Stochastic Time Series Models Research Articles

Stochastic simulation of nonstationary oscillation hydroclimatic processes using empirical mode decomposition

Nonstationary oscillation (NSO) processes are observed in a number of hydroclimatic data series. Stochastic simulation models are useful to study the impacts of the climatic variations induced by NSO processes into hydroclimatic regimes. Reproducing NSO processes in a stochastic time series model is, however, a difficult task because of the complexity of the nonstationary behaviors. In the current study, a novel stochastic simulation technique that reproduces the NSO processes embedded in hydroclimatic data series is presented. The proposed model reproduces NSO processes by utilizing empirical mode decomposition (EMD) and nonparametric simulation techniques (i.e., k‐nearest‐neighbor resampling and block bootstrapping). The model was first tested with synthetic data sets from trigonometric functions and the Rössler system. The North Atlantic Oscillation (NAO) index was then examined as a real case study. This NAO index was then employed as an exogenous variable for the stochastic simulation of streamflows at the Romaine River in the province of Quebec, Canada. The results of the application to the synthetic data sets and the real‐world case studies indicate that the proposed model preserves well the NSO processes along with the key statistical characteristics of the observations. It was concluded that the proposed model possesses a reasonable simulation capacity and a high potential as a stochastic model, especially for hydroclimatic data sets that embed NSO processes.

사무소건물의 슬래브축냉을 위한 내부발열부하의 확률적 성상 모델화

It has been shown that the air-conditioning system with slab cooling storage is effective in cutting peak load and utilizing nighttime electric power. The stochastic properties of internal heat generation which has great influence on the cooling load are examined in this paper. Based on the measured cooling load and electric power consumption in an office building with slab cooling storage, stochastic time series models to simulate these random processes are investigated. Furthermore, a calculated result by an optimal control method of thermal analysis taking into account the internal heat is compared with the measured cooling load.

Distributional modeling and short-term forecasting of electricity prices by Generalized Additive Models for Location, Scale and Shape

In the context of the liberalized and deregulated electricity markets, price forecasting has become increasingly important for energy company's plans and market strategies. Within the class of the time series models that are used to perform price forecasting, the subclasses of methods based on stochastic time series and causal models commonly provide point forecasts, whereas the corresponding uncertainty is quantified by approximate or simulation-based confidence intervals. Aiming to improve the uncertainty assessment, this study introduces the Generalized Additive Models for Location, Scale and Shape (GAMLSS) to model the dynamically varying distribution of prices. The GAMLSS allow fitting a variety of distributions whose parameters change according to covariates via a number of linear and nonlinear relationships. In this way, price periodicities, trends and abrupt changes characterizing both the position parameter (linked to the expected value of prices), and the scale and shape parameters (related to price volatility, skewness, and kurtosis) can be explicitly incorporated in the model setup. Relying on the past behavior of the prices and exogenous variables, the GAMLSS enable the short-term (one-day ahead) forecast of the entire distribution of prices. The approach was tested on two datasets from the widely studied California Power Exchange (CalPX) market, and the less mature Italian Power Exchange (IPEX). CalPX data allow comparing the GAMLSS forecasting performance with published results obtained by different models. The study points out that the GAMLSS framework can be a flexible alternative to several linear and nonlinear stochastic models.

Stochastic Excitation Model of Strip Rolling Mill

The stochastic excitation power spectral density (PSD) model and ARMA time series model are established based on the stochastic rolling force acquisition data, which is processed into stationary, normal and zero mean from a aluminum hot strip tandem mill. Characteristics of rolling force ARMA time series models are discussed by means of random process theory. The rolling forces PSD function of facilitating engineering application is obtained by utilizing Levenberg-Marquardt combined with generalized global planning algorithm, and the stochastic excitation model is established. It provides the basis for the prediction of rolling force.

