Forecasting Of Non-stationary Time Series Research Articles

A nonstationary stochastic simulator for clustered regional hydroclimatic extremes to Characterize compound flood risk

Traditional approaches to flood risk management assume flood events follow an independent, identically distributed (i.i.d.) random process from which static risk measures are computed. Modern risk accounting strategies also consider nonstationarity or long-term trends in the mean and moments of the associated flood probability distributions. However, few approaches consider how extreme hydroclimatic events cluster in both space and time, compounding damage risks. Here we introduce a compound flood risk simulator that models and conditionally forecasts future variability in regional flooding events that cluster in time, given trends and oscillations in a variable climate signal. A modular, novel integration of wavelet signal processing, nonstationary time series forecasting, k-nearest neighbor (KNN) bootstrapping, multivariate copulas, and modified Neyman-Scott (NS) event clustering process provides users the ability to model interannual and sub-annual clustering of flood risk. Our semi-parametric flood generator specifically targets the clustered temporal dynamics of jointly modeled flood intensity, duration, and frequency over a finite future period of a decade or more, thereby providing a foundation for adaptation approaches that integrate temporally clustered flood risk into planning, response and recovery.

Forecasting of Solar Power Using GRU–Temporal Fusion Transformer Model and DILATE Loss Function

Solar power is a clean and sustainable energy source that does not emit greenhouse gases or other atmospheric pollutants. The inherent variability in solar energy due to random fluctuations introduces novel attributes to the power generation and load dynamics of the grid. Consequently, there has been growing attention to developing an accurate forecast model using various machine and deep learning techniques. Temporal attention mechanisms enable the model to concentrate on the critical components of the input sequence at each time step, thereby enhancing the accuracy of the prediction. The suggested GRU–temporal fusion transformer (GRU-TFT) model was trained and validated employing the “Daily Power Production of Solar Panels” Kaggle dataset. Furthermore, an innovative loss function termed DILATE is introduced to train the proposed model specifically for multistep and nonstationary time series forecasting. The outcomes have been subjected to a comparative analysis with alternative algorithms, such as neural basis expansion analysis for interpretable time series (N-BEATS), neural hierarchical interpolation for time series (N-HiTS), and extreme gradient boosting (XGBoost), using several evaluation metrics, including the absolute percentage error (MAE), mean square error (MSE), and root mean square error (RMSE). The model presented in this study exhibited significant performance improvements compared with traditional statistical and machine learning techniques. This is evident from the achieved values of MAE, MSE, and RMSE, which were 1.19, 2.08, and 1.44, respectively. In contrast, the machine learning approach utilizing the Holt–Winters method for time series forecasting in additive mode yielded MAE, MSE, and RMSE scores of 4.126, 29.105, and 5.3949, respectively.

Forecasting nonstationary time series

AbstractMany variables show a tendency to increase over time in line with their nonstationary nature. It is notable, however, that the original time series can be transformed into a sequence of jumps measured by time distances between the successive maxima and present the resulting series as the compound Poisson process, which has powerful consequences discussed in the paper. Firstly, the jump‐generating process is stationary, unlike the one generating the original data. Secondly, the dynamics of a variable can be determined using solely the properties of the derived stationary counterpart. Thirdly, using this framework for prediction offers substantial advantages. The proposed methodology allows forecasting the number of periods necessary for a process to achieve the desired level and decomposing the path leading to that level into jumps of different size. It also gives a unique insight into the shape of the trajectory over the prediction horizon, which the traditional approach to the forecasting of nonstationary time series is incapable of providing.

Forecasting Wind Speed Using the Proposed Wavelet Neural Network

Wind energy is one of the speedy processing technologies in the energy generation industry and the most economical methods of electrical power generation. For the reliability of system, it is wanted to improve highly appropriate wind speed forecasting methods. The wavelet transform is a powerful mathematical technique that converts an analyzed signal into a time-frequency representation. This technique has proven useful in a nonstationary time series forecasting. The aims of this study are to propose a wavelet function by derivation of a quotient from two different Lucas polynomials, as well as a comparison between an artificial neural network (ANN) and wavelet-artificial neural network (WNN). We used the proposed wavelet, Mexican hat, Morlet, Gaussian, Haar, Daubechies, and Coiflet to transform the wind speed data using the continuous wavelet transform (CWT). MATLAB software was used to implement the CWT and ANN. The proposed models were applied in the meteorological field to forecast the daily wind speed data that were collected from the meteorological directorate of Sulaymaniyah which is a city located in the Kurdistan region of Iraq for the period (Jan. 2011–Dec. 2020). Five different performance criteria during calibration and validation, the root mean square error ( R M S E ), mean square error ( M S E ), mean absolute percentage error M A P E , mean absolute error M A E , and coefficient of determination ( R 2 ), were evaluated. When studying, analyzing, and comparing these models, the results of the study concluded that the proposed wavelet-ANN is the best result ( M S E = 0.00072 , R M S E = 0.02683 , M A P E = 2.32400 , and R 2 = 0.99983 .

