Parametric Time Series Models Research Articles

Short-term forecasting of German generation-based CO2 emission factors using parametric and non-parametric time series models

This study focuses on forecasting German generation-based CO2 emission factors to develop accurate prediction models, which help to shift flexible loads in time with low emissions. While most existing research relies on point forecasts to predict CO2 emission factors, the presented methods are utilized to perform interval forecasts. In addition, compared to other studies, recent data that extends over a long period is used. The study describes the used data and discusses the concept of walk-forward validation. Further, various models are employed and tuned to forecast the emission factors, including benchmark, parametric (e.g., SARIMAX), and non-parametric (bagging, random forest, gradient boosting, CNN, LSTM, MLP) models. The study reveals that all applied parametric and non-parametric models yield better results than the benchmark models, while the gradient boosting model has the lowest mean absolute error with 40.66 gCO2/kWh, the lowest mean absolute percentage error 8.17%, and the random forest has the lowest root mean square error with 57.61 gCO2/kWh. However, the potential of the deep learning models was not fully exploited. In a live application, the implementation effort should be evaluated against the benefit of better prediction.

Estimation of Runoff Using USDA SCS-Curve Number and Autoregressive Time Series Model Parameters for Kachhinda Watershed, Morena District, Madhya Pradesh, India

Hydrological modeling is an influential method for examining hydrologic systems, serving as a valuable tool in investigating these systems for both present studies involving two hydrologic runoff models viz. Soil Conservation Service Two methods, namely the Soil Conservation Service-Curve Number (SCS-CN) method and the Autoregressive Time Series model, were utilized in the Kachhinda watershed to estimate surface runoff, CN, and AMC conditions. The study area covers 600 hectares and is sited in Morena district of M.P. in Chambal division. The SCS-CN technique was employed to determine the curve number and estimate surface runoff by using the potential maximum retention. The CN of the watershed was calculated and compared to observed and estimated surface runoff, which were found to be in close agreement with each other. Additionally, an Autoregressive Time Series model was developed to establish the correlation between observed and estimated runoff, resulting in a correlation coefficient of 0.974. Different orders of AR time series models (0, 1, and 2) were tested to predict annual stream flow, and the model goodness of fit was evaluated using the Box-Pierce Portmanteau test and the Akaike Informations Principle. The Akaike Information Criterions value for the Autoregressive (1) model for runoff was found to be 0.919158, which is within the range of the values obtained for Autoregressive (0) (0.207433) and Autoregressive (2) (5.9767) models.

Estimation of prediction error in time series

Summary The accurate estimation of prediction errors in time series is an important problem, which has immediate implications for the accuracy of prediction intervals as well as the quality of a number of widely used time series model selection criteria such as the Akaike information criterion. Except for simple cases, however, it is difficult or even impossible to obtain exact analytical expressions for one-step and multi-step predictions. This may be one of the reasons that, unlike in the independent case (see Efron, 2004), up to now there has been no fully established methodology for time series prediction error estimation. Starting from an approximation to the bias-variance decomposition of the squared prediction error, a method for accurate estimation of prediction errors in both univariate and multivariate stationary time series is developed in this article. In particular, several estimates are derived for a general class of predictors that includes most of the popular linear, nonlinear, parametric and nonparametric time series models used in practice, with causal invertible autoregressive moving average and nonparametric autoregressive processes discussed as lead examples. Simulations demonstrate that the proposed estimators perform quite well in finite samples. The estimates may also be used for model selection when the purpose of modelling is prediction.

Robust online detection in serially correlated directed network

AbstractAs the complexity of production processes increases, the diversity of data types drives the development of network monitoring technology. This paper mainly focuses on an online algorithm to detect serially correlated directed networks robustly and sensitively. First, we consider a transition probability matrix to resolve the double correlation of primary data. Further, since the sum of each row of the transition probability matrix is one, it standardizes the data, facilitating subsequent modeling. Then we extend the spring length based method to the multivariate case and propose an adaptive cumulative sum (CUSUM) control chart on the strength of a weighted statistic to monitor directed networks. This novel approach assumes only that the process observation is associated with nearby points without any parametric time series model, which is in line with reality. Simulation results and a real example from metro transportation demonstrate the superiority of our design.

Systems monitoring based on robust estimation of stochastic time series models

The problem of system monitoring under conditions of stochastic data heterogeneity based on time series models is considered. The stability of monitoring is proposed to be ensured through the use of convex-concave loss functions. An algorithm for estimating the variance of the main error distribution is proposed. This allows using robust procedures for estimating the parameters of stochastic time series models without a priori information about the variance value of the main error distribution. Using the Monte Carlo statistical test method, the estimates of the proposed robust methods are compared with the known methods of least squares, least modules, and Huber. It is shown that the introduced robust estimates of the parameters of stochastic models of time series win in accuracy and allow increasing the reliability of monitoring the state of systems.

