A Comparative Study of Autoregressive, Autoregressive Moving Average, Gene Expression Programming and Bayesian Networks for Estimating Monthly Streamflow

Autoregressive Integrated Moving Average (ARIMA) Box-Jenkins models combine the autoregressive and moving average models to a stationary time series after the appropriate transformation, while the nonlinear autoregressive (N.A.R.) or the autoregressive neural network (ARNN) models are of the kind of multi-layer perceptron (M.L.P.), which compose an input layer, hidden layer and an output layer. Monthly streamflow at the downstream of the Euphrates River (Hindiya Barrage) /Iraq for the period January 2000 to December 2019 was modeled utilizing ARIMA and N.A.R. time series models. The predicted Box-Jenkins model was ARIMA (1,1,0) (0,1,1), while the predicted artificial neural network (N.A.R.) model was (M.L.P. 1-3-1). The results of the study indicate that the traditional Box-Jenkins model was more accurate than the N.A.R. model in modeling the monthly streamflow of the studied case. Performing a one-step-ahead forecast during the year 2019, the forecast accuracy between the forecasted and recorded monthly streamflow for both models was as follows: the Box-Jenkins model gave root mean squared error (RMSE = 48.7) and the coefficient of determination = 0.801), while the (NAR) model gave (RMSE = 93.4) and = 0.269). Future projection of the monthly stream flow through the year 2025, utilizing the Box-Jenkins model, indicated the existence of long-term periodicity.

Hybrid artificial intelligence-time series models for monthly streamflow modeling

An autoregressive moving average (ARMA) is a time series model that is applied in everyday life for pattern recognition and forecasting. The ARMA model contains a noise which is assumed to have a specific distribution. The noise is often considered to have a Gaussian distribution. However in applications, the noise is sometimes found that does not have a Gaussian distribution. The first objective is to develop the ARMA model in which noise has a Laplacian distribution. The second objective is to estimate the parameters of the ARMA model. The ARMA model parameters include ARMA model orders, ARMA model coefficients, and noise variance. The parameter estimation of the ARMA model is carried out in the Bayesian framework. In the Bayesian framework, the ARMA model parameters are treated as a variable that has a prior distribution. The prior distribution for the ARMA model parameters is combined with the likelihood function for the data to get the posterior distribution for the parameter. The posterior distribution for parameters has a complex form so that the Bayes estimator cannot be determined analytically. The reversible jump Markov chain Monte Carlo (MCMC) algorithm was adopted to determine the Bayes estimator. The first result, the ARMA model can be developed by assuming Laplacian distribution noise. The second result, the performance of the algorithm was tested using simulation studies. The simulation shows that the reversible jump MCMC algorithm can estimate the parameters of the ARMA model correctly.

Modelos de series de tiempo aplicados a los expedientes de la Comisión de Derechos Humanos del Distrito Federal

Are hybrid models integrated with data preprocessing techniques suitable for monthly streamflow forecasting? Some experiment evidences

Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir

Investigating the dynamic characteristic of hydrological processes is of vital significance for environmental protection. In this study, the stepwise cluster analysis (SCA) method was used for monthly streamflow simulation in a hypothetical case. According to SCA, a cluster tree was formulated through training the data of monthly temperature, precipitation and streamflow from 2004 to 2010. Then, the generated tree was used to reproduce monthly streamflow in calibration period (i.e., 2004-2010) and validation period (i.e., 2011-2013). A comparison of SCA and multiple linear regression (MLR) was conducted to reflect the complex relationship of meteorological parameters (e.g., precipitation) and hydrological parameters. Model performance was assessed using Nash-Sutcliffe efficiencies (NSE), the determination coefficient (R 2), the root-mean-square error (RMSE) and the mean absolute error (MAE). NSE and R2 obtained from SCA are higher than that obtained from MLR. RMSE and MAE obtained from SCA are smaller than that obtained from MLR, indicating a better coincidence between simulated streamflow and the observed values in SCA. Results indicated that SCA has advantage in revealing the nonlinear relationship among precipitation, temperature and streamflow.

This article considers fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived. An algorithm for approximate maximum likelihood (ML) estimation is presented. The asymptotic properties of ML estimators, which include consistency and asymptotic normality, are discussed. The large-sample distributions of the residual autocorrelations and the square-residual autocorrelations are obtained, and two portmanteau test statistics are established for checking model adequacy. In particular, non-stationary FARIMA(p, d, q)-GARCH(r, s) models are also considered. Some simulation results are reported. As an illustration, the proposed model is also applied to the daily returns of the Hong Kong Hang Seng index (1983–1984).

