Standard Autoregressive Models Research Articles

LSTM Network for the Oxygen Concentration Modeling of a Wastewater Treatment Plant

The activated sludge process is a well-known method used to treat municipal and industrial wastewater. In this complex process, the oxygen concentration in the reactors plays a key role in the plant efficiency. This paper proposes the use of a Long Short-Term Memory (LSTM) network to identify an input–output model suitable for the design of an oxygen concentration controller. The model is identified from easily accessible measures collected from a real plant. This dataset covers almost a month of data collected from the plant. The performances achieved with the proposed LSTM model are compared with those obtained with a standard AutoRegressive model with eXogenous input (ARX). Both models capture the oscillation frequencies and the overall behavior (ARX Pearson correlation coefficient ρ = 0.833 , LSTM ρ = 0.921), but, while the ARX model fails to reach the correct amplitude (index of fitting FIT = 41.20%), the LSTM presents satisfactory performance (FIT = 60.56%).

On the vector-valued generalized autoregressive models

The classical autoregressive type models are widely used in time series modelling. Recently, a class of models known as generalized autoregressive, recognized by an additional parameter, has been proposed in order to reveal some hidden features which cannot be characterized by the standard autoregressive models. In this paper, the generalized autoregressive models are extended to the vector-valued autoregressive models which provide a flexible framework for modelling the dependent data. The properties of the new model such as stationary conditions, some explicit form of the auto-covariance function and the spectral density matrices are investigated. Unknown parameters are then estimated and compared with other kinds of traditional methods. The numerical results obtained by means of simulation studies are then reported. Finally, the traditional autoregressive model and generalized autoregressive model are fitted to a well-known bivariate time series, respectively, and the performance of the proposed models and the estimation methods are discussed.

Bank deposits and Google searches in a crisis economy: Bayesian non‐linear evidence for Greece (2009–2015)

AbstractDue to a variety of reasons, the Greek economy faced a severe crisis being a member of EMU. Nonetheless, the country's banking system experienced a dramatic outflow of deposits, in the period 2009–2015. The present paper attempts to shed light on the possibility of forecasting bank deposits, based on the keyword “Grexit” of Google searches. In this context, apart from standard forecasting models like AR (p) and ARDL (p, q) we estimate a novel Neural Network ARDL (p, q, G) model and its respective Bayesian modification. We show that extending standard autoregressive models with the information provided by Internet Searches leads to significant improvement in the forecasting accuracy of the Bank Deposits, compared with other standard models. Furthermore, the forecasting performance of the models, which are extended with Google searches, is shown to be better than models containing only the well‐known indicators. Our findings are robust and econometrically sound.

Clinically Accurate Prediction of Glucose Levels in Patients with Type 1 Diabetes.

Background and Aims: Accurate prediction of glucose levels in patients with type 1 diabetes mellitus (T1DM) is critical both for their glycemic control and for the development of closed-loop systems. Methods: In this study, we utilized real-life, retrospective, continuous glucose monitoring data from 141 T1DM patients (9,083 connection days, 1,592,506 glucose measurements) and in silico data generated by the UVA/Padova T1DM simulator to evaluate different computational methods for glucose prediction. We evaluated the performance of the models using both measures of numerical accuracy, measured by the root mean square error, and clinical accuracy, measured by the percentage of time in each of the Clarke error grid (CEG) zones, and compared the predictions done by autoregressive (AR) models, tree-based methods, artificial neural networks, and a novel model that we devised and optimized for this task. Results: Our novel model, constructed on real-life data, achieved clinical accuracy of 99.3% and 95.8% in predicting the glucose level 30 and 60 min ahead, respectively, and reduced the percentage of glucose predictions in zones C-E of the CEG by 60.6% and 38.4% in these prediction horizons, compared with a standard AR model. The model was superior to all other models across all age groups and achieved higher clinical accuracy in subgroups of patients with high glucose variability and greater time spent in hypoglycemia. Compared with real-life data, when evaluated on in silico data, the model had a higher clinical and numerical accuracy. Conclusions: A model that optimizes for CEG zones may significantly improve clinical accuracy and clinical outcomes of treatment decisions in T1DM patients. Results obtained from simulated data may overestimate the performance of models on real-life data.