Investment Portfolio Construction in the Beijing-Tianjin-Hebei Region of the CSI 300

How to construct an optimal investment portfolio has become the mainstream of research with the increasing demands of investors to preserve values and returns. This paper is based on the background of the construction of the millennium plan of Xiongan New Area and the gradual improvement of the integration of Beijing, Tianjin and Hebei. The author selects 5 stocks related to infrastructure construction in related area from CSI 300 to construct optimal investment stocks. After processing and analyzing the original data, the time series model is used to predict the future stock data, and the mean variance model is used to construct the investment portfolio to obtain the optimal Sharpe ratio. The final simulation result shows the superiority of portfolio construction with a high yield of 0.346 and the Sharpe ratio value is 2.473, which can provide a reasonable reference investment in enterprises in the Beijing-Tianjin-Hebei region. This paper has important reference value in data selection and optimization of time series model parameters.

Bayesian nonlinear expectation for time series modelling and its application to Bitcoin

This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or misspecification in the conditional mean and volatility. At the first stage, a reference or approximating time series model is specified and estimated. At the second stage, Bayesian nonlinear expectations are introduced to incorporate model uncertainty or misspecification in prediction via specifying a family of alternative models. The Bayesian nonlinear expectations for prediction are constructed from closed-form Bayesian credible intervals evaluated using conjugate priors and residuals of the estimated approximating model. Using real Bitcoin data including some periods of Covid 19, applications of the proposed method to forecasting and risk evaluation of Bitcoin are discussed via three major parametric nonlinear time series models, namely the self-exciting threshold autoregressive model, the generalized autoregressive conditional heteroscedasticity model and the stochastic volatility model.

Improving the Estimation and Predictions of Small Time Series Models

Abstract A new approach is developed for improving the point estimation and predictions of parametric time-series models. The method targets performance criteria such as estimation bias, root mean squared error, variance, or prediction error, and produces closed-form estimators focused towards these targets via a computational approximation method. This is done for an autoregression coefficient, for the mean reversion parameter in Vasicek and CIR diffusion models, for the binomial thinning parameter in integer-valued autoregressive (INAR) models, and for predictions from a CIR model. The success of the prediction targeting approach is shown in Monte Carlo simulations and in out-of-sample forecasting of the US Federal Funds rate.

SOME REGIME-SWITCHING MODELS FOR ECONOMIC TIME SERIES: A COMPARATIVE STUDY

This paper mainly discusses some regime-switching models and explore their usefulness in modeling the economic time series. In recent years, several time series models have been proposed which shape the idea of the existence of different regimes produced by a stochastic process. Especially, nonlinear time series models have gained more attention because linear time series models faced various limitations. The purpose of this study is to establish the methodology of the Self-Exciting Threshold Autoregressive (SETAR) model, Smooth Transition Autoregressive (STAR) model and Markov-Switching (MSW) model from parametric nonlinear time series models in the mean and to compare these models with each other through two financial data sets. For this purpose, some theoretical information on the subject models are given without going into too much detail. In the light of the obtained theoretical information, all models are modeled by using two financial data sets. The obtained models are compared with the help of some performance criteria, measurement of relative efficiency and graph showing the relation of the actual-fitted values of the models.

Threshold Autoregressive Nearest-Neighbour Models for Claims Reserving

Motivated by claims reserving in run-off triangles, a class of threshold autoregressive nearest-neighbour (TAR-NN) models extending a major class of parametric nonlinear time series models, namely threshold autoregressive (TAR) models, is introduced. The proposed class of models also introduces a flexible regime-switching mechanism to nearest-neighbour models. Attention is given to a sub-class of TAR-NN models, namely self-exciting threshold autoregressive nearest-neighbour models (SETAR-NN), for uses in claims reserving. The (strict) stationarity and geometric ergodicity of the SETAR-NN model, and more generally, a two-dimensional nonlinear autoregressive random field, are discussed. The conditional least-square (CLS) method is used to estimate the SETAR-NN model and some of its nested models. Simulation studies on the parameter estimates from the CLS method are conducted. Using real insurance claims data and stochastic simulations, the applications of the SETAR-NN model and the nested models for projecting future claims liabilities are discussed. Comparisons of those models with the Bootstrap-Chain-Ladder (BCL) model for claims reserving are provided.

