scholarly journals Testing and modelling autoregressive conditional heteroskedasticity of streamflow processes

2005 ◽  
Vol 12 (1) ◽  
pp. 55-66 ◽  
Author(s):  
W. Wang ◽  
P. H. A. J. M Van Gelder ◽  
J. K. Vrijling ◽  
J. Ma
Keyword(s):  
Seasonal Variation ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Conditional Heteroskedasticity ◽  
Daily Streamflow ◽  
Arch Effect ◽  
Monthly Streamflow ◽  
Autoregressive Conditional Heteroskedasticity ◽  
Residual Series

Abstract. Conventional streamflow models operate under the assumption of constant variance or season-dependent variances (e.g. ARMA (AutoRegressive Moving Average) models for deseasonalized streamflow series and PARMA (Periodic AutoRegressive Moving Average) models for seasonal streamflow series). However, with McLeod-Li test and Engle's Lagrange Multiplier test, clear evidences are found for the existence of autoregressive conditional heteroskedasticity (i.e. the ARCH (AutoRegressive Conditional Heteroskedasticity) effect), a nonlinear phenomenon of the variance behaviour, in the residual series from linear models fitted to daily and monthly streamflow processes of the upper Yellow River, China. It is shown that the major cause of the ARCH effect is the seasonal variation in variance of the residual series. However, while the seasonal variation in variance can fully explain the ARCH effect for monthly streamflow, it is only a partial explanation for daily flow. It is also shown that while the periodic autoregressive moving average model is adequate in modelling monthly flows, no model is adequate in modelling daily streamflow processes because none of the conventional time series models takes the seasonal variation in variance, as well as the ARCH effect in the residuals, into account. Therefore, an ARMA-GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) error model is proposed to capture the ARCH effect present in daily streamflow series, as well as to preserve seasonal variation in variance in the residuals. The ARMA-GARCH error model combines an ARMA model for modelling the mean behaviour and a GARCH model for modelling the variance behaviour of the residuals from the ARMA model. Since the GARCH model is not followed widely in statistical hydrology, the work can be a useful addition in terms of statistical modelling of daily streamflow processes for the hydrological community.

A Novel Adaptive Integrated Navigation Filtering Method Based on ARMA/GARCH Model

2013 ◽  
Vol 462-463 ◽  
pp. 259-266
Author(s):  
Xin Zhao ◽  
Hong Lei Qin ◽  
Li Cong
Keyword(s):  
Moving Average ◽  
Garch Model ◽  
Main Idea ◽  
Arma Model ◽  
Statistical Characteristics ◽  
Autoregressive Moving Average ◽  
Integrated Navigation ◽  
Conditional Mean ◽  
Filtering Method ◽  
Residual Series

This paper proposes a novel adaptive integrated navigation filtering method based on autoregressive moving average (ARMA) model and generalized autoregressive conditional heteroscedasticity (GARCH) model. The main idea in this study is to employ ARMA/GARCH model to estimate statistical characteristics of filtering residual series online, namely, the conditional mean and conditional standard deviation, and then the filter parameters are adaptively adjusted based on forecasted results of ARMA/GARCH model in order to improve the reliability of the system when there are abnormal disturbance and other uncertain factors in real condition. On this basis, experiment is used to verify the validity of the method. The simulation results demonstrate that the ARMA/GARCH model can well capture the unusual condition of GPS receiver output, and this adaptive filtering method can effectively improve the reliability of the system.

scholarly journals Currency and Index Futures Markets Dynamics: Asymmetric Volatility, Leverage Effects and Long-memory Characteristics

2021 ◽  
Vol 39 (3) ◽  
Author(s):  
John Francis Diaz ◽  
Kai-Hong Goh, Imba Goh
Keyword(s):  
Long Memory ◽  
Futures Markets ◽  
Moving Average ◽  
Memory Models ◽  
Autoregressive Moving Average ◽  
Conditional Heteroskedasticity ◽  
Index Futures ◽  
Asymmetric Volatility ◽  
Autoregressive Conditional Heteroskedasticity ◽  
Asymmetric Power

