Stationary Time Series Models Research Articles

Modelling Palaeoecological Time Series Using Generalised Additive Models

In the absence of annual laminations, time series generated from lake sediments or other similar stratigraphic sequences are irregularly spaced in time, which complicates formal analysis using classical statistical time series models. In lieu, statistical analyses of trends in palaeoenvironmental time series, if done at all, have typically used simpler linear regressions or (non-) parametric correlations with little regard for the violation of assumptions that almost surely occurs due to temporal dependencies in the data or that correlations do not provide estimates of the magnitude of change, just whether or not there is a linear or monotonic trend. Alternative approaches have used LOESS-estimated trends to justify data interpretations or test hypotheses as to the causal factors without considering the inherent subjectivity of the choice of parameters used to achieve the LOESS fit (e.g. span width, degree of polynomial). Generalized additive models (GAMs) are statistical models that can be used to estimate trends as smooth functions of time. Unlike LOESS, GAMs use automatic smoothness selection methods to objectively determine the complexity of the fitted trend, and as formal statistical models, GAMs, allow for potentially complex, non-linear trends, a proper accounting of model uncertainty, and the identification of periods of significant temporal change. Here, I present a consistent and modern approach to the estimation of trends in palaeoenvironmental time series using GAMs, illustrating features of the methodology with two example time series of contrasting complexity; a 150-year bulk organic matter δ15N time series from Small Water, UK, and a 3000-year alkenone record from Braya-So, Greenland. I discuss the underlying mechanics of GAMs that allow them to learn the shape of the trend from the data themselves and how simultaneous confidence intervals and the first derivatives of the trend are used to properly account for model uncertainty and identify periods of change. It is hoped that by using GAMs greater attention is paid to the statistical estimation of trends in palaeoenvironmental time series leading to more a robust and reproducible palaeoscience.

A Time Series Model Comparison for Monitoring and Forecasting Water Quality Variables

The monitoring and prediction of water quality parameters are important tasks in the management of water resources. In this work, the performances of time series statistical models were evaluated to predict and forecast the dissolved oxygen (DO) concentration in several monitoring sites located along the main river Vouga, in Portugal, during the period from January 2002 to May 2015. The models being compared are a regression model with correlated errors and a state-space model, which can be seen as a calibration model. Both models allow the incorporation of water quality variables, such as time correlation or seasonality. Results show that, for the DO variable, the calibration model outperforms the regression model for sample modeling, that is, for a short-term forecast, while the regression model with correlated errors has a better performance for the forecasting h-steps ahead framework. So, the calibration model is more useful for water monitoring using an online or real-time procedure, while the regression model with correlated errors can be applied in order to forecast over a longer period of time.

A procedure to increase the power of Granger-causal analysis through temporal smoothing

BackgroundHow the human brain coordinates network activity to support cognition and behavior remains poorly understood. New high-resolution recording modalities facilitate a more detailed understanding of the human brain network. Several approaches have been proposed to infer functional networks, indicating the transient coordination of activity between brain regions, from neural time series. One category of approach is based on statistical modeling of time series recorded from multiple sensors (e.g., multivariate Granger causality). However, fitting such models remains computationally challenging as the history structure may be long in neural activity, requiring many model parameters to fully capture the dynamics. New MethodWe develop a method based on Granger causality that makes the assumption that the history dependence varies smoothly. We fit multivariate autoregressive models such that the coefficients of the lagged history terms are smooth functions. We do so by modelling the history terms with a lower dimensional spline basis, which requires many fewer parameters than the standard approach and increases the statistical power of the model. ResultsWe show that this procedure allows accurate estimation of brain dynamics and functional networks in simulations and examples of brain voltage activity recorded from a patient with pharmacoresistant epilepsy. Comparison with Existing MethodThe proposed method has more statistical power than the Granger method for networks of signals that exhibit extended and smooth history dependencies. ConclusionsThe proposed tool permits conditional inference of functional networks from many brain regions with extended history dependence, furthering the applicability of Granger causality to brain network science.