A Latent Factor Model for Forecasting Realized Variances

Abstract This article proposes a parsimonious model to forecast large vectors of realized variances (RVar) by exploiting their common dynamics within a latent factor structure. Their long persistence is captured by aggregating latent factors with AR(1) dynamics. The model has obvious advantages over standard autoregressive models not only in terms of parametrization, but also in terms of efficiency, when increasing the dimension of the vector, as it provides more information on the commonality of the series’ dynamics. The model easily accommodates further empirical features of RVars, such as conditional heteroskedasticity. For estimation purposes, we use the maximum likelihood method based on Kalman filter and the efficient method of moments, both being easy to implement and providing accurate estimates. Our empirical illustration on real data shows that the model we propose often outperforms standard models, most of which are, for vectors of RVar series, only implementable under heavy parametric restrictions.

Cluster and forecasting analysis of the residential market in Turkey

Purpose The main purpose of this study is to detect homogeneous housing market areas among 196 districts of 5 major cities of Turkey in terms of house sale price indices. The second purpose is to forecast these 196 house sale price indices. Design/methodology/approach In this paper, the authors use the monthly house sale price indices of 196 districts of 5 major cities of Turkey. The authors propose an autoregressive (AR) model-based fuzzy clustering approach to detect homogeneous housing market areas and to forecast house price indices. Findings The AR model-based fuzzy clustering approach detects three numbers of homogenous property market areas among 196 districts of 5 major cities of Turkey where house sale price moves together (or with similar house sales dynamic). This approach also provides better forecasting results compared to standard AR models by higher data efficiency and lower model validation and maintenance effort. Research limitations/implications In this study, the authors could not use any district-based socioeconomic and consumption behavioral indicators and any discrete geographical and property characteristics because of the data limitation. Practical implications The finding of this study would help property investors for establishing more effective property management strategies by taking different geographical location conditions into account. Social implications From the government side, knowing future rises, falls and turning points of property prices in different locations can allow the government to monitor the property price changes and control the speculation activities that cause a dramatic change in the market. Originality/value There is no previous research paper focusing on neighborhood-based clusters and forecasting house sale price indices in Turkey. At this point, it is the first academic study.

Autoregressive Modeling with Error Percentage Spread based Triangular Fuzzy Number

Data collected by various methods are often prone to uncertainty of measurement which may affect the information conveyed by the quantitative result. This causes the developed predicted model to be less accurate because of the uncertainty contained in the input data used. Hence, preparing the data by means of handling inherent uncertainties is necessary to avoid the developed prediction model to be less accurate. In this paper, the standard autoregressive model is extended to the case where inherent uncertainty exist in the time series data input is handled by triangular fuzzy number. A systematic strategy to construct a symmetry triangular fuzzy number based on percentage error method to build the autoregressive model is presented. Three different spreads of 1%, 3% and 5% are evaluated under percentage error method. This method is applied to forecast the exchange rate of Association of South East Asian Nation (ASEAN) based on time series data. The enhancement made in data preparation of building fuzzy triangles in this study affirms that the proposed method can produce a better accuracy in predicting as compared to the standard auto regressive model. Importantly, the difficulties to build a triangular fuzzy number to treat the fuzziness which is contained in data is addressed. From the result, we could rank the best percentage error spread which gives higher accuracy among 1%, 3% and 5% model.

Changing dynamics: Time-varying autoregressive models using generalized additive modeling.

