Stochastic Time Series Models Research Articles

Modelling the GDP of KSA using linear and non-linear NNAR and hybrid stochastic time series models.

Gross domestic product (GDP) serves as a crucial economic indicator for measuring a country's economic growth, exhibiting both linear and non-linear trends. This study aims to analyze and propose an efficient and accurate time series approach for modeling and forecasting the GDP annual growth rate (%) of Saudi Arabia, a key financial indicator of the country. Stochastic linear and non-linear time series modeling, along with hybrid approaches, are employed and their results are compared. Initially, conventional linear and nonlinear methods such as ARIMA, Exponential smoothing, TBATS, and NNAR are applied. Subsequently, hybrid models combining these individual time series approaches are utilized. Model diagnostics, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), are employed as criteria for model selection to identify the best-performing model. The findings demonstrated that the neural network autoregressive (NNAR) model, as a non-linear approach, outperformed all other models, exhibiting the lowest values of MAE, RMSE and MAPE. The NNAR(5,3) projected the GDP of 1.3% which is close to the projection of IMF benchmark (1.9) for the year 2023. The selected model can be employed by economists and policymakers to formulate appropriate policies and plans. This quantitative study provides policymakers with a basis for monitoring fluctuations in GDP growth from 2022 to 2029 and ensuring the sustained progression of GDP beyond 2029. Additionally, this study serves as a guide for researchers to test these approaches in different economic dynamics.

A novel comparative study of NNAR approach with linear stochastic time series models in predicting tennis player's performance

BackgroundPrediction models have gained immense importance in various fields for decision-making purposes. In the context of tennis, relying solely on the probability of winning a single match may not be sufficient for predicting a player's future performance or ranking. The performance of a tennis player is influenced by the timing of their matches throughout the year, necessitating the incorporation of time as a crucial factor. This study aims to focus on prediction models for performance indicators that can assist both tennis players and sports analysts in forecasting player standings in future matches.MethodologyTo predict player performance, this study employs a dynamic technique that analyzes the structure of performance using both linear and nonlinear time series models. A novel approach has been taken, comparing the performance of the non-linear Neural Network Auto-Regressive (NNAR) model with conventional stochastic linear and nonlinear models such as Auto-Regressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS), and TBATS (Trigonometric Seasonal Decomposition Time Series).ResultsThe study finds that the NNAR model outperforms all other competing models based on lower values of Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). This superiority in performance metrics suggests that the NNAR model is the most appropriate approach for predicting player performance in tennis. Additionally, the prediction results obtained from the NNAR model demonstrate narrow 95% Confidence Intervals, indicating higher accuracy and reliability in the forecasts.ConclusionIn conclusion, this study highlights the significance of incorporating time as a factor when predicting player performance in tennis. It emphasizes the potential benefits of using the NNAR model for forecasting future player standings in matches. The findings suggest that the NNAR model is a recommended approach compared to conventional models like ARIMA, ETS, and TBATS. By considering time as a crucial factor and employing the NNAR model, both tennis players and sports analysts can make more accurate predictions about player performance.

Stochastic Time Series Analysis, Modeling, and Forecasting of Weekly Rainfall Using Sarima Model

Rainfall holds critical significance for water resource applications, particularly in rainfed agricultural systems. This study employs the Autoregressive Integrated Moving Average (ARIMA) technique, a data mining approach commonly used for time series analysis and future forecasting. Given the increasing importance of climate change forecasting in averting unexpected natural hazards such as floods, frost, forest fires, and droughts, accurate weather data forecasting becomes imperative. The objective of this study was to develop a Seasonal Auto-Regressive Integrative Moving Average (SARIMA) model for forecasting weekly rainfall in Junagadh Station, Gujarat. Utilizing 53 years of historical data (1963 to 2016), the SARIMA model predicts weekly rainfall for the subsequent five years (2018 to 2022). Through comprehensive evaluation using ACF and PACF plots, AIC, SBC, MAPE, and MAE values, the study identifies SARIMA (0,0,4)(0,1,1)52 as the optimal model, offering the most accurate prediction. The robust results affirm that the SARIMA model provides reliable and satisfactory weekly rainfall predictions. This research contributes valuable insights into the precision and efficacy of SARIMA models for rainfall forecasting, aiding in strategic water resource management in the Junagadh region.