Nonlinear Time Series Modeling: A Unified Perspective, Algorithm and Application

A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution-based Legendre Polynomial (LP)-like nonlinear transformations of the original time series {Y(t)} that enable us to adapt all the existing stationary linear Gaussian time series modeling strategies and make them applicable to non-Gaussian and nonlinear processes in a robust fashion. The emphasis of the present paper is on empirical time series modeling via the algorithm LPTime. We demonstrate the effectiveness of our theoretical framework using daily S&P 500 return data between 2 January 1963 and 31 December 2009. Our proposed LPTime algorithm systematically discovers all the ‘stylized facts’ of the financial time series automatically, all at once, which were previously noted by many researchers one at a time.

Improving the prediction of arbovirus outbreaks: A comparison of climate-driven models for West Nile virus in an endemic region of the United States

Models that forecast the timing and location of human arboviral disease have the potential to make mosquito control and disease prevention more effective. A common approach is to use statistical time-series models that predict disease cases as lagged functions of environmental variables. However, the simplifying assumptions required for standard modeling approaches may not capture important aspects of complex, non-linear transmission cycles. Here, we compared a set of alternative models of human West Nile virus (WNV) in 2004–2017 in South Dakota, USA. We used county-level logistic regressions to model historical human case data as functions of distributed lag summaries of air temperature and several moisture indices. We tested two variations of the standard model in which 1) the distributed lag functions were allowed to change over the transmission season, so that dependence on past meteorological conditions was time varying rather than static, and 2) an additional predictor was included that quantified the mosquito infection growth rate estimated from mosquito surveillance data. The best-fitting model included temperature and vapor pressure deficit as meteorological predictors, and also incorporated time-varying lags and the mosquito infection growth rate. The time-varying lags helped to predict the seasonal pattern of WNV cases, whereas the mosquito infection growth rate improved the prediction of year-to-year variability in WNV risk. These relatively simple and practical enhancements may be particularly helpful for developing data-driven time series models for use in arbovirus forecasting applications.

Volatility models applied to geophysics and high frequency financial market data

This work is devoted to the study of modeling geophysical and financial time series. A class of volatility models with time-varying parameters is presented to forecast the volatility of time series in a stationary environment. The modeling of stationary time series with consistent properties facilitates prediction with much certainty. Using the GARCH and stochastic volatility model, we forecast one-step-ahead suggested volatility with ±2 standard prediction errors, which is enacted via Maximum Likelihood Estimation. We compare the stochastic volatility model relying on the filtering technique as used in the conditional volatility with the GARCH model. We conclude that the stochastic volatility is a better forecasting tool than GARCH (1,1), since it is less conditioned by autoregressive past information.

Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts

This paper examines a bivariate count time series with some curious statistical features: Saffir–Simpson Category 3 and stronger annual hurricane counts in the North Atlantic and eastern Pacific Ocean Basins. As land and ocean temperatures on our planet warm, an intense climatological debate has arisen over whether hurricanes are becoming more numerous, or whether the strengths of the individual storms are increasing. Recent literature concludes that an increase in hurricane counts occurred in the Atlantic Basin circa 1994. This increase persisted through 2012; moreover, the 1994–2012 period was one of relative inactivity in the eastern Pacific Basin. When Atlantic activity eased in 2013, heavy activity in the eastern Pacific Basin commenced. When examined statistically, a Poisson white noise model for the annual severe hurricane counts is difficult to resoundingly reject. Yet, decadal cycles (longer term dependence) in the hurricane counts is plausible. This paper takes a statistical look at the issue, developing a stationary multivariate count time series model with Poisson marginal distributions and a flexible autocovariance structure. Our auto- and cross-correlations can be negative and have long-range dependence; features that most previous count models cannot achieve in tandem. Our model is new in the literature and is based on categorizing and super-positioning multivariate Gaussian time series. We derive the autocovariance function of the model and propose a method to estimate model parameters. In the end, we conclude that severe hurricane counts are indeed negatively correlated across the two ocean basins. Some evidence for long-range dependence is also presented; however, with only a 49-year record, this issue cannot be definitively judged without additional data.

