Autoregressive Moving-average Time Series Models Research Articles

Nonparametric Control Charts for Monitoring Serial Dependence based on Ordinal Patterns

We consider the problem of monitoring for the existence of serial dependence in real-valued and continuously distributed processes. These can exist when a process goes out-of-control. Besides, as many control charts are designed under the assumption of independent and identically distributed observations, the validity of this assumption needs to be checked. In the literature, the majority of studies handled this problem by using a specific case of autoregressive moving-average time series models. Also a moving-window approach is often considered, which leads to the drawback that at least a window length of observations need to be collected before an out-of-control situation can be detected. Here, we use ordinal patterns and propose charts that are fully nonparametric and distribution-free, have a unique chart design, and can be used almost instantaneously at the start of process monitoring. The proposed control charts do not require any model fitting, thus, eliminating the problems associated with estimation errors, but might be used as part of a Phase-I study. Through a comprehensive performance comparison study under various out-of-control scenarios, the effectiveness of the charts in uncovering serial dependence is shown and recommendations for selection are given. Implementations of the proposed charts are illustrated by using batch yield data from a chemical process.

Dispatch optimization of a concentrating solar power system under uncertain solar irradiance and energy prices

The integration of thermal energy storage into a concentrating solar power system allows for mitigating some of the risk associated with uncertain solar irradiance and uncertain energy prices. We solve a 48 h dispatch optimization model with continually updated conditional point forecasts of both direct normal irradiance (DNI) and electricity prices with a rolling-horizon scheme at hourly resolution over the course of a year. Joint, conditional forecasts for DNI and prices are formed using an autoregressive moving-average time series model with exogenous weather predictors. We guide dispatch using a mixed-integer programming model, but in order to evaluate performance we use the System Advisor Model (SAM) of the National Renewable Energy Laboratory. SAM is a techno-economic simulation model that accounts for plant thermodynamics with higher fidelity. Our conditional DNI forecasts improve annual revenue by 4%–12% over using historical forecasts based on data from previous years. Conditional price forecasts improve annual revenue by 6%–19% in the real-time market over analogous historical forecasts. Updating these forecasts every six hours, rather than every 24 h, further improves annual revenue by 5%–6%. We also investigate a method that values terminal inventory in our dispatch optimization model, again when used in a rolling-horizon scheme.

Evaluating a seasonal autoregressive moving average model with an exogenous variable for short-term timber price forecasting

In this paper roundwood prices were forecasted by means of the following time series models: (1) classical univariate autoregressive moving average (ARIMA), (2) seasonal univariate (SARIMA), and (3) seasonal bivariate with an exogenous variable (SARIMAX). The data consisted of time series of the nominal prices of pine, spruce, beech, birch, and alder roundwood and the construction confidence index (CCI) in Poland for the years 2005–2020. The results indicate that roundwood prices can be evaluated by the implemented time series models, with forecast accuracy depending on the time horizon, the model applied, and tree species. The incorporation of a separate component directly describing seasonal fluctuations into a conventional ARIMA time series model significantly improved the accuracy of roundwood price forecasts exhibiting seasonal variation. The CCI lagged by one to three quarters were found to be significantly correlated with the prices of roundwood. A SARIMAX model incorporating the CCI as a leading variable was able to account for changes in the business cycle, thus increasing the accuracy of short-term forecasts of the prices of roundwood used in the construction industry.

On strong consistency and asymptotic normality of one-step Gauss-Newton estimators in ARMA time series models

ABSTRACT One-step Gauss-Newton estimators for causal and invertible autoregressive moving-average (ARMA) time series models with an unknown mean are considered. A proof of the strong consistency and asymptotic normality of these estimators is provided. In a simulation study, their empirical properties are illustrated in ARMA models and compared to a other estimators: the estimators based on the innovations algorithm procedure, the estimators based on the spectral methods of [Krampe J, Kreiss J-P, Paparoditis E. Estimated Wold representation and spectral-density-driven bootstrap for time series. J R Stat Soc: Ser B (Statist Method). 2018;80:703–726.], and the one-step Gauss-Newton estimators using these methods as preliminary estimators. In the order-one moving-average model, we included the estimator based on the method of moments. The sample mean is used as a preliminary estimator to estimate the mean. These estimators are compared empirically to the maximum Gaussian likelihood estimator with respect to exact biases and mean squared errors.

