Stochastic Subspace Model Identification and One-step Prediction on Time Series Data

2008 ◽  
pp. 367-376
Author(s):  
Na Meng ◽  
Yi-qi Zhou
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Model Identification ◽  
Series Data ◽  
One Step

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

scholarly journals Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

Vibration ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 25-46 ◽  
Author(s):  
Merten Stender ◽  
Sebastian Oberst ◽  
Norbert Hoffmann
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Time Series Data ◽  
Model Identification ◽  
Transient Behavior ◽  
Series Data ◽  
Special Focus ◽  
Suitable Model ◽  
Reconstruction Method ◽  
Minimal Models

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

scholarly journals KAJIAN MODEL PERAMALAN KUNJUNGAN WISATAWAN MANCANEGARA DI BANDARA KUALANAMU MEDAN TANPA DAN DENGAN KOVARIAT

2019 ◽  
Vol 3 (1) ◽  
pp. 18-32
Author(s):  
Isti Rochayati ◽  
Utami Dyah Syafitri ◽  
I Made Sumertajaya ◽  
Indonesian Journal of Statistics and Its Applications IJSA
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Model Identification ◽  
Series Data ◽  
Explanatory Variables ◽  
Foreign Tourist ◽  
Currency Exchange ◽  
Inflation Rates ◽  
Internal And External Factors

Foreign tourist arrivals could be considered as time series data. Modelling these data could make use of internal and external factors. The techniques employed here to model these time series data are SARIMA, SARIMAX, VARIMA, and VARIMAX. SARIMA is a model for seasonal data and VARIMA is a model for multivariate time series data. If some explanatory variables are incorporated and have significant influence on the response, the former two models become SARIMAX and VARIMAX respectively. Three stages of creating the model are model identification, parameter estimation, and model diagnostics. The variables used in this study were foreign tourist visits, international passenger arrivals, inflation rates, currency exchange rates, and Gross Regional Domestic Product (GRDP) over the period of 2010-2017. All four models fulfill their model assumptions and therefore could be applied. The best model of foreign tourist arrivals was VARIMA with the value of MAPE testing data = 6.123.

scholarly journals Self-Identification ResNet-ARIMA Forecasting Model

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Time Series Data ◽  
Moving Average ◽  
Arima Model ◽  
Model Identification ◽  
Series Data ◽  
Percentage Error ◽  
Forecasting Model ◽  
Partial Autocorrelation Function

The challenging endeavor of a time series forecast model is to predict the future time series data accurately. Traditionally, the fundamental forecasting model in time series analysis is the autoregressive integrated moving average model or the ARIMA model requiring a model identification of a three-component vector which are the autoregressive order, the differencing order, and the moving average order before fitting coefficients of the model via the Box-Jenkins method. A model identification is analyzed via the sample autocorrelation function and the sample partial autocorrelation function which are effective tools for identifying the ARMA order but it is quite difficult for analysts. Even though a likelihood based-method is presented to automate this process by varying the ARIMA order and choosing the best one with the smallest criteria, such as Akaike information criterion. Nevertheless the obtained ARIMA model may not pass the residual diagnostic test. This paper presents the residual neural network model, called the self-identification ResNet-ARIMA order model to automatically learn the ARIMA order from known ARIMA time series data via sample autocorrelation function, the sample partial autocorrelation function and differencing time series images. In this work, the training time series data are randomly simulated and checked for stationary and invertibility properties before they are used. The result order from the model is used to generate and fit the ARIMA model by the Box-Jenkins method for predicting future values. The whole process of the forecasting time series algorithm is called the self-identification ResNet-ARIMA algorithm. The performance of the residual neural network model is evaluated by Precision, Recall and F1-score and is compared with the likelihood basedmethod and ResNET50. In addition, the performance of the forecasting time series algorithm is applied to the real world datasets to ensure the reliability by mean absolute percentage error, symmetric mean absolute percentage error, mean absolute error and root mean square error and this algorithm is confirmed with the residual diagnostic checks by the Ljung-Box test. From the experimental results, the new methodologies of this research outperforms other models in terms of identifying the order and predicting the future values.

scholarly journals Time-series forecasting with deep learning: a survey

2021 ◽  
Vol 379 (2194) ◽  
pp. 20200209
Author(s):  
Bryan Lim ◽  
Stefan Zohren
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Time Series Data ◽  
Time Series Forecasting ◽  
Series Data ◽  
Climate Modelling ◽  
Weather And Climate ◽  
Recent Developments ◽  
One Step ◽  
Learning Architectures

Numerous deep learning architectures have been developed to accommodate the diversity of time-series datasets across different domains. In this article, we survey common encoder and decoder designs used in both one-step-ahead and multi-horizon time-series forecasting—describing how temporal information is incorporated into predictions by each model. Next, we highlight recent developments in hybrid deep learning models, which combine well-studied statistical models with neural network components to improve pure methods in either category. Lastly, we outline some ways in which deep learning can also facilitate decision support with time-series data. This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