Adaptive Broad Echo State Network for Nonstationary Time Series Forecasting

Time series forecasting provides a vital basis for the control and management of various systems. The time series data in the real world are usually strongly nonstationary and nonlinear, which increases the difficulty of reliable forecasting. To fully utilize the learning capability of machine learning in time series forecasting, an adaptive broad echo state network (ABESN) is proposed in this paper. Firstly, the broad learning system (BLS) is used as a framework, and the reservoir pools in the echo state network (ESN) are introduced to form the broad echo state network (BESN). Secondly, for the problem of information redundancy in the reservoir structure in BESN, an adaptive optimization algorithm for the BESN structure based on the pruning algorithm is proposed. Thirdly, an adaptive optimization algorithm of hyperparameters based on the nonstationary test index is proposed. In brief, the structure and hyperparameter optimization algorithms are studied to form the ABESN based on the proposed BESN model in this paper. The ABESN is applied to the data forecasting of air humidity and electric load. The experiments show that the proposed ABESN has a better learning ability for nonstationary time series data and can achieve higher forecasting accuracy.

Crude Oil Prices Forecasting: An Approach of Using CEEMDAN-Based Multi-Layer Gated Recurrent Unit Networks

Accurate prediction of crude oil prices is meaningful for reducing firm risks, stabilizing commodity prices and maintaining national financial security. Wrong crude oil price forecasts can bring huge losses to governments, enterprises, investors and even cause economic and social instability. Many classic econometrics and computational approaches show good performance for the ordinary time series prediction tasks, but not satisfactory in crude oil price predictions. They ignore the characteristics of non-linearity and non-stationarity of crude oil prices data, which hinder an accurate prediction and eventually lead to poor accuracy or the wrong result. Empirical mode decomposition (EMD) and ensemble EMD (EEMD) solve the problems of non-stationary time series forecasting, but they also generate new problems of mode mixing and reconstruction errors. We propose a hybrid method that is combination of the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and multi-layer gated recurrent unit (ML-GRU) neural network to solve the abovementioned issues. This not only deals with the issue of mode mixing effectively, but also makes the reconstruction error of data close to zero. Multi-layer GRU has an excellent ability of nonlinear data-fitting. The experimental results of real WTI crude oil dataset show that the proposed approach perform better in crude oil prices forecasts than some state-of-the-art models.

Integrated system analysis and forecasting of non-stationary processes

This article proposes an integrated system analysis and forecasting of non-stationary time series in order to improve the adequacy of the developed models of non-stationary processes. The methodology is proposed for modeling non-stationary processes that includes the following stages: the preliminary data processing, estimation of the model structure and its parameters, computing of forecasts estimates. Examples are provided of the use of this system for the analysis and prediction of prices of Food Production Company and for the financial processes prediction. The results indicate that the integrated system for the analysis, modeling, and forecasting of non-stationary processes performs automated processing of data, automatically determines the structure of the model, and selects the best forecasting models.

Double Layer Interval Graph Model: The Universal Tool for Data Driven Market Analysis and Forecasting

This scientific work is dedicated to the development, improvement and application of double layer interval weighted graphs (DLIG) for non-stationary time series forecasting. This model appears to be the universal and easy-to-use tool for modeling the non-stationary time series and forecasting. We observe the double layer version of the model because it's the most representative way in the sense of main idea though you can add several layers more for different purposes. The first layer of the graph is based on empirical fluctuations of system and displays the most potential fluctuations of the system at the time of system training. The second layer of the graph as a superstructure of the first layer displays the degree of modeling error and it's connected with the first layer nodes by edges. The second layer is the way of supervised training implementation with the aim of error minimization.

Hybrid mathematical models and methods of time series forecasting taking into account external factors

В работе предложены математические модели прогнозирования нестационарных временных рядов с учётом внешних факторов и методы их структурной идентификации, основанные на совместном использовании многомерного варианта метода «Гусеница»-SSA и моделей SARIMAX, расширенных для прогнозирования временных рядов с несколькими сезонными составляющими и с учётом нескольких экзогенных переменных. Экспериментальные результаты показывают высокую эффективность предложенных моделей прогнозирования при выборе подходящих структурных параметров в сравнении с моделями SARIMAX.

