Periodic Autoregressive Model Research Articles

Investigating the ability of periodically correlated (PC) time series models to forecast the climate index

Considering the importance of climate change and its effects, especially in recent decades, the forecast of future climate conditions can be useful in managing and planning to reduce its impacts. The hypothesis of this study is that in periodic data series, such as seasonal (3-month) and monthly data, the periodically correlated time series models (PC) have a more ability to predict data series. Therefore, in this research using climatic data series of 18 synoptic stations during 1967–2017 over Iran (with different climate conditions and suitable spatial distribution), initially, the climate conditions based on united nation environmental program (UNEP) aridity index (UAI) in seasonal time scale were assessed, and then, using PC models including Periodic Autoregressive Moving Average (PARMA), Periodic Moving Average (PMA) and Periodic Autoregressive (PAR) the UAI from 2018 to 2030 were predicted and finally, for increasing the applicability of the results of the research the trend of changes in UAI data series on observed data (during 1967–2017) and observed and forecasted data (during 1967–2030) were assessed and compared. The results showed calculated UAI at all stations were periodical (significantly at 0.05% level) and among different PC time series models such as PARMA, PMA and PAR, the PAR model with order 22 [PAR (22)] was the best time series model that fitted in all data series at all stations. The R-squared between the observed and the simulated [based on PAR (22) model] UAI from 1967 to 2017 at all stations were more than 0.610 (significantly at 0.01% level) and the R-squared between the observed and the predicted [based on PAR (22) model] UAI from 2013 to 2017 for validating fitted models at all stations were more than 0.659 (significantly at 0.01% level). Trend assessment of climate conditions showed the climate conditions will be dryer at 94.44% (17 out of 18) of stations (only at Gorgan, the climate conditions will be more humid).

S6CRISPR GENOME EDITING BASED ISOGENIC INDUCED PLURIPOTENT STEM CELL SYSTEM FOR SCHIZOPHRENIA DISEASE MODELING

Among the solutions to improve the integration of intermittent solar system, solar irradiation prediction is an essential process. This kind of prediction is a highly complex problem and requires highly robust and reliable statistical models for its simulation. The current research is devoted on the implementation of time series formalism which is based on the periodic autoregressive model (PAR) coupled with a power transform (Box–Cox; BC) of data to stabilize variance. A new and robust functional model is proposed based on the prediction intervals approach whose results in term of efficiency (prediction interval coverage probability) and interest (normalized mean interval length) are similar or better than classical prediction tools based on bootstrap utilization. In the deterministic case, the PAR coupled with BC transform gives more mixed results, but for most cases, the classical tools, like persistence, smart persistence, auto-regression, and artificial neural network fail to compete with PAR or PAR-BC models.

Multiple changepoint detection for periodic autoregressive models with an application to river flow analysis

In river flow analysis and forecasting there are some key elements to consider in order to obtain reliable results. For example, seasonality is often accounted for in statistical models because climatic oscillations occurring every year have an obvious impact on river flow. Further sources of alteration could be caused by changes in reservoir management, instrumentation or even unexpected shifts in climatic conditions. When these changes are ignored the statistical results can be strongly misleading. This paper develops an automatic procedure to estimate number and locations of changepoints in Periodic AutoRegressive models. These latter have been extensively used for modelling seasonality in hydrology, climatology, economics and electrical engineering, but there are very few papers devoted also to changepoints detection, moreover being limited to changes in mean or variance. In our proposal we allow the model structure as a whole to change, and estimation is performed by optimizing an objective function derived from the Information Criterion using Genetic Algorithms. The proposed methodology is brought out through the example of three river flows, for which we built models with possible changepoints and evaluated their forecasting accuracy by means of Root Mean Square Error, Mean Absolute Error and Mean Absolute Percentage Error. The last years of data sets have been omitted from the selection and estimation procedure and were then used to forecast. Comparisons with literature on river flow forecasting confirms the efficiency of our proposal.

Periodic autoregressive models with closed skew-normal innovations

This paper is concerned with the estimation problem of a periodic autoregressive model with closed skew-normal innovations. The closed skew-normal (CSN) distribution has some useful properties similar to those of the Gaussian distribution. Maximum likelihood (ML), Maximum a posteriori (MAP) and Bayesian approaches are proposed and compared in order to estimate the model parameters. For the Bayesian approach, the Gibbs sampling algorithm and for computing the ML and MAP estimations, the expectation–maximization algorithms are performed. The simulation studies are then conducted to compare the frequentist average losses of competing estimators and to study the asymptotic properties of the given estimators. The proposed model and methods developed in this paper are also applied to a real time series. The accuracy of the CSN and Gaussian models is compared by cross validation criterion.

