Position time series from permanent Global Navigation Satellite System (GNSS) stations are commonly used for estimating secular velocities of discrete points on the Earth’s surface. An understanding of background noise in the GNSS position time series is essential to obtain realistic estimates of velocity uncertainties. The current study focuses on the investigation of background noise in position time series obtained from thirteen permanent GNSS stations located in Nepal Himalaya using the spectral analysis method. The power spectrum of the GNSS position time series has been estimated using the Lomb–Scargle method. The iterative nonlinear Levenberg–Marquardt (LM) algorithm has been applied to estimate the spectral index of the power spectrum. The power spectrum can be described by white noise in the high frequency zone and power law noise in the lower frequency zone. The mean and the standard deviation of the estimated spectral indices are ��1:46#6;0:14;��1:39#6;0:16 and ��1:53#6;0:07 for north, east and vertical components, respectively. On average, the power law noise extends up to a period of ca. 21 days. For a shorter period, i.e. less than ca. 21 days, the spectra are white. The spectral index corresponding to random walk noise (ca. –2) is obtained for a site located above the base of a seismogenic zone which can be due to the combined effect of tectonic and nontectonic factors rather than a spurious monumental motion. Overall, the usefulness of investigating the background noise in the GNSS position time series is discussed.
The aim of the paper was an attempt at applying the time-series analysis to the control of the melting process of grey cast iron in production conditions. The production data were collected in one of Polish foundries in the form of spectrometer printouts. The quality of the alloy was controlled by its chemical composition in about 0.5 hour time intervals. The procedure of preparation of the industrial data is presented, including OCR-based method of transformation to the electronic numerical format as well as generation of records related to particular weekdays. The computations for time-series analysis were made using the author’s own software having a wide range of capabilities, including detection of important periodicity in data as well as regression modeling of the residual data, i.e. the values obtained after subtraction of general trend, trend of variability amplitude and the periodical component. The most interesting results of the analysis include: significant 2-measurements periodicity of percentages of all components, significance 7-day periodicity of silicon content measured at the end of a day and the relatively good prediction accuracy obtained without modeling of residual data for various types of expected values. Some practical conclusions have been formulated, related to possible improvements in the melting process control procedures as well as more general tips concerning applications of time-series analysis in foundry production.
The article presents results of the influence of the GMDH (Group Method of Data Handling) neural network input data preparation method on the results of predicting corrections for the Polish timescale UTC(PL). Prediction of corrections was carried out using two methods, time series analysis and regression. As appropriate to these methods, the input data was prepared based on two time series, ts1 and ts2. The implemented research concerned the designation of the prediction errors on certain days of the forecast and the influence of the quantity of data on the prediction error. The obtained results indicate that in the case of the GMDH neural network the best quality of forecasting for UTC(PL) can be obtained using the time-series analysis method. The prediction errors obtained did not exceed the value of ± 8 ns, which confirms the possibility of maintaining the Polish timescale at a high level of compliance with the UTC.
The aim of the article is to construct an asymptotically consistent test, based on a subsampling approach, to verify hypothesis about existence of the individual or common deterministic cycle in coordinates of multivariate macroeconomic time series. By the deterministic cycle we mean the periodic or almost periodic fluctuations in the mean function in cyclical fluctuations. To construct test we formulate a multivariate non-parametric model containing the business cycle component in the unconditional mean function. The construction relies on the Fourier representation of the unconditional expectation of the multivariate Almost Periodically Correlated time series and is related to fixed deterministic cycle presented in the literature. The analysis of the existence of common deterministic business cycles for selected European countries is presented based on monthly industrial production indexes. Our main findings from the empirical part is that the deterministic cycle can be strongly supported by the data and therefore should not be automatically neglected during analysis without justification.
In economics we often face a system which intrinsically imposes a structure of hierarchy of its components, i.e., in modeling trade accounts related to foreign exchange or in optimization of regional air protection policy. A problem of reconciliation of forecasts obtained on different levels of hierarchy has been addressed in the statistical and econometric literature many times and concerns bringing together forecasts obtained independently at different levels of hierarchy. This paper deals with this issue with regard to a hierarchical functional time series. We present and critically discuss a state of art and indicate opportunities of an application of these methods to a certain environment protection problem. We critically compare the best predictor known from the literature with our own original proposal. Within the paper we study a macromodel describing the day and night air pollution in Silesia region divided into five subregions.