In psychology, the use of intensive longitudinal data has steeply increased during the past decade. As a result, studying temporal dependencies in such data with autoregressive modeling is becoming common practice. However, standard autoregressive models are often suboptimal as they assume that parameters are time-invariant. This is problematic if changing dynamics (e.g., changes in the temporal dependency of a process) govern the time series. Often a change in the process, such as emotional well-being during therapy, is the very reason why it is interesting and important to study psychological dynamics. As a result, there is a need for an easily applicable method for studying such nonstationary processes that result from changing dynamics. In this article we present such a tool: the semiparametric TV-AR model. We show with a simulation study and an empirical application that the TV-AR model can approximate nonstationary processes well if there are at least 100 time points available and no unknown abrupt changes in the data. Notably, no prior knowledge of the processes that drive change in the dynamic structure is necessary. We conclude that the TV-AR model has significant potential for studying changing dynamics in psychology. (PsycINFO Database Record

INAR implementation of newsvendor model for serially dependent demand counts

The classic newsvendor model was developed under the assumption that period-to-period demand is independent over time. In real-life applications, the notion of independent demand is often challenged. In this paper, we propose a dynamic implementation of the newsvendor model based on a class of integer-valued autoregressive (INAR) models when facing correlated discrete demand. Motivated by application, we consider INAR models with underlying Poisson error innovations and with underlying negative-binomial error innovations to accommodate overdispersion scenarios. We numerically compare our proposal with the standard newsvendor solution and with a standard autoregressive-based newsvendor solution. Our results show that an appropriately specified INAR-based newsvendor solution not only outperforms the standard case but also the approximating forecasting approaches. Moreover, even in the presence of autocorrelation, the use of the standard autoregressive model as an approximating approach can lead to increased costs over and above the standard implementation of the newsvendor model based on no forecasting.

Laplace mixture autoregressive models

Autoregressive (AR) models are an important tool in the study of time series data. However, the standard AR model only allows for unimodal marginal and conditional densities, and cannot capture conditional heteroscedasticity. Previously, the Gaussian mixture AR (GMAR) model was considered to remedy these shortcomings by using a Gaussian mixture conditional model. We introduce the Laplace mixture (LMAR) model that utilizes a Laplace mixture conditional model, as an alternative to the GMAR model. We characterize the LMAR model and provide conditions for stationarity. An MM (minorization–maximization) algorithm is then proposed for maximum pseudolikelihood (MPL) estimation of an LMAR model. Conditions for asymptotic inference and a rule for model selection for the MPL estimator are considered. An example analysis of data arising from the calcium imaging of a zebrafish brain is performed.

Asymptotic properties of least squares estimation for a new fuzzy autoregressive model

In this paper, we extend the standard autoregressive model to the case where the explanatory and response variables are random fuzzy variables. The fuzzy least-squares estimators (FLSE) of the model parameters are derived and their asymptotic properties are established. A simulation is conducted to evaluate our method, and it is found that the proposed method provides a better performance. AMS Subject Classification:94D05, 62F12.

Information theory, model error, and predictive skill of stochastic models for complex nonlinear systems

Many problems in complex dynamical systems involve metastable regimes despite nearly Gaussian statistics with underlying dynamics that is very different from the more familiar flows of molecular dynamics. There is significant theoretical and applied interest in developing systematic coarse-grained descriptions of the dynamics, as well as assessing their skill for both short- and long-range prediction. Clustering algorithms, combined with finite-state processes for the regime transitions, are a natural way to build such models objectively from data generated by either the true model or an imperfect model. The main theme of this paper is the development of new practical criteria to assess the predictability of regimes and the predictive skill of such coarse-grained approximations through empirical information theory in stationary and periodically-forced environments. These criteria are tested on instructive idealized stochastic models utilizing K-means clustering in conjunction with running-average smoothing of the training and initial data for forecasts. A perspective on these clustering algorithms is explored here with independent interest, where improvement in the information content of finite-state partitions of phase space is a natural outcome of low-pass filtering through running averages. In applications with time-periodic equilibrium statistics, recently developed finite-element, bounded-variation algorithms for nonstationary autoregressive models are shown to substantially improve predictive skill beyond standard autoregressive models.