A novel time-varying stepwise decomposition ensemble framework for forecasting nonstationary and nonlinear streamflow

Accurate prediction of the streamflow has a significantly importance in water resources management. In this study, two time series models, Autoregressive Moving Average model (ARMA) and Autoregressive Integrated Moving Average model (ARIMA) are used for predicting streamflow based on observed monthly streamflow data from 2000 to 2020. The statistics related to first 16 years were used to train the models and last 5 years (2016-2020) were used to forecast. The accuracy of the models was assessed using statistical metrics such as the Nash efficiency (NE), the Root Mean Square Error (RMSE) and mean absolute percentage error (MAPE). The findings show the following values for the performance criteria: The root mean square error was, 52.525 for ARIMA against 59.273 for ARMA. The mean absolute percentage error was 18.245 for ARIMA against 21.642 for ARMA and the Nash efficiency was 0.848 for ARIMA against 0.839 for ARMA. From these results, it is found that ARIMA model performs better than the ARMA models. The results of this research could assist policymakers in managing water resources, agriculture, and mitigating flood risks in the ORB of West Africa.

Stream and river monitoring have an influential role in agriculture, the fishing industry, land surveillance, the oil and gas industry, etc. Recognizing sudden changes in the behavior of streamflow could also provide tremendous insight for decision-making and administration purposes. The primary purpose of this study is to offer a new robust Regime Shift Change Detection (RSCD) algorithm which can identify periods and regime changes without any assumptions regarding the length of these periods. A regime shift algorithm using two different refined method approaches is proposed in this article. The RSCD with Relative Difference (RSCD-RD) and RSCD with Growth Rate (RSCD-GR) are the two main specializations of this regime shift algorithm. We compared these two specializations on train and test datasets and commented on the advantages and each specialization. RSCD-GR and RSCD-RD were equally effective in detecting regime changes when thresholds were pinpointed for each station and season. However, RSCD-RD outperformed RSCD-GR when general thresholds were used for cold and warm months. A strength of RSCD-GR is the ability to investigate newly observed data separately, while RSCD-RD may require re-investigation of historical data in some cases. A regime change was detected in the monthly streamflow data of the Athabasca River at Athabasca (07BE001) in May 2007, while no such change was observed in the monthly streamflow data of the Athabasca River below Fort McMurray (07DA001). The discrepancy could be attributed to factors such as the clarity of the river water from Saskatchewan or the utilization of industrial water. Additional investigation might be required to determine the underlying causes.

지금까지 많은 연구를 통하여 제안된 다양한 가뭄지수들은 사전에 정의된 등급을 통하여 가뭄을 평가하기 때문에 가뭄현상에 내재된 불확실성을 고려하지 못하고 있다. 본 연구에서는 월 유출량 자료에 내재되어 있는 불확실성을 고려하기 위해 은닉 마코프 모형(HMM) 기반의 가뭄지수(HMDI)를 제안하고, 이를 이용하여 수문학적 가뭄에 대한 확률론적 평가를 수행하였다. WAMIS에서 제공하는 한강유역의 평창강과 남한강상류의 월평균 유출량 자료(1966~2009)를 이용하여 3, 6, 12개월씩 누적시킨 후, HMM에 적용하여 은닉상태의 사후확률을 계산하였다. 연구방법의 검증을 위해 HMM을 이용하여 추정된 각 은닉상태 별 사후확률(HMDI)과 기준값에 의해 가뭄을 평가하는 방법 중 하나인 표준유출지수(SSI)와 비교를 하였다. 분석결과, 기존 가뭄지수(SSI)를 사용하였을 때는 하나의 지수로 특정 시점에서의 가뭄 상태를 판단하였지만, HMDI는 자료에내재된 불확실성을 이용하여 가뭄의 상태를 분류하였고, 이는 특정 시점에서 가뭄 상태들이 나타날 확률로 표현되었다. 또한, 실제 가뭄사례와의 비교를 통해서 HMDI가 SSI에 비하여 가뭄에 대한 재현능력이 우수한 것으로 나타났다. Various drought indices developed from previous studies can not consider the inherent uncertainty of drought because they assess droughts using a pre-defined threshold. In this study, to consider inherent uncertainty embedded in monthly streamflow data, Hidden Markov Model (HMM) based drought index (HMDI) was proposed and then probabilistic assessment of hydrologic drought was performed using HMDI instead of using pre-defined threshold. Using monthly streamflow data (1966~2009) of Pyeongchang river and Upper Namhan river provided by Water Management Information System (WAMIS), applying the HMM after moving-averaging the data with 3, 6, 12 month windows, this study calculated the posterior probability of hidden state that becomes the HMDI. For verifying the method, this study compared the HMDI and Standardized Streamflow Index (SSI) which is one of drought indices using a pre-defined threshold. When using the SSI, only one value can be used as a criterion to determine the drought severity. However, the HMDI can classify the drought condition considering inherent uncertainty in observations and show the probability of each drought condition at a particular point in time. In addition, the comparison results based on actual drought events occurred near the basin indicated that the HMDI outperformed the SSI to represent the drought events.