“Caterpillar”-SSA and Box-Jenkins hybrid models and methods for time series forecasting

Trend and decomposition approaches to non-stationary time series forecasting are considered in the paper. According to them, various hybrid models for non-stationary time series forecasting, as well as identification methods for these models based on the combined use of the “Caterpillar”-SSA and Box-Jenkins methods were proposed. Hybrid mathematical models of the trend approach to forecasting, based on the “Caterpillar”-SSA and Box-Jenkins methods lie in modeling the process as deviation of actual time series values with respect to the trend component, which is represented in the proposed models by the linear recurrence formula (LRF) of the “Caterpillar”-SSA method and its approximation by the SARIMA model. The main goal of the decomposition approach to forecasting based on the “Caterpillar”-SSA and Box-Jenkins methods is the decomposition of the original time series into multiple time series with a simpler structure, considered independently of each other using the “Caterpillar”-SSA method; forecasting the data of decomposition components by SARIMA models and calculating the total forecast by combining forecasts of the constructed simplified models. The proposed models were tested on the electricity and natural gas consumption time series, and their forecasting results were compared with the results, obtained by classical probabilistic SARIMA models, generalized for the case of several seasonal components. The obtained results allow to conclude that for effective forecasts, it is necessary to carry out decomposition of the studied time series and combine different models, describing both statistical and deterministic time series components that provides the best forecasting quality.

On the neural network approach for forecasting of nonstationary time series on the basis of the Hilbert-Huang transform

The two-stage adaptive approach for time series forecasting is proposed. The first stage involves the decomposition of the initial time series into basis functions and application to them of the Hilbert transform. At the second stage the obtained functions and their instantaneous amplitudes are used as input variables of neural network forecasting. The efficiency of the developed approach is displayed in real time series in the electric power problem of forecasting the sharply variable implementations of active power flows.

Robust Forecasting of Non-Stationary Time Series

This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable forecasts in the presence of outliers, non-linearity, and heteroscedasticity. In the absence of outliers, the forecasts are only slightly less precise than those based on a localized Least Squares estimator. An additional advantage of the MM-estimator is that it provides a robust estimate of the local variability of the time series.

Robust Forecasting of Non-Stationary Time Series

Robust Forecasting of Non-Stationary Time Series

Multiscale local change point detection with applications to value-at-risk

This paper offers a new approach to modeling and forecasting of nonstationary time series with applications to volatility modeling for financial data. The approach is based on the assumption of local homogeneity: for every time point, there exists a historical interval of homogeneity, in which the volatility parameter can be well approximated by a constant. The proposed procedure recovers this interval from the data using the local change point (LCP) analysis. Afterward, the estimate of the volatility can be simply obtained by local averaging. The approach carefully addresses the question of choosing the tuning parameters of the procedure using the so-called “propagation” condition. The main result claims a new “oracle” inequality in terms of the modeling bias which measures the quality of the local constant approximation. This result yields the optimal rate of estimation for smooth and piecewise constant volatility functions. Then, the new procedure is applied to some data sets and a comparison with a standard GARCH model is also provided. Finally, we discuss applications of the new method to the Value at Risk problem. The numerical results demonstrate a very reasonable performance of the new method.

Modeling of nonstationary time-series data. Part I. Data with regular periodic trends

This paper is Part-I of a two-part paper in which composite modeling approach to nonstationary time series forecasting is proposed. Time-series data with regular periodic trends are considered in this paper and data with dynamic trends are treated in the second part of the paper. The major data comprising components are generalized by deterministic models identified through three-step sequential fitting procedure using non-linear regression technique. The proposed modeling approach has been applied to two data sets obtained from two different fields and both containing regular periodic trends.