PERAMALAN JUMLAH PENUMPANG KERETA API MENGGUNAKAN METODE ARIMA, INTERVENSI DAN ARFIMA (Studi Kasus : Penumpang Kereta Api Kelas Lokal EkonomiDAOP IV Semarang)

Autoregressive Integrated Moving Average (ARIMA) is stationary time series model after differentiation. Differentiation value of ARIMA method is an integer so it is only able to model in the short term. The best model using ARIMA method is ARIMA([13]; 1; 0) with an MSE value of 1,870844. The Intervention method is a model for time series data which in practice has extreme fluctuations both up and down. In the data plot the number of train passengers was found to be extreme fluctuation. The data used was from January 2009 to June 2017 where fluctuation up significantly in January 2016 (T=85 to T=102) so the intervention model that was suspected was a step function. The best model uses the Intervention step function is ARIMA ([13]; 1; 1) (b=0; s=18; r=0) with MSE of 1124. Autoregressive Fractionally Integrated Moving Average (ARFIMA) method is a development of the ARIMA method. The advantage of the ARFIMA method is the non-integer differentiation value so that it can overcome long memory effect that can not be solve with the ARIMA method. ARFIMA model is capable of modeling high changes in the long term (long term persistence) and explain long-term and short-term correlation structures at the same time. The number of local economy class train passengers in DAOP IV Semarang contains long memory effects, so the ARFIMA method is used to obtain the best model. The best model obtained is the ARMA(0; [1,13]) model with the differential value is 0,367546, then the model can be written into ARFIMA (0; d; [1,13]) with an MSE value of 0,00964. Based on the analysis of the three methods, the best method of analyzing the number of local economy class train passengers in DAOP IV Semarang is the ARFIMA method with the model is ARFIMA (0; 0,367546; [1,13]). Keywords: Train Passengers, ARIMA, Intervention, ARFIMA, Forecasting

Statistical Modeling of Time Series for Ice Accretion Detection on Bridge Cables

AbstractIn the northern regions, ice accretion on bridge cables poses serious risks to the structure as well as to vehicular traffic when ice falls from the cables onto the road. The detection and ...

A least squares-based parallel hybridization of statistical and intelligent models for time series forecasting

Abstract Combining different models is one of the most well established strategies in the literature in order to capture different patterns of the data, lifting limitations of single models, and improve forecasting accuracy. In recent decades, various hybrid models have been developed by combining different models such as linear/nonlinear, supervised/unsupervised fuzzy/crisp, and statistical/intelligent together. Intelligent and statistical techniques due to their unique advantages are one of the most popular and the most widely-used candidates to build hybrid models for time series forecasting. These models are generally combined together in two different schemas: series and parallel. In series schema, components are sequentially used for modeling the underlying data; while in parallel schema, components are separately used and then their results are combined together. In this paper, a new parallel hybrid model is proposed, incorporating autoregressive integrated moving average (ARIMA) and multilayer perceptrons (MLPs), which are one of the most important intelligent and statistical time series models. In addition, a least squares process is used in order to find the optimum weights of each component. The main idea of the proposed model is to employ special features of ARIMA and MLP models in modeling linear and nonlinear patterns in the data simultaneously and to yield the best performance by reasonable computational costs. To evaluate the effectiveness of the least squares based proposed hybrid model (LPHM) in financial forecasting, three well-known benchmark data sets including the closing of Standard & Poor’s 500 index (S&P500), the closing of the Shenzhen Integrated Index (SZII), and the opening of Dow Jones Industrial Average Index (DJIAI) are elected. Empirical results indicate that LPHM outperforms its constituent as well as genetic algorithm based hybrid model (GAHM) and simple average hybrid model (SAHM) in stock price forecasting. While, the computational cost of the proposed model is significantly lower than the GAHM and roughly equal to the SAHM.

