Presence Of Deterministic Components Research Articles

Identification of the components of the time series of hydrological data

Conducting research on the hydrological data objects is an important step in monitoring their condition. Changes in the quality and quantity of surface waters has social, environmental and economic consequences and require careful monitoring and, if necessary, quick response to adverse changes. This article discusses the computational scheme for the allocation of components in the time series, as well as the implementation and analysis of the above scheme using the example of hydrological monitoring data.The developed computational scheme processes the data presented in the form of time series.The first step in the analysis of hydrological data is the determination of the primary statistical characteristics of the object under study. Among these characteristics: average, minimum and maximum values of the time series; median, variance, coefficient of variation, kurtosis and asymmetry of the time series. The preliminary assumptions about the presence of deterministic components in the time series are made on the basis of a correlogram analysis based on the initial data.To test the hypothesis of the presence in the time series of the trend component, the Fosters-Stewarts method is used. When confirming the hypothesis that a trend in the time series is present, the trend component is removed by the described linear regression model, the parameters of which are calculated by the least squares method. Identification of periodic component of a time series is carried out using the methods of the Fourier analysis. The dynamics of the series are determined with using the methods of linear and nonlinear regression, in particular: polynomial (3 degrees), power, exponential, Phillips curve and Engel curve, whose parameters are calculated by the least squares method; modified exponential, the parameters of which are calculated by the method of three points. The analysis of the adequacy of the regression models is checked using the coefficient of determination and the adjusted coefficient of determination, also as the average approximation error. The Akaike information criterion and Bayesian information criterion Schwartz are used to determine the best model. The results of the study are accompanied by appropriate graphs and tables.

Multiharmonic model of seismic activity in Kamchatka

Based on the uniform catalogue of earthquakes of the minimum energy class 8.5 for 1962–2008, multiharmonic models of seismic activity in Kamchatka are developed. The main harmonic components with periods from a few days to 12 years are identified. Both the entire catalogue and its modified versions obtained by the elimination of aftershocks and clusters, as well as nonoverlapping time series were used to study the stability of the models. The forward-prediction testing showed that in the models with weekly averaged initial data, periods of increased and reduced seismic activity lasting for several weeks are predicted with high confidence on an interval of up to 1.8% of the education period. This testifies for the presence of deterministic components in the seismic activity.

Critical values for the augmented efficient Wald test for fractional unit roots

This paper presents response surface estimates of finite sample critical values of the Efficient Wald test for Fractional Unit Roots of Lobato and Velasco (Econometrica 75:575–590, 2007) in the presence of deterministic components. Lag-adjusted critical values of the augmented versions of the tests illustrate that as in the context of traditional unit root and stationarity tests, incorporating adjustments for serial correlation affects the finite sample distributions of the test statistics.

Critical values of the augmented fractional Dickey–Fuller test

This paper presents response surface estimates of finite sample critical values of the Augmented Fractional Dickey–Fuller test of Dolado et al. (Testing I(1) against I(d) alternatives in the presence of deterministic components. Universidad Carlos III, Madrid, mimeo, 2006). The null hypothesis that a series contains a unit root is tested against the alternative that it is fractionally integrated. It is shown that finite sample critical values depend critically on the lag order used to construct the test statistic as well as the hypothesized value of the fractional differencing parameter under the alternative. Non-linear non-parametric response surfaces provide a novel approach to constructing estimates of finite sample critical values.

Poincaré plot indexes of heart rate variability capture dynamic adaptations after haemodialysis in chronic renal failure patients.

The hypothesis that the Poincaré plot indexes of heart rate variability (HRV) detect dynamic changes after haemodialysis (HD) over the HRV in haemodynamically stable chronic renal failure (CRF) patients was examined. Minor axis (SD1), major axis (SD2) and the SD1/SD2 ratio were compared against standard HRV indexes in time and frequency domain, in a group of healthy subjects and in a group of CRF patients before and after HD. These indexes were estimated from Poincaré plots reconstructed with lags of one, two and four heartbeats. The surrogate data analysis technique was applied in order to discern if only random components or linear features of HRV contribute to its dynamics. None of the standard linear HRV indexes changed after HD. The Poincaré plot indexes measured from CRF patients were smaller than the ones measured from healthy subjects. In CRF patients the SD1/SD2 ratio decreased after HD, when a lag of four heartbeats was used (0.68 +/- 0.19 before HD versus 0.55 +/- 0.12 after HD, P<0.05). The presence of deterministic components in HRV were confirmed for all measures of the SD1/SD2 ratio. Moreover, a loss of non-linear components after HD was detected by the surrogate analysis over the SD1/SD2 ratio with a lag of four heartbeats. In conclusion, the SD1/SD2 ratio measured at lag of 4 heartbeats capture dynamic changes after HD upon the HRV of CRF patients that are not solely related to linear autocorrelations of HRV. This suggests that the SD1/SD2 ratio reflects non-linear information of HRV.

Forecasting autoregressive time series in the presence of deterministic components

This paper studies the error in forecasting an autoregressive process with a deterministic component. We show that when the data are strongly serially correlated, forecasts based on a model that detrends the data using OLS before estimating the autoregressive parameters are much less precise than those based on an autoregression that includes the deterministic components, and the asymptotic distribution of the forecast errors under the two-step procedure exhibits bimodality. We explore the conditions under which feasible GLS trend estimation can lead to forecast error reduction. The finite sample properties of OLS and feasible GLS forecasts are compared with forecasts based on unit root pretesting. The procedures are applied to 15 macroeconomic time series to obtain real time forecasts. Forecasts based on feasible GLS trend estimation tend to be more efficient than forecasts based on OLS trend estimation. A new finding is when a unit root pretest rejects non-stationarity, use of GLS yields smaller forecast errors than OLS. When the series to be forecasted is highly persistent, GLS trend estimation in conjunction with unit root pretests can lead to sharp reduction in forecast errors.