Time Series Models in Econometrics, Finance and Other Fields

Statistical Aspects of ARCH and Scholastic Volatility Likelihood-Based Inference for Cointegration of Some Non-Stationary Time Series Forecasting in Macroeconomics Longitudinal Panel Data: An Overview of Current Methodology

Discussion of the Paper by Whittle

Journal of the Royal Statistical Society: Series B (Methodological)Volume 53, Issue 3 p. 529-538 DiscussionFree Access Discussion of the Paper by Whittle First published: 1991 https://doi.org/10.1111/j.2517-6161.1991.tb01843.xAboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat REFERENCES IN THE DISCUSSION Akaike, H. (1980) Seasonal adjustment by a Bayesian modeling. J. Time Ser. Anal., 1, 1– 13. Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B, 11, 211– 229. Bartlett, M. S. (1961) Equations for stochastic path integrals. Proc. Camb. Phil. Soc., 57, 568– 573. Bartlett, M. S. (1981) Population and community structure and interaction. In The Mathematical Theory of the Dynamics of Biological Populations II (eds R. W. Hiorns and D. Cook), pp. 119– 137. New York: Academic Press. van den Bol, M. E. (1987) The analysis of a mixed model. Genstat Newslett., no. 20, 7– 12. Brotherton, T. and Gersch, W. (1981) A data analytic approach to the smoothing problem and some of its variations. In Proc. IEEE Conf. Decision and Control. San Diego: IEEE. Duncan, D. B. and Horn, S. D. (1972) Linear dynamic recursive estimation from the point of view of regression analysis. J. Am. Statist. Ass., 67, 815– 821. Hannan, E. J. and Deistler, M. (1988) The Statistical Theory of Linear Systems. New York: Wiley. Harvey, A. C. (1984) A unified view of statistical forecasting procedures. J. Forecast., 3, 245– 275. Harvey, A. C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press. Henderson, C. R. (1953) Estimation of variance and covariance components. Biometrics, 9, 226– 252. Jakeman, A. J. and Young, P. C. (1984) Recursive filtering and the inversion of ill-posed causal problems. Util. Math., 25, 351– 376. de Jong, P. (1988) The likelihood for a state space model. Biometrika, 75, 165– 169. Kitagawa, G. (1981) Anon-stationary time-series model and its fitting by a recursive filter. J. Time Ser., 2, 103– 116. Kohn, R. and Ansley, C. F. (1986) Estimation, prediction and interpolation for ARIMA models with missing data. J. Am. Statist. Ass., 81, 751– 761. Kydland, F. E. and Prescott, E. C. (1990) Business cycles: real facts and a monetary myth. Q. Rev. Fed. Reserve Bank, Minneap., 14, 3– 18. Lukas, M. A. (1980) Regularisation. In The Application and Numerical Solution of Integral Equations (eds R. S. Anderrsen et al.). Sijthoff and Noordhoff. Ng, C. N. and Young, P. C. (1990) Recursive estimation and forecasting of nonstationary time-series. J. Forecast., 9, 173– 204. Reinsch, C. H. (1967) Smoothing by spline functions. Numer. Math., 10, 177– 183. Schiller, R. (1973) A distributed lag estimator derived from smoothness priors. Econometrica, 41, 775– 778. Simon, H. A. (1956) Dynamic programming under uncertainty with a quadratic criterion function. Econometrica, 24, 74– 81. Stigler, S. M. (1978) Mathematical statistics in the early states. Ann. Statist., 6, 239– 265. Theil, H. (1957) A note on certainty equivalence in economic planning. Econometrica, 25, 346– 349. West, M., Harrison, P. J. and Migon, H. S. (1985) Dynamic generalised linear models and Bayesian forecasting (with discussion). J. Am. Statist. Ass., 80, 73– 97. Whittaker, E. T. (1923) On a new method of graduation. Proc. Edinb. Math. Soc., 63– 75. Whittle, P. (1957) Curve and periodogram smoothing. J. R. Statist. Soc. B, 19, 38– 47. Whittle, P. (1963) Prediction and Regulation. London: English Universities Press. Whittle, P. (1983) Prediction and Regulation, 2nd edn. Oxford: Blackwell. Whittle, P. (1990) A risk-sensitive maximum principle. Syst. Control Lett., 15, 183– 192. Whittle, P. (1991) A risk-sensitive maximum principle; the case of imperfect state observation. IEEE Trans. Autotn. Control, to be published. Young, P. C. (1988) Recursive extrapolation, interpolation and smoothing of nonstationary time-series. In Identification and System Parameter Estimation (ed. H. F. Chen), pp. 33– 44. Oxford: Pergamon. Young, P. C. (1990) State space forecasting and seasonal adjustment. J. Forecast., 9, 2. Young, P. C. and Ng, C. N. (1989) Variance intervention. J. Forecast., 8, 399– 416. Young, P. C., Ng, C. N. and Armitage, P. (1989) A systems approach to economic forecasting and seasonal adjustment. Int. J. Comput. Math. Applic., 18, 481– 501. Volume53, Issue31991Pages 529-538 This article also appears in:Discussion Papers ReferencesRelatedInformation