Effect of ligand binding on the intraminimum dynamics of proteins

Effects of ligand binding on protein dynamics are studied via molecular dynamics (MD) simulations on two different enzymes, dihydrofolate reductase (DHFR) and triosephosphate isomerase (TIM), in their unliganded (free) and liganded states. Domain motions in MD trajectories are analyzed by collectivities and rotation angles along the principal components (PCs). DHFR in the free state has well-defined domain rotations, whereas rotations are slightly damped in the binary complex with nicotinamide adenine dinucleotide phosphate (NADPH), and remarkably distorted in the presence of NADP(+) , showing that NADP(+) is solely responsible for the loss of correlation of the domains in DHFR. Although mean square fluctuations of MD simulations in the same PC subspaces are similar for different ligation states, linear stochastic time series models show that backbone flexibility along the first five PCs is decreased upon NADPH and NADP(+) binding in subpicosecond scale. This shows that mobility of the protein along the PCs is closely related with intraminimum dynamics, and alterations in ligation states may change the intraminimum dynamics significantly. Low vibrational frequencies of the alpha-carbon atoms of DHFR are determined from the time series models of a larger number of low indexed PCs, and it is found that number of modes in the lowest frequencies is reduced upon ligand binding. A similar result is obtained for TIM in the unliganded and dihydroxyacetone phosphate bound states. We suggest that stochastic time series modeling is a promising method to be used in determining subtle perturbations in protein dynamics.

Real-Time Short-Term Traffic Speed Level Forecasting and Uncertainty Quantification Using Layered Kalman Filters

Short-term traffic condition forecasting has long been argued as essential for developing proactive traffic control systems that could alleviate the growing congestion in the United States. In this field, short-term traffic condition level forecasting and short-term traffic condition uncertainty forecasting play an equally important role. Past literature showed that linear stochastic time series models are promising in modeling and hence forecasting traffic condition levels and traffic conditional variance with workable performance. On the basis of this finding, an autoregressive moving average plus generalized autoregressive conditional heteroscedasticity structure was proposed for modeling the station-by-station traffic speed series. An online algorithm based on layered Kalman filter was developed for processing this structure in real time. Empirical results based on real-world station-by-station traffic speed data showed that the proposed online algorithm can generate workable short-term traffic speed level forecasts and associated prediction confidence intervals. Future work is recommended to develop and test a proactive traffic control system in a simulated environment, to refine the uncertainty modeling through a stochastic volatility model, and to extend uncertainty modeling and forecasting to link level and network level.

Analysis of metal cutting acoustic emissions by time series models

We analyse some acoustic emission time series obtained from a lathe machining process. Considering the dynamic evolution of the process we apply two classes of well known stationary stochastic time series models. We apply a preliminary root mean square (RMS) transformation followed by an ARMA analysis; results thereof are mainly related to the description of the continuous part (plastic deformation) of the signal. An analysis of acoustic emission, as some previous works show, may also be performed with the scope of understanding the evolution of the ageing process that causes the degradation of the working tools. Once the importance of the discrete part of the acoustic emission signals (i.e. isolated amplitude bursts) in the ageing process is understood, we apply a stochastic analysis based on point processes waiting times between bursts and to identify a parameter with which to characterise the wear level of the working tool. A Weibull distribution seems to adequately describe the waiting times distribution.

Stochastic Variance Models in Discrete Time with Feedforward Neural Networks

The study overcomes the estimation difficulty in stochastic variance models for discrete financial time series with feedforward neural networks. The volatility function is estimated semiparametrically. The model is used to estimate market risk, taking into account not only the time series of interest but extra information on the market. As an application, some stock prices series are studied and compared with the nonlinear ARX-ARCHX model.

Evaluation of a statistical downscaling procedure for the estimation of climate change impacts on droughts