Chain Binomial Models and Binomial Autoregressive Processes

We establish a connection between a class of chain-binomial models of use in ecology and epidemiology and binomial autoregressive (AR) processes. New results are obtained for the latter, including expressions for the lag-conditional distribution and related quantities. We focus on two types of chain-binomial model, extinction-colonization and colonization-extinction models, and present two approaches to parameter estimation. The asymptotic distributions of the resulting estimators are studied, as well as their finite-sample performance, and we give an application to real data. A connection is made with standard AR models, which also has implications for parameter estimation.

The Asymmetric Cycling of U.S. Soybeans and Brazilian Coffee Prices: An Opportunity for Improved Forecasting and Understanding of Price Behavior

The behavior of agricultural commodity markets can arguably result in markedly asymmetric price cycles, that is, downward cycles of substantially different length and breadth than upward cycles. This study assesses whether asymmetric-cycle models can enhance the understanding of the dynamics and provide for a better forecasting of U.S. soybeans and Brazilian coffee prices. The forecasts from asymmetric cycle models are found to be substantially mode precise than those obtained from standard autoregressive models. The asymmetric cycle models also provide useful insights on the markedly different dynamics of the upward vs. the downward cycles exhibited by the prices of these two commodities.

Measuring market integration for apples on the South African fresh produce market: a threshold error correction model

Apples constitute the bulk of deciduous fruit produced in South Africa, i.e. in 2000, apples made up the largest percentage of the deciduous fruit crop (43%). From 991/92 to 2002/03 production averaged 574 850 tons per annum with a standard deviation of 43 922 tons. The average distribution of the apple crop between the local market, exports and processing is more or less even. Because of its potential lucrative nature much emphasis in the apple industry is afforded to exports, but relatively little is known about how price transmission takes place on the domestic fresh produce markets (FPMs). Moreover, it is increasingly recognized that the formulation of market-enhancing policies to increase the performance of the local market requires a better understanding of how the market functions. Aggregate market performance is better understood by studying the level of market integration that exists, which in turn is affected by transaction costs in the value chain. Hence, the primary objective of this study was to measure market integration for apples on the South African FPMs to determine the existence of long-run price relationships and spatial market linkages. Specific issues addressed in this study include, (i) determination of the effect of deregulation of the marketing of agricultural products in 1997 on average real market prices, price spread and volatility (risk), (ii) determination of how FPMs where apples are sold are linked and how prices are transmitted across these markets, (iii) determination of the threshold prices beyond which markets adjust and return to equilibrium, and (iv) establish the response of the FPMs to price shocks and how long it takes for shocks to be eliminated. The FPMs included in this study are Johannesburg, Cape Town, Tswhane, Bloemfontein, Port Elizabeth, Durban, Kimberley and Pietermaritzburg. The criteria for selecting the FPMs were based on net market positions (surplus or deficit area), geographical distribution, the volume of trade and the importance of the market to the national apple trade flow. The investigation revealed a statistically significant decline in real prices in six of the eight markets investigated, a statistically significant relation in prices (price spread) between the Johannesburg FPM and five other FPMs, as well as that the price spreads between these markets declined after deregulation, and that the variation in real apple prices declined for five of the eight markets after deregulation. Standard autoregressive (AR) and threshold autoregressive (TAR) error correction models were compared to determine whether transaction cost has significant effects in measuring market integration. Larger adjustment coefficients were found in the TAR model. This is an indication that price adjustments are faster in threshold autoregressive TAR models than in AR models. Also half-life deviations in the TAR model are much smaller than in the AR model. The TAR model requires less time for one-half of the deviation from equilibrium to be eliminated than the standard AR model. Therefore, it is better to use TAR models than AR models because TAR models give a more reliable result. In addition, the parameter estimates of the threshold vector error correction model were analyzed. The results show that bidirectional and unidirectional causality exist between Johannesburg FPM prices and other markets. Regime switching estimates to investigate market integration in the selected markets show that no persistent deviation from equilibrium existed for all but one market pair and no clear evidence was found to support improved market integration after market deregulation in 1997. A nonlinear impulse response function to investigate the impact of positive and negative price shocks in the Johannesburg FPM on other FPMs revealed that it takes about six to twelve months for positive and negative shocks to be completely eliminated in all the markets. Generally, the results obtained confirmed strong market integration in terms of apples for selected FPMs.