Nonlinear GARCH-type models for ordinal time series

AbstractDespite their relevance in various areas of application, only few stochastic models for ordinal time series are discussed in the literature. To allow for a flexible serial dependence structure, different ordinal GARCH-type models are proposed, which can handle nonlinear dependence as well as kinds of an intensified memory. The (logistic) ordinal GARCH model accounts for the natural order among the categories by relying on the conditional cumulative distributions. As an alternative, a conditionally multinomial model is developed which uses the softmax response function. The resulting softmax GARCH model incorporates the ordinal information by considering the past (expected) categories. It is shown that this latter model is easily combined with an artificial neural network response function. This introduces great flexibility into the resulting neural softmax GARCH model, which turns out to be beneficial in three real-world time series applications (air quality levels, fear states, cloud coverage).

Forecasting river daily discharge using decision tree and time series methods

River floods disrupt communication and transportation networks, damage buildings and infrastructure, destroy agricultural products and livestock, cause capital losses and endanger human life. Accurate and proper flood prediction and forecasting are major challenges in hydrology and water resources management. The aim of this study was to forecast and estimate the daily flows of three rivers in Iran using four tree-based data-mining methods, two ensemble bagging methods and the stochastic time series model Arima (auto-regressive integrated moving average). A comparison of these different methodologies is the main contribution of this work. Five statistical measures were used to evaluate the accuracy of these models based on 4 years of daily discharge flow data. The hold-out method was used to divide the data into training (70%) and testing (30%) sets. It was found that the ensemble tree-based chi-square automatic interaction detector provided the most precise forecasts. The overall results indicate that the data-mining methods of ensemble models and tree-based models improved the average accuracy of the models by 25.0% and 15.5% compared with the stochastic Arima model, respectively, indicating the superiority of their potential in capturing the non-linear behaviour of flow discharges.

Bias Correction and Statistical Modeling of Variable Oceanic Forcing of Greenland Outlet Glaciers

AbstractVariability in oceanic conditions directly impacts ice loss from marine outlet glaciers in Greenland, influencing the ice sheet mass balance. Oceanic conditions are available from Atmosphere‐Ocean Global Climate Model (AOGCM) output, but these models require extensive computational resources and lack the fine resolution needed to simulate ocean dynamics on the Greenland continental shelf and close to glacier marine termini. Here, we develop a statistical approach to generate ocean forcing for ice sheet model simulations, which incorporates natural spatiotemporal variability and anthropogenic changes. Starting from raw AOGCM ocean heat content, we apply: (a) a bias‐correction using ocean reanalysis, (b) an extrapolation accounting for on‐shelf ocean dynamics, and (c) stochastic time series models to generate realizations of natural variability. The bias‐correction reduces model errors by ∼25% when compared to independent in‐situ measurements. The bias‐corrected time series are subsequently extrapolated to fjord mouth locations using relations constrained from available high‐resolution regional ocean model results. The stochastic time series models reproduce the spatial correlation, characteristic timescales, and the amplitude of natural variability of bias‐corrected AOGCMs, but at negligible computational expense. We demonstrate the efficiency of this method by generating >6,000 time series of ocean forcing for >200 Greenland marine‐terminating glacier locations until 2100. As our method is computationally efficient and adaptable to any ocean model output and reanalysis product, it provides flexibility in exploring sensitivity to ocean conditions in Greenland ice sheet model simulations. We provide the output and workflow in an open‐source repository, and discuss advantages and future developments for our method.