Abstract. Despite uncertainties in future climates, there is considerable evidence that there will be substantial impacts on the environment and human interests. Climate change will affect the hydrology of a region through changes in the timing, amount, and form of precipitation, evaporation and transpiration rates, and soil moisture, which in turn affect also the drought characteristics in a region. Droughts are long-term phenomena affecting large regions causing significant damages both in human lives and economic losses. The most widely used approach in regional climate impact studies is to combine the output of the General Circulation Models (GCMs) with an impact model. The outputs of Global Circulation Model CGCMa2 were applied for two socioeconomic scenarios, namely, SRES A2 and SRES B2 for the assessment of climate change impact on droughts. In this study, a statistical downscaling method has been applied for monthly precipitation. The methodology is based on multiple regression of GCM predictant variables with observed precipitation developed in an earlier paper (Loukas et al., 2008) and the application of a stochastic timeseries model for precipitation residuals simulation (white noise). The methodology was developed for historical period (1960–1990) and validated against observed monthly precipitation for period 1990–2002 in Lake Karla watershed, Thessaly, Greece. The validation indicated the accuracy of the methodology and the uncertainties propagated by the downscaling procedure in the estimation of a meteorological drought index the Standardized Precipitation Index (SPI) at multiple timescales. Subsequently, monthly precipitation and SPI were estimated for two future periods 2020–2050 and 2070–2100. The results of the present study indicate the accuracy, reliability and uncertainty of the statistical downscaling method for the assessment of climate change on hydrological, agricultural and water resources droughts. Results show that climate change will have a major impact on droughts but the uncertainty introduced is quite large and is increasing as SPI timescale increases. Larger timescales of SPI, which, are used to monitor hydrological and water resources droughts, are more sensitive to climate change than smaller timescales, which, are used to monitor meteorological and agricultural droughts. Future drought predictions should be handled with caution and their uncertainty should always be evaluated as results demonstrate.

Hierarchical Bayesian Modeling for Estimating Shared Hidden States with Application to Tracking

We consider a problem of estimating shared hidden states of stochastic time–series models from individual observations. To solve the problem, we formulate the problem with hierarchical Bayesian Models and propose a particle filter, which yields a numerical solution to sequential Bayesian estimation, for the hierarchical models. The proposed method can be applied to the problem of tracking an extended object or a group of objects moving in formation. We decompose the state space into the shared and unshared substates, assuming that the individual unshared substate independently evolves with time. This assumption enables us to treat multiple targets individually. Experiments with numerical and real image sequences show the effectiveness of the proposed method.

Stochastic volatility models for ordinal-valued time series with application to finance

In this paper, we introduce a new class of models, called ordinal-response stochastic volatility models, by combining an ordinal-response model and the idea of stochastic volatility. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation, we develop an efficient grouped move multigrid Monte Carlo sampler. This sampler is based on a scale transformation group, whose elements operate on the random samples of a certain conditional distribution. Also volatility estimates are provided. For illustration, we apply our new model class to price changes of the IBM stock. Dependencies on covariates are quantified and compared with theoretical results for such processes.

A comparative modeling analysis of multiscale temporal variability of rainfall in Australia

The effects of long‐term natural climate variability and human‐induced climate change on rainfall variability have become the focus of much concern and recent research efforts. In this paper, we present the results of a comparative analysis of observed multiscale temporal variability of rainfall in the Perth, Newcastle, and Darwin regions of Australia. This empirical and stochastic modeling analysis explores multiscale rainfall variability, i.e., ranging from short to long term, including within‐storm patterns, and intra‐annual, interannual, and interdecadal variabilities, using data taken from each of these regions. The analyses investigated how storm durations, interstorm periods, and average storm rainfall intensities differ for different climate states and demonstrated significant differences in this regard between the three selected regions. In Perth, the average storm intensity is stronger during La Niña years than during El Niño years, whereas in Newcastle and Darwin storm duration is longer during La Niña years. Increase of either storm duration or average storm intensity is the cause of higher average annual rainfall during La Niña years as compared to El Niño years. On the other hand, within‐storm variability does not differ significantly between different ENSO states in all three locations. In the case of long‐term rainfall variability, the statistical analyses indicated that in Newcastle the long‐term rainfall pattern reflects the variability of the Interdecadal Pacific Oscillation (IPO) index, whereas in Perth and Darwin the long‐term variability exhibits a step change in average annual rainfall (up in Darwin and down in Perth) which occurred around 1970. The step changes in Perth and Darwin and the switch in IPO states in Newcastle manifested differently in the three study regions in terms of changes in the annual number of rainy days or the average daily rainfall intensity or both. On the basis of these empirical data analyses, a stochastic rainfall time series model was developed that incorporates the entire range of multiscale variabilities observed in each region, including within‐storm, intra‐annual, interannual, and interdecadal variability. Such ability to characterize, model, and synthetically generate realistic time series of rainfall intensities is essential for addressing many hydrological problems, including estimation of flood and drought frequencies, pesticide risk assessment, and landslide frequencies.