This research examines the performance of return and volatility models on the long-memory, asymmetric volatility, and leverage effects by comparing the two most active futures markets globally, Currency and Index Futures. The study uses daily data from the database Quandl.com website, from January 2000 to March 2018. This study utilizes two short-memory models, the autoregressive moving average – exponential generalized autoregressive conditional heteroskedasticity (ARMA-EGARCH); and  autoregressive moving average – asymmetric power autoregressive conditional heteroskedasticity (ARMA-APARCH); and two long-memory models, autoregressive fractionally-integrated moving average – fractionally-integrated exponential generalized autoregressive conditional heteroskedasticity (ARFIMA-FIEGARCH); and autoregressive fractionally-integrated moving average – fractionally-integrated asymmetric power autoregressive conditional heteroskedasticity (ARFIMA-FIAPARCH). The paper shows that portfolio managers and traders can benefit in holding Index futures, because of their steady returns, but with a relatively higher risk for the whole sample period. The study also finds that Currency futures has better safe-haven properties during crisis period, but Index futures performs better after crisis period. Findings suggest that both long-memory models are capable of accurate forecast, especially on the volatility of Currency and Index futures. The proper modelling of Currency and Index futures time-series data can provide traders, fund managers and investors in creating well-defined trading strategies, especially in high volatility regimes.

THE SPILLOVER AND LEVERAGE EFFECTS OF EQUITY EXCHANGE-TRADED NOTES (ETNS)

2019 ◽  
Vol 19 (03) ◽  
pp. 1950013
Author(s):  
JO-HUI CHEN ◽  
JOHN FRANCIS DIAZ
Keyword(s):  
Moving Average ◽  
The Other ◽  
Autoregressive Moving Average ◽  
Conditional Heteroskedasticity ◽  
Negative Relation ◽  
Stock Indices ◽  
Autoregressive Conditional Heteroskedasticity ◽  
Exchange Traded Notes

This research utilizes the Autoregressive Moving Average–General Autoregressive Conditional Heteroskedasticity (ARMA–GARCH) and Autoregressive Moving Average–Exponential General Autoregressive Conditional Heteroskedasticity (ARMA–EGARCH) in studying the spillover and leverage effects of returns and volatilities of seven equity exchange-traded notes (ETNs) and their tracked stock indices. This study finds positive returns transmissions between the two investment instruments. Unilateral influence and bilateral relationships also exist that may help investors in finding investment clues to approximate possible movements of ETNs about stock indices and vice versa. This paper also observes negative returns and volatility transmissions that may caution traders in the possible reversal of movement of the other instrument. Disinvestments, transfer of allocation, and inverse investing strategies are some of the possible reasons attributable to this negative relation.

Application of Kalman Filtering for Natural Gray Image Denoising

2011 ◽  
Vol 187 ◽  
pp. 92-96 ◽  
Author(s):  
Zhi Kai Huang ◽  
De Hui Liu ◽  
Xing Wang Zhang ◽  
Ling Ying Hou
Keyword(s):  
Kalman Filter ◽  
Image Denoising ◽  
Kalman Filtering ◽  
Moving Average ◽  
Arma Model ◽  
Adaptive Method ◽  
Natural Image ◽  
Autoregressive Moving Average ◽  
Processing Step ◽  
Reduction Methods

Image denoising is one of the classical problems in digital image processing, and has been studied for nearly half a century due to its important role as a pre-processing step in various image applications. In this work, a denoising algorithm based on Kalman filtering was used to improve natural image quality. We have studied noise reduction methods using a hybrid Kalman filter with an autoregressive moving average (ARMA) model that the coefficients of the AR models for the Kalman filter are calculated by solving for the minimum square error solutions of over-determined linear systems. Experimental results show that as an adaptive method, the algorithm reduces the noise while retaining the image details much better than conventional algorithms.

Long-memory Modelling and Forecasting of the Returns and Volatility of Exchange-traded Notes (ETNs)

2017 ◽  
Vol 11 (1) ◽  
pp. 23-53 ◽  
Author(s):  
Argel S. Masa ◽  
John Francis T. Diaz
Keyword(s):  
Long Memory ◽  
Moving Average ◽  
Weak Form ◽  
Jel Classification ◽  
Warning Sign ◽  
Conditional Heteroskedasticity ◽  
Long Memory Process ◽  
Long Run ◽  
Autoregressive Conditional Heteroskedasticity ◽  
Exchange Traded Notes