Model Identification with Time Series Data

2002 ◽  
pp. 173-185
Author(s):  
Byron K. Williams ◽  
James D. Nichols ◽  
Michael J. Conroy
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Model Identification ◽  
Series Data

scholarly journals Application of Seasonal Autoregressive Moving Average Models to Analysis and Forecasting of Time Series Monthly Rainfall Patterns in Embu County, Kenya

2019 ◽  
pp. 1-15
Author(s):  
Tartisio Njoki Filder ◽  
Moses Mahugu Muraya ◽  
Robert Mathenge Mutwiri
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Rainfall Variability ◽  
Model Fitting ◽  
Model Identification ◽  
Monthly Rainfall ◽  
Series Data ◽  
Estimation Model ◽  
Rainfall Variation

Rainfall is of critical importance for many people, particularly those whose livelihoods depend on rain-fed agriculture. Predicting the trend of rainfall is a difficult task, and statistical approaches such as time series analysis provide a means for predicting the patterns of rainfall. The models also offer the potential to improve areas such as increased food production, profitability, and improved food security policing. However, these forecasts and information systems may, in some instances, not be suitable for direct use by stakeholders in their decision-making. The objective of this study was to investigate rainfall variability and develop a Seasonal Auto-Regressive Integrated Moving Average (SARIMA) model for fitting the monthly rainfall using time series data. Secondary monthly data from 1998 to 2017 for Embu County was collected from the Kenya Meteorological Department, Embu and recorded into an excel sheet. R-software was utilized to analyse data for descriptive statistics, rainfall variability, and model fitting. The coefficient of variation for annual and seasonal rainfall was calculated. The Box Jenkin's ARIMA modelling procedure (model identification, model estimation, model validation) was used to determine the best models for the data. The main study findings indicated the existence of annual variability of 34%, March-April-May rainfall variability of 44%, and October-November-December variability of 44%. A first-order differenced SARIMA (1, 1, 1) (0, 1, 2)12 model with an AIC score of 9.99356 was found suitable for predicting rainfall pattern in Embu, County. The study outcome revealed that Embu County experiences high seasonal and rainfall variation of rainfall, thus requires a reliable model for better prediction. 

scholarly journals Multistep Forecasting for Highly Volatile Data using A New Box-Jenkins and GARCH Procedure

2020 ◽  
pp. 1-6
Author(s):  
Siti Roslindar Yaziz ◽  
Roslinazairimah Zakaria ◽  
John Boland
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Gold Price ◽  
Series Data ◽  
R Language ◽  
Price Series ◽  
Forecasting Performance ◽  
Out Of Sample ◽  
One Step ◽  
Multiple Step

The study of the multistep ahead forecast is significant for practical application purposes using the proposed statistical model. This study proposes a new procedure of Box-Jenkins and GARCH (or BJ-G) in evaluating the multistep forecasting performance for a highly volatile time series data. The promising results from one-step ahead out-of-sample forecast series using the BJ-G model has motivated the extension to multiple step ahead forecast. In order to achieve the objective, the procedure of multistep ahead forecast for BJ-G model is proposed using R language. In evaluating the performance of the multistep ahead forecast, the proposed procedure is employed to daily world gold price series of 5-year data. Based on the empirical results, the proposed procedure of multistep ahead forecast enhances the existing procedure of BJ-G which is able to provide a promising procedure to assess the performance of the BJ-G model in forecasting a highly volatile time series data. The procedure adds the value of BJ-G model since it allows the model to describe efficiently the characteristics of the volatile series up to n-step ahead forecast. Keywords: Box-Jenkins, GARCH, highly volatile data, multistep forecast; gold price

scholarly journals Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

2018 ◽  
Author(s):  
Merten Stender ◽  
Sebastian Oberst ◽  
Norbert Hoffmann
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Time Series Data ◽  
Model Identification ◽  
Transient Behavior ◽  
Series Data ◽  
Special Focus ◽  
Suitable Model ◽  
Reconstruction Method ◽  
Minimal Models

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for a) describing the dynamics and b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and non-linearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of non-linearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

Fallability in the Visual Assessment of Behavioural Interventions: Time-Series Statistics to Analyse Time-Series Data

1986 ◽  
Vol 3 (1) ◽  
pp. 26-33 ◽  
Author(s):  
Christopher Sharpley
Keyword(s):  
Time Series ◽  
Visual Analysis ◽  
Time Series Data ◽  
Model Identification ◽  
Interrupted Time Series ◽  
Visual Assessment ◽  
Series Data ◽  
Behavioural Interventions ◽  
Data Points ◽  
Clinical Conditions

The use of visual analysis alone to determine the presence of significant and generalizable effects in typical behavioural interventions is subject to a series of possible errors which result in high levels of unreliability when data are analysed in this way. The presence of autocorrelation in most behavioural data poses a serious threat to visual and traditional analysis of such data, a threat which can be avoided by use of the more appropriate interrupted time-series (TMS) statistics. Although previously suggested as reasons for not using TMS procedures, the issues of model-identification and number of data points required for TMS are discussed and shown to be invalid arguments against the use of TMS. A case is made for visual analysis of behavioural data as an appropriate procedure only under certain constrained clinical conditions.

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