Parsimonious periodic autoregressive models for time series with evolving trend and seasonality

This paper proposes an extension of Periodic AutoRegressive (PAR) modelling for time series with evolving features. The large scale of modern datasets, in fact, implies that the time span may subtend several evolving patterns of the underlying series, affecting also seasonality. The proposed model allows several regimes in time and a possibly different PAR process with a trend term in each regime. The means, autocorrelations and residual variances may change both with the regime and the season, resulting in a very large number of parameters. Therefore as a second step we propose a grouping procedure on the PAR parameters, in order to obtain a more parsimonious and concise model. The model selection procedure is a complex combinatorial problem, and it is solved basing on genetic algorithms that optimize an information criterion. The model is tested in both simulation studies and real data analysis from different fields, proving to be effective for a wide range of series with evolving features, and competitive with respect to more specific models.

Empirical study of robust estimation methods for PAR models with application to the air quality area

This paper compares three estimators for periodic autoregressive (PAR) models. The first is the classical periodic Yule-Walker estimator (YWE). The second is a robust version of YWE (RYWE) which uses the robust autocovariance function in the periodic Yule-Walker equations, and the third is the robust least squares estimator (RLSE) based on iterative least squares with robust versions of the original time series. The daily mean particulate matter concentration (PM10) data is used to illustrate the methodologies in a real application, that is, in the Air Quality area.

SEASONAL AND PERIODIC AUTOREGRESSIVE TIME SERIES MODELS USED FOR FORECASTING ANALYSIS OF RAINFALL DATA

The amount of rainfall received over an area is an important factor in assessing availability of water to meet various demands for agriculture, industry, irrigation, generation of hydroelectricity and other human activities. In our study, we consider seasonal and periodic time series models for statistical analysis of rainfall data of Punjab, India. In this research paper we apply the Seasonal Autoregressive Integrated Moving Average and Periodic autoregressive model to analyse the rainfall data of Punjab. For evaluation of the model identification and periodic stationarity the statistical tool used are PeACF and PePACF. For model comparison we use Root mean square percentage error and forecast encompassing test. The results of this research will provide local authorities to develop strategic plans and appropriate use of available water resources.

Pronóstico de caudales medios mensuales del rio caplina, aplicando redes neuronales artificiales (rna) y modelo autorregresivo periódico de primer orden par (1)

Pronóstico de caudales medios mensuales del rio caplina, aplicando redes neuronales artificiales (rna) y modelo autorregresivo periódico de primer orden par (1) Forecast for mean monthly discharge of the caplina river, by applying artificial neural network (rna) and periodic Autoregressive model par (1) Pino Vargas Edwin, Siña Espinoza Luis, Román Arce Carmen Programa de Doctorado en Recursos Hídricos / U.N.Agraria La Molina, Lima Perú, epino68@hotmail.com Universidad Nacional Jorge Basadre G. Tacna, lucho_sies@hotmail.com Universidad Nacional Jorge Basadre G. Tacna, roman_carmen@hotmail.com DOI: https://doi.org/10.33017/RevECIPeru2011.0025/ RESUMEN El rio Caplina es el principal tributario de la cuenca hidrográfica del mismo nombre; tiene una extensión de 4 239,09 km2, esto hace que sea una de las principales fuentes de abastecimiento de agua para distintos usos en la ciudad de Tacna. Por esta razón diversas entidades se han interesado en conocer la disponibilidad hídrica actual y futura del rio Caplina, ya que conocer dichos valores es de fundamental importancia para el planeamiento y manejo de los sistemas de recursos hídricos. Los modelos estocásticos han sido durante largo tiempo, la alternativa más común en la predicción de caudales. Actualmente, las herramientas de computación inteligente como las redes neuronales artificiales, especialmente las redes multi-capas con algoritmo de retro-propagación. En este contexto, la actual investigación centro sus esfuerzos en la aplicación de las redes neuronales a la predicción de los caudales medios mensuales del río Caplina-Estación Bocatoma Calientes, desarrollo de modelos de redes neuronales a partir de datos de caudales, precipitación y evaporación, así como la evaluación de la capacidad de desempeño frente a modelos estocásticos. De esta manera, se desarrollaron 10 modelos de redes neuronales artificiales con distintas arquitecturas, cuyo entrenamiento se realizo con un primer subconjunto de datos correspondientes al periodo 1939 – 1999, y su validación con un segundo subconjunto de datos del periodo 2000 – 2006. Los modelos de redes neuronales artificiales mostraron comparativamente mejor desempeño en materia de predicción frente a un modelo autorregresivo periódico de primer orden PAR (1). Descriptores: Cuenca Caplina, Redes Neuronales Artificiales, Series de Tiempo. ABSTRACT Caplina river is the main tributary of the hydrographic basin of the same name, It has an extension of 4 239,09 km2, because of this reason it is one of the principal sources of water supply for different uses in Tacna's city. For this reason diverse entities have been interested in knowing the water current and future availability of the river Caplina, because know the above mentioned values performs is the fundamental importance for the planning and managing of the systems of water resources. The stochastic models have been during long time, the most common alternative in the prediction of flows. Nowadays, the tools of intelligent computation like the artificial neural networks, specially the networks you multi-geld with algorithm of retro-spread. In this context, the current investigation center his efforts on the application of the neural networks to the prediction of the average monthly flows of the river Caplina-station Bocatoma Calientes, model development of neural networks from information of flows, rainfall and evaporation, as well as the evaluation of the capacity of performance opposite to stochastic models. So, 10 models of artificial neural networks were developed with different architectures, which training was realize with the first subset of information corresponding to the period 1939 - 1999, and his validation with the second subset of information of the period 2000 - 2006. The models of artificial neural networks showed comparatively better performance as for prediction opposite to a periodic autoregressive model of the first order PAR (1). Keywords: Caplina Basin, artificial neural networks, Series of Time.