Investigation of the accuracy of linear and nonlinear time series models in modeling and forecasting of pan evaporation in IRAN

Water evaporation process is one of the main components of the hydrological cycle, according to which the correct estimation of this phenomenon plays an important role in irrigation management and river flow forecasting. Statistical and random models in the form of time series analysis are commonly used methods of estimation and forecasting. In this study, ARMA (autoregressive moving average), ARIMA (autoregressive integrated moving average), PARMA (periodic autoregressive moving average), and BL (bilinear) time series models (TSMs) are used to predict the annual and monthly pan evaporation values from the evaporation stations in several provinces of Iran in a 20-year statistical period. Results showed that PARMA model’s accuracy in term of correlation coefficient and Nash–Sutcliffe efficiency for almost all 31 stations had a precise forecasting among other proposed TSMs. For PARMA model, the forecasting accuracy in term of NSE indicated that PARMA model almost was the promising model among other linear and nonlinear TSMs in prediction of Epan for all stations, except Arak (NSE = 0.94) and Qom (NSE = 0.93). The ARIMA model for Khorramabad and Bandar Abbas with NSE = 0.52 had the unreliable prediction for Epan compared with other stations. In addition, Arak station in term of RMSE had the least error, 23.79 mm/day and 10.90 mm/day, respectively, for training and testing stages among the other stations.

Using AR, MA, and ARMA Time Series Models to Improve the Performance of MARS and KNN Approaches in Monthly Precipitation Modeling under Limited Climatic Data

Precipitation is one of the most important components of the hydrologic cycle as it is required for multi-objective applications including flood estimation, drought monitoring, watersheds management, hydrology, agriculture, etc. Therefore, its estimation and modeling via a suitable method is a challenging task for hydrologists. The present study seeks to model monthly precipitation at two stations located in Iran. Two artificial intelligence (AI)-based models consisting of multivariate adaptive regression splines (MARS) and k-nearest neighbors (KNN) were used as the modeling techniques. In doing so, nine single-input scenarios under limited climatic data are implemented using minimum, maximum, and mean air temperatures, dew point temperature, station pressure, vapor pressure, relative humidity, wind speed, and antecedent precipitation data. The attained results illustrate that the performance of single MARS and KNN is relatively poor when modeling the monthly precipitation. Additionally, this study develops hybrid models to enhance the precipitation modeling through combining the MARS and KNN models with three diverse types of the time series (TS) models, namely autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA). The most important justification for integrating the models applied is that the AI and TS-based models are respectively capable of modeling the non-linear and linear terms of the hydrological variables such as precipitation. It is therefore necessary to be considered both of the aforementioned terms in the modeling procedure. A performance comparison of the single and hybrid models denotes the higher accuracy of hybrid models than the single ones. However, the hybrid models generated by combining the KNN and the TS models used are the best-performing models.

On the Prediction of Upwelling Events at the Colombian Caribbean Coasts from Modis-SST Imagery.

The upwelling cores on the Caribbean Colombian coasts are mainly located at the Peninsula de la Guajira and Cabo de la Aguja. We used monthly averaged Moderate Resolution Imaging Spectroradiometer (MODIS) sea surface temperature as the only information to build up a prediction model for the upwelling events. This comprised two steps: (i) the reduction of the complexity by means of the Karhunen–Loève transform and (ii) a prediction model of time series. Two prediction models were considered: (a) a parametric autoregressive-moving average (ARMA) time series from the Box–Jenkins methodology and (b) a harmonic synthesis model. The harmonic synthesis also comprised of two steps: the maximum entropy spectral analysis and a least-squares harmonic analysis on the set of frequencies. The parametric ARMA time series model failed at the time of prediction with a very narrow range, and it was quite difficult to apply. The harmonic synthesis allowed prediction with a horizon of six months with a correlation of about 0.80. The results can be summarized using the time series of the weights of the different oscillation modes, their spatial structures with the nodal lines, and a high confidence model with a horizon of prediction of about four months.

A Comparative Study of Autoregressive, Autoregressive Moving Average, Gene Expression Programming and Bayesian Networks for Estimating Monthly Streamflow

In the recent years, artificial intelligence techniques have attracted much attention in hydrological studies, while time series models are rarely used in this field. The present study evaluates the performance of artificial intelligence techniques including gene expression programming (GEP), Bayesian networks (BN), as well as time series models, namely autoregressive (AR) and autoregressive moving average (ARMA) for estimation of monthly streamflow. In addition, simple multiple linear regression (MLR) was also used. To fulfill this objective, the monthly streamflow data of Ponel and Toolelat stations located on Shafarood and Polrood Rivers, respectively in Northern Iran were used for the period of October 1964 to September 2014. In order to investigate the models’ accuracy, root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) were employed as the error statistics. The obtained results demonstrated that the single AR and ARMA time series models had better performance in comparison with the single GEP, BN and MLR methods. Furthermore, in this study, six hybrid models known as GEP-AR, GEP-ARMA, BN-AR, BN-ARMA, MLR-AR and MLR-ARMA were developed to enhance the estimation accuracy of the monthly streamflow. It was concluded that the developed hybrid models were more accurate than the corresponding single artificial intelligence and time series models. The obtained results confirmed that the integration of time series models and artificial intelligence techniques could be of use to improve the accuracy of single models in modeling purposes related to the hydrological studies.