Determinants and rates of land degradation: Application of stationary time-series model to data from a semi-arid environment in Kenya

The causes of land degradation in the African drylands have been shown to vary. Some researchers consider climate to be the major contributor to degradation, with anthropogenic factors playing a minor role. Others reverse the significance of these two factors. A third group attributes land degradation to climate and anthropogenic factors equally. This study was undertaken to establish the factors influencing land degradation in a semi-arid environment in southeastern Kenya and the rate of change in vegetation types for a period of 35 years (1973–2007). The reduction in grassland cover was used as an indicator of land degradation. Causes of land degradation were determined by a multiple regression analysis. A log-linear regression analysis was used to establish the rate of vegetation change. The multiple and log-linear regression analyses showed: (1) woody vegetation, livestock population and cultivated area to be the main contributors of reduction in grassland cover in the area, and (2) an increase in undesirable woody species, livestock population and cultivated area had a significant (P<0.05) negative effect on grassland vegetation. Increased human population, low amounts of rainfall and drought showed no significant negative effect on grassland vegetation cover. In conclusion, human and livestock population growth and increased agricultural land have contributed to intensive crop cultivation and overgrazing in the semi-arid lands. This overuse of the semi-arid rangelands has worsened the deterioration of the natural grassland vegetation.

Trends of Tuberculosis in Somaliland’s Young Children after the Conflict and the Role Khat Marfishes Play Its Transmission

After the fall of the central government and the emergence of the recurrent civil conflict in Somalia, many new sociocultural phenomenons that have appeared across the country contributed to the spread of many infectious diseases including TB. One of these social phenomena is a wide spread use of the illicit drug Khat which is predominately used by the Somali males. Mostly khat is chewed in small overcrowded, unhygienic and unventilated makeshift huts known as Marfishes. These Marfishes became the launch pad and the breeding grounds of many infectious diseases that have affected the lives of many Somalis including children. Under-five mortality in somalia is estimated at 200 deaths per 1000 births, which is one of the highest in the world. Approximately one third of these are neonatal deaths, occurring during the first month of life, pneumonia and diarrhea are the main killers each contributing 20-25 percent of all under-five mortality. While these diseases still remained the top major killers, communicable diseases including TB are also a leading cause of death. This paper investigates the incidence and the trends of tuberculosis among the Somali children by using time series statistical models.

Wavelet analysis of uniformly time-modulated processes

ABSTRACTUniformly time-modulated processes (UTMP) offer a simple, though convenient model for many non stationary time series. However, in many applications, dependency is considered as a disturbing factor. For the UTMP using Weierstrass representation of modulating function, we demonstrated that the correlation between coefficients in wavelet domain is a decreasing function of number of wavelet vanishing moments and tends to zero in progressive rate as we move from finer scales to coarser scales.

The strategy of investment in the stock market using modified support vector regression model

Stock indices forecasting has become a popular research issue in recent years. Although many statistical time series models have been applied in stock indices forecasting, they are limited to certain assumptions. Accordingly, the traditional statistical time series models might not be suitable for forecasting real-life stock indices data. Hence, this paper proposes a novel forecasting model to assist investors in determining a strategy for investments in the stock market. The proposed model is called the modified support vector regression model, which is composed of the correlation coefficient method, the sliding window algorithm and the support vector regression model. The results show that the forecasting accuracy of the proposed model is more stable than the existing models in terms of average and standard deviation of the root mean square error (RMSE) and the mean absolute percentage error (MAPE). Accordingly, the proposed model would be used to assist investors in determining a strategy for investing in stocks.

Forecasting models for predicting pod damage of pigeonpea in Varanasi region

Present investigation considers comparison of time series statistical models like autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) with explanatory multiple linear regression model for predicting per cent pod damage in pigeonpea by pod borer for Varanasi region of Uttar Pradesh using 27 years of data (1985-86 to 2011-12).The evaluation of best suited model was assessed by root mean squared error (RMSE). Based on empirical studies, ANN was found to be best suited model with lowest RMSE having forecasted per cent pod damage in pigeonpea by pod borer during the year 2012-13 for Varanasi region.

Evaluation of the “Angelina Jolie Effect” on Screening Mammography Utilization in an Academic Center

PurposeThe aim of this study was to understand the impact on screening mammography at our institution, comparing weekly utilization in the 2 years before and the 2 years after Ms Angelina Jolie disclosed in the New York Times on May 13, 2013, that she had had a prophylactic double mastectomy. MethodsAll 48,110 consecutive screening mammograms conducted at our institution between May 16, 2011, and May 16, 2015, were selected from our electronic medical record system. We used interrupted time series statistical models and graphical methods on utilization data to understand utilization changes before and after Ms Jolie’s news. ResultsThe graphed trend of weekly screening mammogram utilization failed to show changes around the time of interest. Analytical models and statistical tests also failed to show a step change increase or acceleration of utilization around May 2013. However, graphical and time series analyses showed a flattening of utilization in the middle of 2014. ConclusionsIn our well-powered analysis in a large regional breast imaging center, we found no support for the hypothesis that this celebrity news drove increased screening.

