data-driven algorithms for fitting SEMIFAR models (Beran, 1999) are proposed. The algorithms combine the data-driven estimation of the nonparametric trend and maximum likelihood estimation of the parameters. For selecting the bandwidth, the proposal of Beran and Feng (1999) based...

Time series in many areas of application often display local or global trends. Typical models that provide statistical explanations of such trends are, for example, polynomial regression, smooth bounded trends that are estimated nonparametrically, and difference-stationary processes such as, for...

The distinction between stationarity, difference stationarity, deterministic trends as well as between short- and long-range dependence has a major impact on statistical conclusions, such as confidence intervals for population quantities or point and interval forecasts. In this paper, recent...

Confidence intervals and tests for the location parameter are considered for time series generated by FEXP models. Since these tests mainly depend on the unknown fractional differencing parameter d, the distribution of d plays a major role. An exact closed form expression for the asymptotic...