An Empirical Investigation of Herd Behaviour in Surplus Economy: Evidences from Muscat Stock Market

This study investigates herd behaviour in the surplus economy of the Sultanate of Oman under Bear and Bull market conditions. The first aim of the study is to determine if the investors at Muscat Stock Market (MSM) exhibit herd behavior or not. The second aim of the study is to compare the different stochastic time-series models commonly used to test and forecast herd behavior. Finally, the study aims to determine whether herd behavior in the MSM is predominantly risk-driven as measured by Cross-Sectional Standard Deviation (CSSD) or return-driven as measured by Cross-Sectional Absolute Deviation (CSAD) of stock returns from the overall market return. Our analyses are based on daily Muscat Stock Market’s (MSM) index returns for the period starting 1st of January 2010 and ending 31^st of December 2019, the pre Covide-19 pandemic. Our findings disclose: (1) that MSM exhibits herd behavior, (2) that there are statistically significant among the different stochastic time-series models used to test and forecast herd behavior in MSM, where ARIMA (1,0,0) model exhibits the highest predictive power of herd behavior in MSM (3), that MSM’s herd behavior is driven more by CSSD than CSAD in the bearish and bullish market conditions.

Impact of the COVID-19 pandemic on the socio-economic development of the region

The article presents an analysis of the consequences of economic instability caused by the COVID‑19 pandemic for the socio‑economic development of the region. The study was carried on the example of the Sverdlovsk region according to the Federal State Statistics Service. The article sets and solves three research problems. First, to assess how the overall socio‑economic condition of the region has changed because of the COVID‑19 pandemic. Second, to identify the impact of the COVID‑19 pandemic on the nature and structure of the relationship between the socio‑economic indicators of the region. Third, to analyze the impact of the COVID‑19 pandemic on the trends in the socio‑economic indicators of the region, considering their possible delay and seasonal fluctuations. The first task is solved using statistical methods of pattern recognition, the second task — by methods of multivariate correlation analysis, and for the third task stochastic time series models are used. The largest contribution to the division into clusters was made by the number of births, the turnover of public catering and the volume of goods, works and services performed on their own; their dynamics most clearly traces the impact of the COVID‑19 pandemic in the Sverdlovsk region. Multidimensional correlation analysis established that because of the introduction of restrictive and supportive measures, multidirectional trends in the socio‑economic indicators of the region were formed, which violated the previously established relationships between them. Based on the obtained coefficients of the autoregressive model, one can find a certain pattern consisting in the growth of the influence of short‑term (lag 1 and 3 months) and the decrease of the long‑term influence (lag 12 months) change in indicators. According to the calculations obtained, the economy of the Sverdlovsk region during the analyzed period failed to overcome the destabilizing effect of the consequences of the COVID‑19 pandemic.

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.

A stochastic time-series model for solar irradiation

We propose a novel stochastic time series model able to explain the stylized features of daily irradiation level data in 5 cities in Germany. The model is suitable for applications to risk management of photovoltaic power production in renewable energy markets. The suggested dynamics is a low-order autoregressive time series with seasonal level given by an atmospheric clear-sky model. Moreover, we detect a skewness property in the residuals which we explain by a winter–summer regime switch. The stochastic variance is modeled by a seasonally varying GARCH-dynamics. The winter and summer standardized residuals are proposed to be a Gaussian mixture model to capture the bimodal distributions. We estimate the model on the observed data, and perform a validation study. An application to energy markets studying the production at risk for a PV-producer is presented.

