A seasonal periodic long memory model for monthly river flows

Based on simple time series plots and periodic sample autocorrelations, we document that monthly river flow data display long memory, in addition to pronounced seasonality. In fact, it appears that the long memory characteristics vary with the season. To describe these two properties jointly, we propose a seasonal periodic long memory model and fit it to the well-known Fraser river data (to be obtained from Statlib at http://lib.stat.cmu.edu/datasets/. We provide a statistical analysis and provide impulse response functions to show that shocks in certain months of the year have a longer lasting impact than those in other months

Fractal Analysis of River Flow Fluctuations (with Erratum)

We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at $s_{1\times}\sim12$ and $s_{2\times}\sim130$ months in the fluctuation function. We discuss how the existence of the crossover timescales are related to a sinusoidal trend. The first crossover is due to the seasonal trend and the value of second ones is approximately equal to the well known cycle of sun activity. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The value of Hurst exponent of the runoff water of rivers without the sinusoidal trend shows a long range correlation behavior. For the Daugava river the value of Hurst exponent is $0.52\pm0.01$ and also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set of Daugava river to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to the broadness of probability density function.Comment: 13 pages, 10 figures, V2: Added comments, references and one more figure, improved numerical calculations with new version of data, accepted for publication in Physica A: Statistical Mechanics and its Applications. The version with Erratum contains some notes concerning Ref. [58

Evaluation of the Land Surface Water Budget in NCEP/NCAR and NCEP/DOE Reanalyses using an Off-line Hydrologic Model

The ability of the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis (NRA1) and the follow-up NCEP/Department of Energy (DOE) reanalysis (NRA2), to reproduce the hydrologic budgets over the Mississippi River basin is evaluated using a macroscale hydrology model. This diagnosis is aided by a relatively unconstrained global climate simulation using the NCEP global spectral model, and a more highly constrained regional climate simulation using the NCEP regional spectral model, both employing the same land surface parameterization (LSP) as the reanalyses. The hydrology model is the variable infiltration capacity (VIC) model, which is forced by gridded observed precipitation and temperature. It reproduces observed streamflow, and by closure is constrained to balance other terms in the surface water and energy budgets. The VIC-simulated surface fluxes therefore provide a benchmark for evaluating the predictions from the reanalyses and the climate models. The comparisons, conducted for the 10-year period 1988–1997, show the well-known overestimation of summer precipitation in the southeastern Mississippi River basin, a consistent overestimation of evapotranspiration, and an underprediction of snow in NRA1. These biases are generally lower in NRA2, though a large overprediction of snow water equivalent exists. NRA1 is subject to errors in the surface water budget due to nudging of modeled soil moisture to an assumed climatology. The nudging and precipitation bias alone do not explain the consistent overprediction of evapotranspiration throughout the basin. Another source of error is the gravitational drainage term in the NCEP LSP, which produces the majority of the model\u27s reported runoff. This may contribute to an overprediction of persistence of surface water anomalies in much of the basin. Residual evapotranspiration inferred from an atmospheric balance of NRA1, which is more directly related to observed atmospheric variables, matches the VIC prediction much more closely than the coupled models. However, the persistence of the residual evapotranspiration is much less than is predicted by the hydrological model or the climate models

Multifractal Detrended Cross-Correlation Analysis of Sunspot Numbers and River Flow Fluctuations

We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, $(12-24)\leq s\leq 130$ months, is $\lambda = 1.17\pm0.04$ which is almost similar for all underlying rivers at $1\sigma$confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are $\lambda\in (0.76, 0.85)$ and $\gamma_{\times}\in(0.30, 0.48)$, respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), $\lambda\approx(h_{\rm sun} + h_{\rm river})/2$ is confirmed.Comment: 9 pages, 8 figures and 1 table. V2: Added comments, references, figures and major corrections. Accepted for publication in Physica A: Statistical Mechanics and its Application

Periodic Heteroskedastic RegARFIMA models for daily electricity spot prices

In this paper we consider different periodic extensions of regression models with autoregressive fractionally integrated moving average disturbances for the analysis of daily spot prices of electricity. We show that day-of-the-week periodicity and long memory are important determinants for the dynamic modelling of the conditional mean of electricity spot prices. Once an effective description of the conditional mean of spot prices is empirically identified, focus can be directed towards volatility features of the time series. For the older electricity market of Nord Pool in Norway, it is found that a long memory model with periodic coefficients is required to model daily spot prices effectively. Further, strong evidence of conditional heteroskedasticity is found in the mean corrected Nord Pool series. For daily prices at three emerging electricity markets that we consider (APX in The Netherlands, EEX in Germany and Powernext in France) periodicity in the autoregressive coefficients is also stablished, but evidence of long memory is not found and existence of dynamic behaviour in the variance of the spot prices is less pronounced. The novel findings in this paper can have important consequences for the modelling and forecasting of mean and variance functions of spot prices for electricity and associated contingent assetsGARCH, Long Memory

Testing Of Nonstationarities In The Unit Circle,Long Memory Processes And Day Of The Week Effects In Financial Data

This paper examines a version of the tests of Robinson (1994) that enables one to test models of the form (1-Lk)dxt = ut, where k is an integer value, d may be any real number, and ut is I(0). The most common cases are those with k = 1 (unit or fractional roots) and k = 4 and 12 (seasonal unit or fractional models). However, we extend the analysis to cover situations such as (1-L5)d xt = ut, which might be relevant, for example, in the context of financial time series data. We apply these techniques to the daily Eurodollar rate and the Dow Jones index, and find that for the former series the most adequate specifications are either a pure random walk or a model of the form xt = xt-5 + εt, implying in both cases that the returns are completely unpredictable. In the case of the Dow Jones index, a model of the form (1-L5)d xt = ut is selected, with d constrained between 0.50 and 1, implying nonstationarity and mean-reverting behaviour

Real time updating of the flood frequency distribution through data assimilation

We explore the memory properties of catchments for predicting the likelihood of floods basing on observations of average flows in pre-flood seasons. Our approach assumes that flood formation is driven by the superimposition of short and long term perturbations. The former is given by the short term meteorological forcing leading to infiltration and/or saturation excess, while the latter is originated 15 by higher-than-usual storage in the catchment. To exploit the above sensitivity to long term perturbations a Meta-Gaussian model is implemented for updating a season in advance the flood frequency distribution, through a data assimilation approach. Accordingly, the peak flow in the flood season is predicted by exploiting its dependence on the average flow in the antecedent seasons. We focus on the Po River at Pontelagoscuro and the Danube river at Bratislava. We found that the shape of 20 the flood frequency distribution is significantly impacted by higher-than-usual flows occurred up to several months earlier. The proposed technique may allow one to reduce the uncertainty associated to the estimation of flood frequenc