Development of Autoregressive Time Series Model for Prediction of Rainfall and Runoff for Manshara Watershed of Lower Gomati Catchment

A study was conducted to develop a stochastic time series model for prediction of annual rainfall and runoff in Manshara watershed of lower Gomati catchment. This is one of the sub-watersheds of lower Gomati catchment and has anareaofll.18 km2• The developed model is based on 13 years data from 1991 to 2003. Autoregressive (AR) model of order 0, 1 and 2 proposed by Kottegoda and Horder (1980) were tried. The goodness off it and adequacy of models were tested by Box-Pierce Portmonteau test, Akaike Information Criterion (AlC) and various statistical characteristics viz., Mean Forecast Error (MFE), Mean Absolute Error (MAE), Mean Relative Error (MRE), Mean Square Error (MSE), Root Mean Square Error (RMSE) and Integral Square Error (lSE). Based on the results, it was concluded that AR (1) model can be effectively used for prediction of rainfall and runoff in Manshara watershed.

A note on pricing inflation-indexed life annuities

This paper deals with the topic of inflation protection of pensions and the pricing process for inflation-indexed life annuities. Several ways of partial indexation of pensions are taken into consideration. Future inflation paths are obtained by simulation of a stochastic time series model. The main advantage of the proposed methodology is that it allows the pricing of partially inflation-indexed pensions. The pricing process is based on the hypothesis that the annuities provider guarantees a certain level of the real interest rate. Certain numerical results are obtained. Taking into account that inflation is generated by autoregressive processes of order one AR(1), empirical distributions of the expected present value (EPV) are determined for some partial inflation-indexed life annuities. Numerical results achieved for an AR(1) model that describes the evolution of the inflation rate in Spain during the period 1962–2005 are also presented. Results gained allow the comparison of the mean and standard deviation calculated on the basis of empirical distributions of the EPV for various types of partially indexed annuities, and also for various values of AR(1) model parameters. By flexible offers, insurers may meet the expectations of the annuitants, regarding both price and guaranteed protection against inflation.

A method for coupling daily and monthly time scales in stochastic generation of rainfall series

Stochastic generation of hydrological time series is a useful tool for the design and management of water resources systems. One of the shortcomings of many available models for stochastic generation of daily rainfall data is that they are unable to preserve satisfactorily key statistical properties simultaneously at daily, monthly and annual time scales. In this paper, a method for coupling two different time scales of stochastic hydrological time series models is introduced. The key feature of the method is to first generate two resembling time series, one preserving key statistical properties at a finer time scale and the other at a coarser time scale. Adjustment is then made to the finer time scale series so that this series becomes consistent with the coarser time scale series. Because the initial two time series resemble each other, the adjustment is kept small. In the paper, the technique for generating two resembling time series is described. The implementation of the method for coupling daily and monthly rainfall series is demonstrated. Test results of the method using rainfall data from a number of sites around Australia showed that the coupling method was able to generate daily rainfall time series that preserved satisfactorily some key statistical properties at daily, monthly and even annual time scales.

Mimicking Protein Dynamics by the Integration of Elastic Network Model with Time Series Analysis

Anisotropic network model (ANM) is a coarse-grained normal mode analysis that is widely used for describing the collective motions of proteins around their native structure. In this work, protein dynamics along ANM modes are constructed by linear stochastic time series models extracted from molecular dynamics (MD) simulations, and these models are simulated to mimic the dynamics of a relatively small protein, tendamistat. It is found that ANM modes are at least as successful as principal components analysis in explaining different conformational subspaces, and the nonstationary character of ANM modes is a further advantage. The significant reduction in computation time makes time series simulations a promising alternative to the standard requirement of performing multiple long MD runs especially in water, provided that a single short MD is available for extracting the models and some energy restrictions are performed during the moves.

