Prediction of Non-stationary Time Series With Replacement Variables

The experimental comparison of methods of forecasting non-stationary time series by replacing the variables. One of these variables is the phase of the process. Currently, in the direction of the change of variables there were two main approaches to the isolation of stable characteristics of the process, and the band-pass filtering on the empirical mode decomposition--The band-pass filtering. Using a band-pass filter that transmits only the frequencies in a small neighborhood of a selected frequency will provide components with clearly highlighted the basic rhythm. One option for the analytical component of the original series is a discrete wavelet transform （DWT） with getting more approximate and detail the factors on levels of decomposition--0n empirical mode decomposition. Empirical method of decomposition （EMD） is based on the simple assumption that any data consist of a variety of simple domestic species fluctuations （MOD）. Each ＂fashion＂ must be a signal with zero mean, Maxima and minima of positive-negative, i.e., between each maximum and minimum signal x（t） necessarily have his schedule with the direct crossing x = 0. Continue to make the variable phase each fashion is Hilbert decomposition. In both cases, instead of the original series we receive several quasi-stationary series that are projected separately. Projection results are reverse-conversion with predictive component series, which gives the forecast. Difficulty at this stage is the selection of forecasting method for sampling small dimension, because according to our research, the length of the memory of the financial series is extremely small. For the same source data give calculations for both approaches using neural network forecasting and sliding fractal Caterpillar SSA. The results show satisfactory as a prediction.     

A bound on the expected overshoot for some concave boundaries

LetX ₁,X ₂,… be i.i.d. with finite meanμ>0,S _n =X ₁+…+X _n . Forf(n)=n ^β ,c>0 we consider the stopping timesT _c =inf{n:S _n >c+f(n)} with overshootR _c =S _{T c} −(c+f(T _c )). For 0<β<1 we give a bound for sup _c≥0 ER _c in the spirit of Lorden’s well-known inequality forf=0.