This research provides evidence in determining the predictability of exchange-traded notes (ETNs). It utilises commodity, currency and equity ETNs as data samples, and examines the performance of the three combinations of long-memory models, that is, autoregressive fractionally integrated moving average and generalised autoregressive conditional heteroskedasticity (ARFIMA-GARCH), autoregressive fractionally integrated moving average and fractionally integrated generalised autoregressive conditional heteroskedasticity (ARFIMA-FIGARCH) and autoregressive fractionally integrated moving average and hyperbolic generalised autoregressive conditional heteroskedasticity (ARFIMA-HYGARCH), and three forecasting horizons, that is, 1-, 5- and 20-step-ahead horizons, to model ETNs returns and volatilities. The article finds long-memory processes in ETNs; however, dual long-memory process in returns and volatilities is not verified. The research also poses a challenge to the weak-form efficiency hypothesis of Fama (1970) because lagged changes determine future values, especially in volatility. The findings also show that differences in the characteristics of commodity, currency and equity ETNs are not concluded because of similarities in ETN traits and several insignificant results. However, the presence of intermediate memory was identified, and should serve as a warning sign for investors not to keep these investments in the long run. Lastly, the ARFIMA-FIGARCH model has a slight edge over the ARFIMA-GARCH and ARFIMA-HYGARCH specifications using 1-, 5- and 20-forecast horizons. JEL Classification: G11, G17

scholarly journals A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 324 ◽  
Author(s):  
Dabuxilatu Wang ◽  
Liang Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Empirical Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Complex Data ◽  
Arma Models ◽  
Linguistic Data ◽  
Series Analysis

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

Parameter Identification of Time Varying System Using Basic Function Expansion

2011 ◽  
Vol 403-408 ◽  
pp. 2800-2804
Author(s):  
En Wei Chen ◽  
Yi Min Lu ◽  
Zheng Shi Liu ◽  
Yong Wang
Keyword(s):  
High Efficiency ◽  
Moving Average ◽  
Arma Model ◽  
Basic Function ◽  
Least Square ◽  
Autoregressive Moving Average ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Time Invariant

Time-varying parameters identification in linear system is considered, which can be changed into time-invariant coefficient polynomials after Taylor expansion. Using response data to establish the time-varying autoregressive moving average (TV-ARMA) model, then utilizing least-square algorithm to obtain time-invariant coefficients of time-varying parameters. According to error analysis, to reduce errors and improve accuracy, the estimation time is divided into small internals and the above method is used in each interval. Simulation shows that, under certain error condition, the time-varying parameters obtained by the method have good agreement with the theoretical values; the measures taken have strong anti-interference and high efficiency.

scholarly journals Minimum Message Length in Hybrid ARMA and LSTM Model Forecasting

2021 ◽  
Author(s):  
Zheng Fang ◽  
David L. Dowe ◽  
Shelton Peiris ◽  
Dedi Rosadi
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Short Term Memory ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Information Theoretic ◽  
Minimum Message Length ◽  
Message Length ◽  
Long Short Term Memory

We investigate the power of time series analysis based on a variety of information-theoretic approaches from statistics (AIC, BIC) and machine learning (Minimum Message Length) - and we then compare their efficacy with traditional time series model and with hybrids involving deep learning. More specifically, we develop AIC, BIC and Minimum Message Length (MML) ARMA (autoregressive moving average) time series models - with this Bayesian information-theoretic MML ARMA modelling already being new work. We then study deep learning based algorithms in time series forecasting, using Long Short Term Memory (LSTM), and we then combine this with the ARMA modelling to produce a hybrid ARMA-LSTM prediction. Part of the purpose of the use of LSTM is to seek capture any hidden information in the residuals left from the traditional ARMA model. We show that MML not only outperforms earlier statistical approaches to ARMA modelling, but we further show that the hybrid MML ARMA-LSTM models outperform both ARMA models and LSTM models.

scholarly journals Groundwater Depth Forecasting Using a Coupled Model

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Manfei Zhang ◽  
Yimeng Wang ◽  
Xiao Wang ◽  
Weibo Zhou
Keyword(s):  
Moving Average ◽  
Coupled Model ◽  
Arma Model ◽  
Groundwater Depth ◽  
Irrigation District ◽  
Autoregressive Moving Average ◽  
Annual Average ◽  
Canal Irrigation ◽  
Leave One Out ◽  
Bp Model

Accurate and reliable prediction of groundwater depth is a critical component in water resources management. In this paper, a new method based on coupling wavelet decomposition method (WA), autoregressive moving average (ARMA) model, and BP neural network (BP) model for groundwater depth forecasting applications was proposed. The relative performance of the proposed coupled model (WA-ARMA-BP) was compared to the regular autoregressive integrated moving average (ARIMA) and BP models for annual average groundwater depth forecasting using leave-one-out cross-validation (LOO-CV). The variables used to develop and validate the models were average groundwater depth data recorded from 1981 to 2010 in Jinghui Canal Irrigation District in the northwest of China. It was found that the WA-ARMA-BP model provided more accurate annual average groundwater depth forecasts compared to the ARIMA and BP models. The results of the study indicate the potential of the WA-ARMA-BP model in forecasting nonstationary time series such as groundwater depth.

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