Hydrological natural inflow and climate variables: Time and frequency causality analysis

Numbers of studies have proved the significant influence of climate variables on hydrological series. Considering the pivotal role of the hydroelectric power plants play in the electricity production in Brazil this paper considers the natural hydrological inflow data from 15 major basins and 8 climate variables containing 7 El Niño Southern Oscillation proxies and the sunspot numbers. The causal relationships between hydrological natural inflows and climate variables are investigated by adopting and comparing 5 different causality detection methods (Granger Causality test, Frequency Domain Causality test, Convergent Cross Mapping Causality test, Single Spectrum Analysis (SSA) Causality test and Periodic Autoregressive Model Causality test) that cover both well established and novel empirical approaches. Both time domain and frequency domain causality tests gain valid evidences of unidirectional causality for a group of series; CCM achieved unidirectional causality for 18% of pairs and overwhelmingly indicated the opposite direction of causality; a mixture of results are concluded by SSA causality test; PAR based causality test obtained six unidirectional causality, but only one is really significant.

On the estimation problem of periodic autoregressive time series: symmetric and asymmetric innovations

ABSTRACTPeriodic autoregressive (PAR) models with symmetric innovations are widely used on time series analysis, whereas its asymmetric counterpart inference remains a challenge, because of a number of problems related to the existing computational methods. In this paper, we use an interesting relationship between periodic autoregressive and vector autoregressive (VAR) models to study maximum likelihood and Bayesian approaches to the inference of a PAR model with normal and skew-normal innovations, where different kinds of estimation methods for the unknown parameters are examined. Several technical difficulties which are usually complicated to handle are reported. Results are compared with the existing classical solutions and the practical implementations of the proposed algorithms are illustrated via comprehensive simulation studies. The methods developed in the study are applied and illustrate a real-time series. The Bayes factor is also used to compare the multivariate normal model versus the multivariate skew-normal model.

Solar radiation synthetic series for power purchase agreements.

The present paper proposes a methodology based on the implementation and assessment of autoregressive (AR) solar radiation models for generating synthetic series and providing guidance on bidding strategies for power purchase agreements. The work considered conventional and periodic AR models with different lag orders, assessing the models against real solar radiation measurements. The synthetic series generation process developed 1000 1-year monthly solar radiation scenarios that were later employed for simulating electric energy production and power purchase agreement models. This application allowed one to evaluate the risk associated with the energy supply security, supporting bidding strategies in energy auctions. A real study case is also illustrated in detail, referring to a spot in the Brazilian best irradiance area.