A class of Minimum Distance Estimators in Markovian Multiplicative Error Models

This paper proposes a class of minimum distance estimators for the underlying parameters in a Markovian parametric multiplicative error time series model. This class of estimators is based on the integrals of the square of a certain marked residual process. The paper derives the asymptotic distributions of the proposed estimators. In a finite sample comparison, some members of the proposed class of estimators dominate a generalized method of moments estimator in terms of the finite sample bias at a variety of chosen error distributions while neither dominate each other in terms of the mean squared error at these error distributions. A real data example is considered to illustrate the proposed estimation procedures.

Confidence Regions for Parameters in Stationary Time Series Models With Gaussian Noise

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical likelihood ratio is obtained which is shown to be asymptotically chi-square distributed. It can be used to construct confidence regions. By adding pseudo samples, we simultaneously eliminate the non-definition of the original empirical likelihood and enhance the coverage probability. Finite sample properties of the empirical likelihood confidence regions are explored through Monte Carlo simulation, and some real data applications are carried out.

Truncated sum-of-squares estimation of fractional time series models with generalized power law trend

We consider truncated (or conditional) sum-of-squares estimation of a parametric fractional time series model with an additive deterministic structure. The latter consists of both a drift term and a generalized power law trend. The memory parameter of the stochastic component and the power parameter of the deterministic trend component are both considered unknown real numbers to be estimated and belonging to arbitrarily large compact sets. Thus, our model captures different forms of nonstationarity and noninvertibility as well as a very flexible deterministic specification. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to non-uniform convergence of the objective function over a large admissible parameter space and due to the competition between stochastic and deterministic components. As expected, parameter estimates related to the deterministic component are shown to be consistent and asymptotically normal only for parts of the parameter space depending on the relative strength of the stochastic and deterministic components. In contrast, we establish consistency and asymptotic normality of parameter estimates related to the stochastic component for the entire parameter space. Furthermore, the asymptotic distribution of the latter estimates is unaffected by the presence of the deterministic component, even when this is not consistently estimable. We also include Monte Carlo simulations to illustrate our results.

Adaptation Parameters of Time Series Models for Forecasting

Prospects for using time series to predict changes in technical parameters in real time are considered. The task is to assess the trend dynamics of the parameter. Adaptive polynomial models of the first and second order, based on the method of multiple exponential smoothing, were selected for forecasting. The models have been modified to adapt to the peculiarities of the computing process in the microcontroller. The initial data, the acceleration values in three axes, were obtained using a three-axis accelerometer installed on the vehicle. Comparison of the forecasting results showed that the second-order adaptive polynomial model is generally more preferable from the point of view of the reduced error. Both models can be used to estimate the change in a parameter for an arbitrary number of prediction intervals. The efficiency of using the models for the forecasting problem largely depends on the determination of the adaptation parameters, such as the smoothing constant and the initial estimates of the coefficients of the time series model. The paper considers the features of the behavior of the models and defines the rules for the selection of adaptation parameters depending on the nature of the change in the technical parameter over time.

Can Recurrent Neural Networks Predict Inflation in Euro Zone as Good as Professional Forecasters?

This paper investigates whether a specific type of a recurrent neural network, in particular Jordan neural network (JNN), captures the expected inflation better than commonly used feedforward neural networks and traditional parametric time-series models. It also considers competing survey-based and model-based expected inflation towards ex-post actual inflation to find whose predictions are more accurate; predictions from survey respondents or forecasting modelers. Further, it proposes neural network modelling strategy when dealing with nonstationary time-series which exhibit long-memory property and nonlinear dependence with respect to lagged inputs and exogenous inputs as well. Following this strategy, overfitting problem was reduced until no improvement in forecasting accuracy of expected inflation is achieved. The main finding is that JNN predicts inflation in euro zone quite accurately within forecasting horizon of 2 years. Regarding rational expectation principle we have found a set of demand-pull and cost-push inflation characteristics as exogenous inputs which helps in reducing overfitting problem of recurrent neural network even more. The sample includes euro zone aggregated monthly observations from January 2000 to December 2019. The results also confirm that inflation expectations obtained from JNN are consistent with Survey of professional forecasters (SPF), and thus, monetary policy makers can use JNN as a complementary tool in shortcomings of other inflation expectations measures.