An iterative order determination method for time-series modeling in structural health monitoring

Statistical time-series modeling has recently emerged as a promising and applicable methodology to structural health monitoring. In this methodology, an important step is to choose robust and optimal orders of time-series models for extracting damage-sensitive features. In this study, an iterative order determination method is proposed to determine optimal orders based on residual analysis. The proposed technique consists of identifying the best time-series model, determining the maximum orders, and selecting the optimal orders that enable the model to extract uncorrelated residuals. The application of low-pass signal filters to the process of order determination is also evaluated. In a comparative study, the influence of optimal orders on damage is assessed to perceive whether features extracted from optimal models, with and without using low-pass filters, are sensitive to damage. Experimental data of a three-story laboratory frame and a large-scale bridge are applied to demonstrate the performance and capability of the proposed method. Results show that the proposed iterative method is an efficient tool for the determination of optimal orders along with the extraction of uncorrelated residuals.

Gramophone Noise Detection and Reconstruction Using Time Delay Artificial Neural Networks

Gramophone records were the main recording medium for more than seven decades and regained widespread popularity over the past several years. Being an analog storage medium, gramophone records are subject to distortions caused by scratches, dust particles, degradation, and other means of improper handling. The observed noise often leads to an unpleasant listening experience and requires a filtering process to remove the unwanted disruptions and improve the audio quality. This paper proposes a novel approach that employs various feed forward time delay artificial neural networks to detect and reconstruct noise in musical sound waves. A set of 800 songs from eight different genres were used to validate the performance of the neural networks. The performance was analyzed according to the outlier detection and interpolation accuracy, the computational time and the tradeoff between the accuracy and the time. The empirical results of both detection and reconstruction neural networks were compared to a number of other algorithms, including various statistical measurements, duplication approaches, trigonometric processes, polynomials, and time series models. It was found that the neural networks’ outlier detection accuracy was slightly lower than some of the other noise identification algorithms, but achieved a more efficient tradeoff by detecting most of the noise in real time. The reconstruction process favored neural networks with an increase in the interpolation accuracy compared to other widely used time series models. It was also found that certain genres such as classical, country, and jazz music were interpolated more accurately. Volatile signals, such as electronic, metal, and pop music were more challenging to reconstruct and were substantially better interpolated using neural networks than the other examined algorithms.

Assessment of Relationship Between Inflation, Growth and Fiscal Deficit in Albania-An Econometric Approach

The relationship between variables growth, inflation and fiscal deficit is largely debated in economic theory; it is studied also empirically. Both theory and ground research suggest negative relationship between growth and inflation, and between inflation and budget deficit, while there is a controversy about relationship between budget deficit and growth. Based on that, IMF suggests programs of macroeconomic stabilization for countries in course of development like Albania. The IMF expertise and support has been available in Albania through bilateral cooperation programs for more than 20 years beginning in 1991. Support of IMF to Albania has been qualified as success. In our research we study the relationship between the three variables, based on Albanian time series data on these variables. We used classical time series regression and stationary time series models, as well ARDL, threshold and switching regression models to investigate these relationships. Our results support the negative relationship between inflation and growth, a positive relationship between inflation and deficit, but we didn’t discover any relationship between fiscal deficit and growth. A threshold nonlinear relationship best describes dependence between growth and inflation.

Copula-Based Factor Models for Multivariate Asset Returns

Recently, several copula-based approaches have been proposed for modeling stationary multivariate time series. All of them are based on vine copulas, and they differ in the choice of the regular vine structure. In this article, we consider a copula autoregressive (COPAR) approach to model the dependence of unobserved multivariate factors resulting from two dynamic factor models. However, the proposed methodology is general and applicable to several factor models as well as to other copula models for stationary multivariate time series. An empirical study illustrates the forecasting superiority of our approach for constructing an optimal portfolio of U.S. industrial stocks in the mean-variance framework.