Análisis de series temporales del coste de los grupos terapéuticos más utilizados en un servicio de medicina intensiva

To determine the evolution of the most common drug treatment groups in an intensive care unit over a period of seven years, characterise the time-cost relationship and establish an ARIMA prediction model using Box-Jenkins methodology. A retrospective analysis of the costs of thirteen drug treatment groups was carried out in an intensive care unit with 19 beds between the period of 1998 to 2004. The monthly cost of these treatment groups constituted the time series. The descriptive analysis was carried out by means of descriptive statistics and graphs. The trend was analysed by means of smoothing by weighted local regression, and seasonality was analysed by multiple linear regression. Stochastic models for time series were developed using Box-Jenkins methodology for descriptive and forecasting purposes. 70% of drug costs are generated by thirteen groups. Three of these groups display a downward trend, four have an upward trend and the remaining groups do not display any significant trend. Seasonality is only relevant in series with upward trends. The ARIMA model allows models to be obtained for seven series. The descriptive cost analysis, the determination of trends and the analysis of seasonality provide information about the dynamics in drug use in an intensive care unit. However, the use of ARIMA models to optimise the planning of treatment resources in these types of hospital units is still extremely limited.

EVALUATION OF THE QUANTILES OF THE NEYMAN-SCOTT RAINFALL MODEL

The serial application of a stochastic rainfall time series model and a rainfall-runoff model is an effective option in the event when historical discharge records are inadequate for determining quantile flood flows crucial in flood control applications. In this study, the Neyman-Scott clustered Poisson rectangular pulse rainfall model was applied to generate synthetic hourly and daily rainfall time series. This model was evaluated for quantiles for the different areas of Kamishiiba (Kyushu), Naha (Okinawa), and Sapporo (Hokkaido) in Japan. Sets of parameters were determined based on combinations of moments of the historical records. The quantiles of each synthetic time series were compared to the historical counterparts, yielding mixed results. In general, the model proved effective in matching the historical quantile except in periods in which a combination of rainfall sources such as convective, typhoon and/or frontal rainfall was dominant. An ideal combination of historical moments for generating model parameters for the objective was determined for the mentioned study areas, although it is recommended to employ a similar methodical test of moment combinations for regions elsewhere.

Reliable conjunctive use rules for sustainable irrigated agriculture and reservoir spill control

We develop optimal conjunctive use water management strategies that balance two potentially conflicting objectives: sustaining irrigated agriculture during droughts and minimizing unnecessary spills and resulting water losses from the reservoir during wet periods. Conjunctive use is specified by a linear operating rule, which determines the maximum surface water release as a function of initial reservoir storage. Optimal strategies are identified using multiobjective interannual optimization for sustainability and spill control, combined with gradient‐based annual profit maximization. Application to historical conditions in the irrigated system of the Yaqui Valley, Mexico, yields a Pareto curve of solutions illustrating the trade‐off between sustaining agriculture and minimizing spills and water losses. Minimal water losses are obtained by maximizing surface water use and limiting groundwater pumping, such that reservoir levels are kept sufficiently low. Maximum agricultural sustainability, on the other hand, results from increased groundwater use and keeping surface water reservoir levels high during wet periods. Selected optimal operating rules from the multiobjective optimization are tested over a large number of equally probable streamflow time series, generated with a stochastic time series model. In this manner, statistical properties, such as the mean sustainability and sustainability percentiles, are determined for each optimal rule. These statistical properties can be used to select rules for water management that are reliable over a wide range of streamflow conditions.

Estimating market risk with neural networks

We consider stochastic volatility models for discrete financial time series of the nonlinear autoregressive-ARCH type with exogenous components.We discuss how the trend and volatility functions determining the process may be estimated nonparametrically by least-squares fitting of neural networks or, more generally, of functions from other parametric classes having a universal approximation property. We prove consistency of the estimates under conditions on the rate of increase of function complexity. The procedure is applied to the problem of quantifying market risk, i.e. of calculating volatility or value-at-risk from the data taking not only the time series of interest but additional market information into account. As an application, we study some stock prices series and compare our approach with the common method based on fitting a GARCH(1,1)-model to the data