(2011-6287) A fuzzy non-parametric time series model based on fuzzy data

Parametric time series models typically consists of model identification, parameter estimation, model diagnostic checking, and forecasting. However compared with parametric methods, nonparametric time series models often providea very flexible approach to bring out the features of the observed time series. This paper suggested a novel fuzzy nonparametric method in time series models with fuzzy observations. For this purpose, a fuzzy forward fit kernel-basedsmoothing method was introduced to estimate fuzzy smooth functions corresponding to each observation. A simple optimization algorithm was also suggested to evaluate optimal bandwidths and autoregressive order. Several common goodness-of-fit criteria were also extended to compare the performance of the proposed fuzzy time series method compared to other fuzzy time series model based on fuzzy data. Furthermore, the effectiveness of the proposed method was illustrated through two numerical examples including a simulation study. The results indicate that the proposed model performs better than the previous ones in terms of both scatter plot criteria and goodness-of-fit evaluations.

Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice

This paper proposes a class of parametric multiple-index time series models that involve linear combinations of time trends, stationary variables and unit root processes as regressors. The inclusion of the three different types of time series, along with the use of a multiple-index structure for these variables to circumvent the curse of dimensionality, is due to both theoretical and practical considerations. The M-type estimators (including OLS, LAD, Huber’s estimator, quantile and expectile estimators, etc.) for the index vectors are proposed, and their asymptotic properties are established, with the aid of the generalized function approach to accommodate a wide class of loss functions that may not be necessarily differentiable at every point. The proposed multiple-index model is then applied to study the stock return predictability, which reveals strong nonlinear predictability under various loss measures. Monte Carlo simulations are also included to evaluate the finite-sample performance of the proposed estimators.

A Bayesian stochastic generator to complement existing climate change scenarios: supporting uncertainty quantification in marine and coastal ecosystems

Available climate change projections, which can be used for quantifying future changes in marine and coastal ecosystems, usually consist of a few scenarios. Studies addressing ecological impacts of climate change often make use of a low- (RCP2.6), moderate- (RCP4.5) or high climate scenario (RCP8.5), without taking into account further uncertainties in these scenarios. In this research a methodology is proposed to generate further synthetic scenarios, based on existing datasets, for a better representation of climate change induced uncertainties. The methodology builds on Regional Climate Model scenarios provided by the EURO-CORDEX experiment. In order to generate new realizations of climate variables, such as radiation or temperature, a hierarchical Bayesian model is developed. In addition, a parameterized time series model is introduced, which includes a linear trend component, a seasonal shape with varying amplitude and time shift, and an additive residual term. The seasonal shape is derived with the non-parametric locally weighted scatterplot smoothing, and the residual term includes the smoothed variance of residuals and independent and identically distributed noise. The distributions of the time series model parameters are estimated through Bayesian parameter inference with Markov chain Monte Carlo sampling (Gibbs sampler). By sampling from the predictive distribution numerous new statistically representative synthetic scenarios can be generated including uncertainty estimates. As a demonstration case, utilizing these generated synthetic scenarios and a physically based ecological model (Delft3D-WAQ) that relates climate variables to ecosystem variables, a probabilistic simulation is conducted to further propagate the climate change induced uncertainties to marine and coastal ecosystem indicators.

A Simple Asymptotically F-Distributed Portmanteau Test for Diagnostic Checking of Time Series Models With Uncorrelated Innovations

We propose a simple asymptotically F-distributed portmanteau test for diagnostically checking whether the innovations in a parametric time series model are uncorrelated while allowing them to exhibit higher-order dependence of unknown forms. A transform of sample residual autocovariances removing the influence of parameter estimation uncertainty makes the test simple. Further, by employing the orthonormal series variance estimator, a special sample autocovariances estimator that is asymptotically invariant to parameter estimation uncertainty, we show that the proposed test statistic is asymptotically F-distributed under fixed-smoothing asymptotics. The asymptotic F-theory accounts for the estimation error of the variance estimator that the asymptotic chi-squared theory ignores. Moreover, an extensive Monte Carlo study demonstrates that the F-test has more accurate finite sample size than existing tests with virtually no power loss. An application to S&P 500 returns illustrates the merits of the proposed methodology.

Sampling properties of color Independent Component Analysis

Independent Component Analysis (ICA) offers an effective data-driven approach for blind source extraction encountered in many signal and image processing problems. Although many ICA methods have been developed, they have received relatively little attention in the statistics literature, especially in terms of rigorous theoretical investigation for statistical inference. The current paper aims at narrowing this gap and investigates the statistical sampling properties of the colorICA (cICA) method. The cICA incorporates the correlation structure within sources through parametric time series models in the frequency domain and outperforms several existing ICA alternatives numerically. We establish the consistency and asymptotic normality of the cICA estimates, which then enables statistical inference based on the estimates. These asymptotic properties are further validated using simulation studies.