Periodic autoregressive forecasting of global solar irradiation without knowledge-based model implementation

Reliable forecasting methods increase the integration level of stochastic production and reduce cost of intermittence of photovoltaic production. This paper proposes a solar forecasting model for short time horizons, i.e. one to six hours ahead. In this time-range, machine learning methods have proven their efficiency. But their application requires that the solar irradiation time series is stationary which can be realized by calculating the clear sky global horizontal solar irradiance index (CSI), depending on certain meteorological parameters. This step is delicate and often generates additional uncertainty if conditions underlying the calculation of the CSI are not well-defined and/or unknown. As a novel alternative, we introduce a so-called periodic autoregressive (PAR) model. We discuss the computation of post-sample point forecasts and forecast intervals. We show the forecasting accuracy of the model via a real data set, i.e., the global horizontal solar irradiation (GHI) measured at two meteorological stations located at Corsica Island, France. In particular, and as opposed to methods based on CSI, a PAR model helps to improve forecast accuracy, especially for short forecast horizons. In all the cases, PAR is more appropriate than persistence, and smart persistence. Moreover, smart persistence based on the typical meteorological year gives more reliable results than when based on CSI.

Strategic bidding for a price-maker hydroelectric producer: Stochastic dual dynamic programming and Lagrangian relaxation

ABSTRACTIn bid-based markets, energy producers seek bidding strategies that maximize their revenue. In this article, we seek the maximum-revenue bidding schedule for a single price-maker hydroelectric producer. We assume the producer sells energy in the day-ahead electricity market and has the ability to impact the market-clearing price with its bids. To obtain the price-maker hydroelectric producer’s bidding schedule, we use a combination of Stochastic Dual Dynamic Programming and Lagrangian relaxation. In this framework, we dualize the water balance equations, allowing an exact representation of the non-concave immediate revenue function, while preserving the concave shape of the future revenue function. We model inflow uncertainty and its stagewise dependence by a periodic autoregressive model. To demonstrate our approaches’ utility, we model Honduras’ electricity market assuming that the thermal producers act as price-takers and that one price-maker hydro producer operates all of the hydroelectric plants.

Forecasting seasonal time series data: a Bayesian model averaging approach

A flexible Bayesian periodic autoregressive model is used for the prediction of quarterly and monthly time series data. As the unknown autoregressive lag order, the occurrence of structural breaks and their respective break dates are common sources of uncertainty these are treated as random quantities within the Bayesian framework. Since no analytical expressions for the corresponding marginal posterior predictive distributions exist a Markov Chain Monte Carlo approach based on data augmentation is proposed. Its performance is demonstrated in Monte Carlo experiments. Instead of resorting to a model selection approach by choosing a particular candidate model for prediction, a forecasting approach based on Bayesian model averaging is used in order to account for model uncertainty and to improve forecasting accuracy. For model diagnosis a Bayesian sign test is introduced to compare the predictive accuracy of different forecasting models in terms of statistical significance. In an empirical application, using monthly unemployment rates of Germany, the performance of the model averaging prediction approach is compared to those of model selected Bayesian and classical (non)periodic time series models.

Functional Autoregressive Models: An Application to Brazilian Hourly Electricity Load

The features of the electrical demand and its response to climate variables impose three main features to the load curves: (1) strong inertia, (2) Each observation is a function and (3) cyclical movements. Based on that, we present a generalization of periodic autoregressive models for functional data with functional covariates. We also estimate a functional autoregressive model, where the periodicity of the parameters is induced by harmonic acceleration operators. Using this method, we handle annual load curves, while the first takes into account the daily load curves. We use splines to represent the smooth functions underlying the points. The estimators of the parameters embody the smoothness restrictions enforced on load curves. We compare the Root Mean Squared Error (RMSE) of our models with the RMSE of a benchmark model. We apply this framework to a dataset from the Southeast/Midwest Brazilian Interconnected Power System, from 2003/01/01 to 2011/01/20.

Estimation and identification of periodic autoregressive models with one exogenous variable

This paper analyzes the identification and estimation procedures for periodic autoregressive models with one exogenous variable (PARX). The identification of the optimal PARX model is based on the use of a genetic algorithm combined with the Bayes information criterion. The estimation of the parameters relies on the least squares method and their asymptotic properties are studied. Two simulation experiments are performed and indicate the success of the suggested method. A PARX model is used to study the relationship between the catch-per-unit-effort and the sea surface temperature as exogenous variable for the shrimp French Guiana fishery from January 1989 to December 2012.