The partial auto-correlation coefficients of most of the series of monthly stream flows recorded in Turkey of lag greater than one are within the 99% confidence band while the lag-one partial correlation coefficient is highly significant. An ARMA(1,1) model to compute synthetic monthly flows up to 5000 years is developed, which is different from the ones presented in relevant sources. Having observed mostly skewed standardized variates, they are normalized by the 3-parameter log-normal distribution whose parameters are computed by the method of maximum-likelihood (LN3-ML). The two parameters of the ARMA(1,1) model are computed so as to minimize the sum of squares of differences of the observed and computed standardized–normalized variates rather than minimizing the sum of squares of the random component terms. Application of the developed model on the 64-year-long monthly flow series of the unregulated Kizilirmak River in Turkey is given here as an example, which reveals plausible results.

In today's financial landscape, individuals face challenges when it comes to determining the most effective investment strategies. Cryptocurrencies have emerged as a recent and enticing option for investment. This paper focuses on forecasting the price of Ethereum using two distinct methods: artificial intelligence (AI)-based methods like Genetic Algorithms (GA), and econometric models such as regression analysis and time series models. The study incorporates economic indicators such as Crude Oil Prices and the Federal Funds Effective Rate, as well as global indices like the Dow Jones Industrial Average and Standard and Poor's 500, as input variables for prediction. To achieve accurate predictions for Ethereum's price one day ahead, we develop a hybrid algorithm combining Genetic Algorithms (GA) and Artificial Neural Networks (ANN). Furthermore, regression analysis serves as an additional prediction tool. Additionally, we employ the Autoregressive Moving Average (ARMA) model to assess the relationships between variables (dependent and independent variables). To evaluate the performance of our chosen methods, we utilize daily historical data encompassing economic and global indices from the beginning of 2019 until the end of 2021. The results demonstrate the superiority of AI-based approaches over econometric methods in terms of predictability, as evidenced by lower loss functions and increased accuracy. Moreover, our findings suggest that the AI approach enhances computational speed while maintaining accuracy and minimizing errors.

In this chapter, we deal with linear dynamic factor models and related topics, such as dynamic principal component analysis (dynamic PCA). The main motivation for the use of such models is the so-called “curse of dimensionality” plaguing modeling of high-dimensional time series by “ordinary” multivariate AR or ARMA models. For instance, consider an AR system for, a say, 20-dimensional time series. Then each of the coefficient matrices contains 400 “free” parameters, if no additional restrictions on the parameter space have been imposed, i.e. in such a case the parameter spaces grow with the square of the output dimension n, whereas the data, for given sample size, grow linearly with n. Thus for moderate sample size and large n (as is the case, e.g. in many situations faced in macroeconomics), reliable parameter estimation in “fully parametrized” AR(X) or ARMA(X) models is hardly possible. On the other hand, e.g. in macroeconomics, for analysis and in particular for short-term forecasting, modeling of “comovement” and of “cross-sectional dependencies” between a large number of univariate time series recently has received increasing attention and appropriate tools for modeling of high-dimensional time series have been developed. Correspondingly, during the last 25 years, a substantial literature has emerged, dealing with such models, methods and applications, in particular for factor models in this context. The first section introduces a general framework for linear dynamic factor models. In the second section, we describe dynamic principal component analysis, which is a generalization of the well-known static principal component analysis to the dynamic case. In practical applications often the generalized dynamic factor model is used, which allows for cross-sectionally weakly dependent noise and assumes strong dependence in latent variables. This model class is suited for very high-dimensional time series.