Modelos de series de tiempo aplicados a los expedientes de la Comisión de Derechos Humanos del Distrito Federal

The document presented here, details the adjustment of ARIMA (Autoregressive Moving Average) time series models that allow to forecast the historic accumulation of files in the Mexico City Human Rights Commission. The purpose is to comprehend the behaviour of these, throughout time and to forecast the number of accumulated files.

Adequacy assessment of generating systems containing wind power considering wind speed correlation

Wind power is an important renewable energy resource. Electrical power generation from wind energy behaves quite differently from that of conventional sources, and maintaining a reliable power supply is an important issue in power systems containing wind energy. In these systems, the wind speeds at different wind sites are correlated to some degree if the distances between the sites are not very large. Genetic algorithm methods are applied here to adjust autoregressive moving-average time series models in order to simulate correlated hourly wind speeds with specified wind speed cross-correlation coefficients of two wind sites. Multi-state wind energy conversion system models are used to incorporate the correlated wind farms in reliability studies of generating systems. A method to generate random numbers with specified correlation coefficients for application in a state-sampling Monte Carlo simulation technique is introduced. It is shown that the proposed method can be used in the adequacy assessment of a generating system incorporating partially dependent wind farms.

A Note on the Information Matrix for Multiplicative Seasonal Autoregressive Moving‐Average Models

. It is shown that there is an invariance property for each of the elements of the information matrix of a multiplicative seasonal autoregressive moving-average time-series model, which enables the integral specification of Whittle (1953a,b) to be solved in a straightforward way. The resulting non-iterative closed procedure shares the property possessed by the piecemeal approach of Godolphin and Bane (2006) of being independent of the seasonal period, but our procedure is preferable if one or more orders of the seasonal components of the model are greater than unity. The procedure is therefore simpler, in general, than the iterative method of Klein and Melard (1990) that depends necessarily on the seasonal period. In the strictly non-seasonal case this invariance property prescribes a non-iterative closed procedure for evaluating the information matrix which improves on the methods of Godolphin and Unwin (1983), Friedlander (1984), McLeod (1984) and Klein and Spreij (2003). Three illustrations of the approach are given.

A seasonal analysis of riverflow trends

This paper presents a trend analysis of monthly riverflows recorded at the Apalachicola River at Chattahoochee, FL during the 1930–2001 water years. The environmental concern is that increasing urbanization upstream (Atlanta and Columbus, GA) increases downstream riverflows. In statistical terms, our objective is to test whether there are months in which riverflows are significantly increasing. For this purpose, a parsimonious periodic autoregressive moving-average time series model is fitted to the error structure of the series. The covariances of this time series model are then used to assess the significance of monthly and yearly linear trend estimators. In the end, we do not find strong evidence of increasing riverflows.

BLENDING GROUND BEEF TO CONTROL FAT CONTENT USING SIMULATED ON–LINE SPECTROSCOPIC MEASUREMENTS

Simulation was used to demonstrate that online visible/nearinfrared spectroscopic measurements of fat contentin the streams of ground beef from grinders can be used effectively to achieve a target fat content in a final blender, eliminatingthe conventional intermediate blending step. Sampletosample measurements were simulated using an autoregressivemoving average time series model while lottolot, blocktoblock, and measurementtoactual variation was treated asrandom. More than 10,000 spectra from 31 blocks of frozen beef, in addition to historical processing plant data, were usedto develop the model. Test conditions were for a nominal 15% fat stream to be blended with a nominal 50% fat stream to createfinal blends of 30%, 35%, and 40% fat. Three styles of control limits were tested for the model: constant limit, tapered limit,and funnel limit. These styles describe the fat content limits that control whether one or both streams will be added to theblender at a particular moment and how these limits change as the blender fills. The control styles that minimized the timeto fill the blender were tapered, funnel, and tapered for 30%, 35%, and 40% fat content targets, respectively. For all three,the target fat content was achieved within a tolerance of .0.75% fat 99.7% of the time.

An Improved Batch Means Procedure for Simulation Output Analysis

We formulate and evaluate the Automated Simulation Analysis Procedure (ASAP), an algorithm for steady-state simulation output analysis based on the method of nonover-lapping batch means (NOBM). ASAP delivers a confidence interval for an expected response that is centered on the sample mean of a portion of a simulation-generated time series and satisfies a user-specified absolute or relative precision requirement. ASAP operates as follows: The batch size is progressively increased until either (a) the batch means pass the von Neumann test for independence, and then ASAP delivers a classical NOBM confidence interval; or (b) the batch means pass the Shapiro-Wilk test for multivariate normality, and then ASAP delivers a correlation-adjusted confidence interval. The latter adjustment is based on an inverted Cornish-Fisher expansion for the classical NOBM t-ratio, where the terms of the expansion are estimated via an autoregressive-moving average time series model of the batch means. After determining the batch size and confidence-interval type, ASAP sequentially increases the number of batches until the precision requirement is satisfied. An extensive experimental study demonstrates the performance improvements achieved by ASAP versus well-known batch means procedures, especially in confidence-interval coverage probability.