Comparison of four updating models for real-time river flow forecasting

Four different error-forecast updating models are investigated in terms of their capability of providing real-time river flow forecast accuracy superior to that of rainfall-runoff models applied in the simulation (nonupdating) mode. The first and most widely used is the single autoregressive (AR) model, the second being an elaboration of that model, namely the autoregressive-threshold (AR-TS) updating model. A fuzzy autoregressive-threshold (FU-AR-TS) updating model is proposed as the third form of model, the fourth and final error-forecast updating model applied being the artificial neural network (ANN) model. In the application of these four updating models, the lumped soil moisture accounting and routing (SMAR) conceptual model has been selected to simulate the observed discharge series on 11 selected test catchments. As expected, it is found that all of these four updating models are very successful in improving the flow forecast accuracy, when operating in real-time forecasting mode. A less expected, but nonetheless welcome, result is that the three updating models having the most parameters, i.e. AR-TS, FU-AR-TS, and ANN, do not show any considerable advantages in improving the real-time flow forecast efficiency over that of the simple standard AR model. Thus it is recommended that, in the context of real-time river flow forecasting based on error-forecast updating, modellers should continue to use the AR model.

Persistence of Excitation Properties for Time-Varying Autoregressive Systems

It is well known that a crucial property for the effective identification of time-varying systems is that the data carry continual information on the parameters to be estimated. As a matter of fact, only in this case can the identification algorithm rely on fresh information in forming a reliable estimate of the current value of these parameters. This concept has been formalized in the system identification literature under the name of persistence of excitation. In this paper, the persistence of excitation property is studied for a class of time-varying systems (that includes the standard autoregressive model as a particular case) and conditions for it to hold are derived.

Long-range persistence in climatological and hydrological time series: analysis, modeling and application to drought hazard assessment

We present power spectra of time-series data for tree ring width chronologies, atmospheric temperatures, river discharges and precipitation averaged over hundreds of stations worldwide. The average power spectrum S for each of these phenomena is found to have a power-law dependence on frequency with exponent − 1 2 : S(f) ∝f − 1 2 . An advection-diffusion model of the vertical transport of heat and water vapor in the atmosphere is presented as a first-order model of climatic and hydrological variability. The model generates variability with the observed spectrum. The model is validated with a correlation analysis of temperature and water vapor concentration measurements from the TIROS operational vertical sounder (TOVS). Drought frequency analyses based on synthetic lognormal streamflows with the above power spectrum are presented. We show that the presence of long memory as implied by the power-law power spectrum has a significant effect on the likelihood of extended droughts compared with the drought hazard implied from standard autoregressive models with short memory.

Forecasting industrial production using non‐linear methods

AbstractNumerous theoretical models suggests that business cycles involve nonlinear processes. In this paper we examine whether two parametric, nonlinear time‐series models—the bilinear and threshold models—can exploit apparent non‐linearity in industrial production to provide forecasts superior to those derived from the standard autoregressive models.

A new autoregressive time series model in exponential variables (NEAR(1))

A new time series model for exponential variables having first-order autoregressive structure is presented. Unlike the recently studied standard autoregressive model in exponential variables (ear(1)), runs of constantly scaled values are avoidable, and the two parameter structure allows some adjustment of directional effects in sample path behaviour. The model is further developed by the use of cross-coupling and antithetic ideas to allow negative dependency. Joint distributions and autocorrelations are investigated. A transformed version of the model has a uniform marginal distribution and its correlation and regression structures are also obtained. Estimation aspects of the models are briefly considered.