PAR(p)-vine copula based model for stochastic streamflow scenario generation

Synthetic streamflow data is vital for the energy sector, as it feeds stochastic optimisation models that determine operational policies. Considered scenarios should differ from each other, but be the same from a statistical point of view, i.e., the scenarios must preserve features of the original time series such as the mean, variance, and temporal dependence structures. Traditionally, linear models are applied for this task. Recently, the advent of copulas has led to the emergence of an alternative that overcomes the drawbacks of linear models. In this context, we propose a methodology based on vine copulas for the stochastic simulation of periodic streamflow scenarios. Copula-based models that focus on single-site inflow simulation only consider lag-one time dependence. Therefore, we suggest an approach that incorporates lags that are greater than one. Furthermore, the proposed model deals with the strong periodicity that is commonly present in monthly streamflow time series. The resulting model is a non-linear periodic autoregressive model. Our results indicate that this model successfully simulates scenarios, preserving features that are observed in historical data.

Periodic Gamma Autoregressive Model: An application to the Brazilian hydroelectric system

Hydrological time series forecasting play a crucial role in the Brazilian Power System since most of the power generated comes from hydroelectric power plants. A minor improvement in the predictive ability of water inflows time series might lead both to: (i) lower costs to final consumers; and (ii) higher power reliability. This paper explores Periodic Gamma Autoregressive Models (PGAR) to model brazilian water inflows time series. This type of time series has some features which seem to be more adaptable to Gamma models, like nonnegative random values and asymmetric pattern. The main purpose of this study is to compare periodic Normal and Lognormal models to PGAR. The results suggest that: (i) both Gamma and Lognormal models perform better than Normal model; and (ii) the Gamma model is a good alternative to the Lognormal model.

Monthly streamflow forecast for National Interconnected System (NIS) using Periodic Auto-regressive Endogenous Models (PAR) and Exogenous (PARX) with climate information

ABSTRACT This study aims to find a seasonal streamflow forecast model simultaneous to all stations of SIN using periodic autoregressive models with exogenous variables (PARX) using climate indexes. Comparing the results from PAR and PARX Models, this research analyzes the impact on forecasts by using climate information. The proposed models for streamflow forecast has been carried out using natural streamflow data from Operador Nacional do Sistema (ONS) and statistical techniques (such as multiple linear regression and stepwise method to choose explanatory variables). On 27 climate indexes utilized, 4 of them are suggested in this work. The performance analysis methodology is based on the ELECTRE method further the NASH coefficient, the mean absolute percentage error, the multi-criteria distance and correlation. Forecasts with one month lead, the PAR models present better results for most stations of SIN within seasons DJF, MAM, and JJA, while for SON season there is greater efficiency from PARX model. This kind of model shows better performance during dry season in the basins at Northern Brazil – Amazonas and Araguaia-Tocantins; Central-Eastern Brazil – Eastern Atlantic and the most rivers located in the Paraná basin.

Previsões multiescala de vazões para o sistema hidrelétrico brasileiro utilizando ponderação bayesiana de modelos (BMA)

RESUMO O uso de sistemas eficientes de previsão de afluências nas diversas escalas temporais permite otimizar a operação do conjunto de reservatórios hidrelétricos brasileiros, elevando o grau de segurança no fornecimento de energia elétrica e minimizando os custos operacionais. Entretanto, os modelos atuais de previsão utilizados pelo Operador Nacional do Sistema Elétrico (ONS) tendem a ser limitados no horizonte de previsão e na modelagem da dependência existente entre as diversas escalas de tempo, reduzindo a qualidade das previsões. Neste trabalho é proposta uma nova contribuição para os modelos de previsão de afluências em uso pelo ONS a partir do conceito de ponderação bayesiana de modelos (BMA), que permite integrar previsões mensais e semanais de vazões com objetivo de melhorar o desempenho das previsões semanais. As previsões mensais são obtidas por meio de um modelo periódico auto-regressivo exógeno (PARX), que busca captar a persistência das vazões na parte auto-regressiva e a contribuição do escoamento superficial na parcela exógena por meio do uso de informações climáticas de larga escala. Previsões semanais de afluência com até seis semanas de antecedência são obtidas a partir das informações disponibilizadas pelo ONS nos relatórios do Programa Mensal de Operação (PMO). A metodologia proposta é aplicada em séries de afluências semanais aos 28 principais reservatórios hidroelétricos brasileiros. Os resultados de previsão semanal de afluências obtidos com a ponderação das saídas dos modelos de previsão semanal e mensal indicam uma melhoria significativa em indicadores de desempenho de previsões (NS, MAPE e DM) quando comparados com os resultados de previsão oriundos do modelo semanal isolado. Os ganhos obtidos nos indicadores de desempenho são mais significativos a partir da segunda semana de antecedência. A abordagem proposta é flexível em termos de implementação, permitindo integrar outras escalas de previsão assim como diferentes modelos preditivos (por exemplo, modelos de base física).