Combining Temporally Correlated Environmental Data from Two Measurement Systems

We consider the problem of combining temporally correlated environmental data from two measurement systems. More specifically, we suppose that an environmental variable has been measured at regular intervals for a relatively long period of time using one measurement system and that a newer, possibly cheaper or more reliable measurement system has been in operation in tandem with the old system for a relatively short period of time. We suppose that, for purposes of detecting changes or trends in the variable over time, the time series corresponding to the new system only is too short so that it is desirable to somehow combine it with the longer time series from the old system. We present two methods for combining the data and for using the combined data to detect trend. The first is a frequentist analysis of an autoregressive moving-average time series model featuring a common time trend, measurement errors with system-specific biases and variances, and missing data. The second method is a Bayesian analysis of a similar model that is implemented by a Markov chain Monte Carlo procedure. We use the methodology to combine and analyze snow water equivalent data from manual snow surveys (an old measurement system) and snow telemetry (a newer system), which are both currently in use in the western United States.

On Fractionally Integrated Autoregressive Moving-Average Time Series Models With Conditional Heteroscedasticity

Abstract This article considers fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived. An algorithm for approximate maximum likelihood (ML) estimation is presented. The asymptotic properties of ML estimators, which include consistency and asymptotic normality, are discussed. The large-sample distributions of the residual autocorrelations and the square-residual autocorrelations are obtained, and two portmanteau test statistics are established for checking model adequacy. In particular, non-stationary FARIMA(p, d, q)-GARCH(r, s) models are also considered. Some simulation results are reported. As an illustration, the proposed model is also applied to the daily returns of the Hong Kong Hang Seng index (1983–1984).

On Fractionally Integrated Autoregressive Moving-Average Time Series Models with Conditional Heteroscedasticity

This article considers fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived. An algorithm for approximate maximum likelihood (ML) estimation is presented. The asymptotic properties of ML estimators, which include consistency and asymptotic normality, are discussed. The large-sample distributions of the residual autocorrelations and the square-residual autocorrelations are obtained, and two portmanteau test statistics are established for checking model adequacy. In particular, non-stationary FARIMA(p, d, q)-GARCH(r, s) models are also considered. Some simulation results are reported. As an illustration, the proposed model is also applied to the daily returns of the Hong Kong Hang Seng index (1983–1984).

Statistical monitoring of multivariable dynamic processes with state‐space models

AbstractIndustrial continuous processes may have a large number of process variables and are usually operated for extended periods at fixed operating points under closed‐loop control, yielding process measurements that are autocorrelated, cross‐correlated, and collinear. A statistical process monitoring (SPM) method based on multivariate statistics and system theory is introduced to monitor the variability of such processes. The statistical model that describes the in‐control variability is based on a canonical‐variate (CV) state‐space model that is an equivalent representation of a vector autoregressive moving‐average time‐series model. The CV state variables obtained from the state‐space model are linear combinations of the past process measurements that explain the variability of the future measurements the most. Because of this distinctive feature, the CV state variables are regarded as the principal dynamic directions A T2 statistic based on the CV state variables is used for developing an SPM procedure. Simple examples based on simulated data and an experimental application based on a high‐temperature short‐time milk pasteurization process illustrate advantages of the proposed SPM method.

LAG WINDOW ESTIMATION OF THE DEGREE OF DIFFERENCING IN FRACTIONALLY INTEGRATED TIME SERIES MODELS

Abstract. In this paper we consider the estimation of the degree of differencing d in the fractionally integrated autoregressive moving‐average time series model ARFIMA (p, d, q). Using lag window spectral density estimators we develop a regression type estimator of d which is easy to calculate and does not require prior knowledge of p and q. Some large sample properties of the estimator are studied and the performance of the estimator for small samples is investigated using the simulation method for a range of commonly used lag windows. Some practical recommendations on the choice of lag windows and the choice of the window parameters are provided.

APPROXIMATE SIMULTANEOUS SIGNIFICANCE INTERVALS FOR RESIDUAL AUTOCORRELATIONS OF AUTOREGRESSIVE MOVING‐AVERAGE TIME SERIES MODELS

Abstract. Bonferroni‐type inequalities are used to approximate probabilities of the joint distribution of residual autocorrelation coefficients from an autoregressive moving‐average time series model. The approximations are useful for testing the goodness of fit of the model:they can be used to find critical values of a test of whether the largest residual autocorrelation is significantly different from zero. The approximation based on the first‐order Bonferroni inequality is simple to use and adequate in practice.