Comparing three types of data-driven models for monthly evapotranspiration prediction under heterogeneous climatic conditions

Evapotranspiration is one of the most important hydro-climatological components which directly affects agricultural productions. Therefore, its forecasting is critical for water managers and irrigation planners. In this study, adaptive neuro-fuzzy inference system (ANFIS) model has been hybridized by differential evolution (DE) optimization algorithm as a novel approach to forecast monthly reference evapotranspiration (ET0). Furthermore, this model has been compared with the classic stochastic time series model. For this, the ET0 rates were calculated on a monthly scale during 1995–2018, based on FAO-56 Penman–Monteith equation and meteorological data including minimum air temperature, maximum air temperature, mean air temperature, minimum relative humidity, maximum relative humidity & sunshine duration. The investigation was performed on 6 stations in different climates of Iran, including Bandar Anzali & Ramsar (per-humid), Gharakhil (sub-humid), Shiraz (semi-arid), Ahwaz (arid), and Yazd (extra-arid). The models’ performances were evaluated by the criteria percent bias (PB), root mean squared error (RMSE), normalized RMSE (NRMSE), and Nash-Sutcliff (NS) coefficient. Surveys confirm the high capability of the hybrid ANFIS-DE model in monthly ET0 forecasting; so that the DE algorithm was able to improve the accuracy of ANFIS, by 16% on average. Seasonal autoregressive integrated moving average (SARIMA) was the most suitable pattern among the time series stochastic models and superior to its competitors, ANFIS and ANFIS-DE. Consequently, the SARIMA was suggested more appropriate for monthly ET0 forecasting in all the climates, due to its simplicity and parsimony. Comparison between the different climates confirmed that the climate type significantly affects the forecasting accuracies: it’s revealed that all the models work better in extra-arid, arid and semi-arid climates, than the humid and per-humid areas.

A Review of the Anthropogenic Global Warming Consensus: An Econometric Forecast Based on the ARIMA Model of Paleoclimate Series

This paper projects a climate change scenario using a stochastic paleotemperature time series model and compares it to the prevailing consensus using Autoregressive Integrated Moving Average Process Model (ARIMA). The parameter estimates of the model were below that established by the anthropogenic experts and governmental organs, such as the IPCC (UN) over a 100-year scenario. Results from the ARIMA model suggest a current period of temperature reduction and a probable cooling. The results from this study add a statistical element of paleoclimate to the debate that contradicts the current scientific consensus.

Sea Level Rise Estimation on the Pacific Coast from Southern California to Vancouver Island

Previous studies have estimated the sea level rise (SLR) at various locations on the west coast of the USA and Vancouver Island in Canada. Here, we construct an entire SLR profile from Vancouver Island in the Pacific Northwest to San Diego in Southern California. First, we process global navigation satellite system (GNSS) measurements at 405 stations blanketing the whole coast to generate a profile of vertical land motion (VLM) known to bias century-long tide gauge (TG) measurements recording relative SLR (RSLR). We are then able to estimate the absolute SLR (ASLR) by correcting the SLR with the VLM. Our study emphasizes the relationship between the various tectonic movements (i.e., the Cascadia subduction zone, the San Andreas strike-slip fault system) along the Pacific coast which renders it difficult to accurately estimate the SLR. That is why we precisely model the stochastic noise of both GNSS and tide gauge time series using a combination of various models and information criterions (ICs). We also use the latest altimetry products and sea surface height (SSH) to compare it with ASLR at the same location as the TGs. This study supports previous analysis that the power law + white noise and generalized Gauss–Markov + white noise models are the best stochastic noise models for the GNSS time series. The new coastal profile confirms the large variability of VLM estimates in the Pacific Northwest around the Cascadia subduction zone in agreement with previous studies, and a similar result when the San Andreas fault comes onshore in Central California (San Francisco Bay). Negative RSLR values are mostly located in the Pacific Northwest (Vancouver Island and Olympic Peninsula). We also observe a much bigger variation (about 90–150%) of the ASLR in the Pacific Northwest which is predominantly due to glacial isostatic adjustment (GIA). Moreover, the comparison between the ASLR and the SSH estimates shows similarities in the center of the studied area (South Washington, Oregon planes, and some parts of Southern California) where the tectonic activity does not significantly influence the TG measurements. Finally, the twentieth-century satellite geocentric ocean height rates show a global mean of 1.5 to 1.9 mm/yr. Our estimates based on ASLR and SSH are within this interval.

A New Look at The Anthropogenic Global Warming Consensus: An Econometric Forecast Based On the Arima Model of Paleoclimate Series

This paper aims to project a climate change scenario using a stochastic paleotemperature time series model and compare it with the prevailing consensus. The ARIMA - Autoregressive Integrated Moving Average Process model was used for this purpose. The results show that the parameter estimates of the model were below what is established by the anthropogenic current and governmental organs, such as the IPCC (UN), considering a 100-year scenario, which suggests a period of temperature reduction and a probable cooling. Thus, we hope with this study to contribute to the discussion by adding a statistical element of paleoclimate in counterpoint to the current scientific consensus and place the debate in a long-term historical dimension, in line with other research already present in the literature

Long-term forecasting of climatic parameters using parametric and non-parametric stochastic modelling

Climatic parameters fluctuate dynamically and their turbulences become more significant as the influence of the climate change increases. A robust model that is able to factor in the recent climate change for long-term climatic parameters forecasting is desired to strategically plan for future anthropogenic activities. In this study, two stochastic time series model, namely the seasonal auto-regressive integrated moving average (SARIMA) model and the artificial neural network (ANN) model are used to predict monthly mean temperature (Tmean), relative humidity (RH), wind speed (u) and pan evaporation (Epan) up to 12 months ahead. This study is conducted using data collected from three meteorological stations in the northern region of the Peninsular Malaysia. The stochastic models forecasted the Tmean with the highest accuracy, followed by RH, u and Epan. Besides, despite the increasing time step (from 1 to 12 months), the accuracy of the models remain consistent. However, both of the models are susceptible to the occurrence of extreme climates. In general, the SARIMA model performs better than the ANN model, probably attributed to its ability to consider the seasonality of the climatic data rather than depending solely on black-box computation.

Time series and neural network to forecast water quality parameters using satellite data

Complex and highly variable parameters of water quality are difficult to predict over time and space. In most cases, predictions of surface chlorophyll-a (Chl-a) and sea surface temperature (SST) are based on coupled ecological-hydrodynamic modeling, which is driven by oceanic and climatic conditions. Since these models are complex, simpler and efficient methods of predictions are required. The objective of this study is to evaluate the performance of stochastic time series models - Seasonal Auto Regressive Integrated Moving Average (SARIMA) and nonlinear neural network (NN) - to predict Chl-a and SST in coastal areas. Additionally, this study examines the sensitivity of the aforementioned models with respect to variation in depth and changes in turbidity. The data used in this study are satellite-derived Chl-a and SST collected for the Arabian Gulf region for a period of 10 years. This region has been selected for the study due to pronounced variability in depth and changes in turbidity in its waters. As a result of this study, it has been shown that SARIMA and NN are able to forecast Chl-a and SST. In the deep & less turbid water, SARIMA and NN models (SARIMA/NN) produced Chl-a R2:RMSE values of (0.5:0.6)/(0.37:0.53) and SST R2:RMSE (0.9:1.36)/(0.8:1.43). However, the NN has performed better than SARIMA in predicting Chl-a in turbid & shallow waters, especially when Chl-a concentrations are high (>2 mgm−3). Based on our analysis, we conclude that SARIMA and NN are capable of forecasting the future values of Chl-a and SST in regions with pre-existing knowledge of the water depth and turbidity.

Quantifying the rarity of extreme multi-decadal trends: how unusual was the late twentieth century trend in the North Atlantic Oscillation?

Climate trends over multiple decades are important drivers of regional climate change that need to be considered for climate resilience. Of particular importance are extreme trends that society may not be expecting and is not well adapted to. This study investigates approaches to assess the likelihood of maximum moving window trends in historical records of climate indices by making use of simulations from climate models and stochastic time series models with short- and long-range dependence. These approaches are applied to assess the unusualness of the large positive trend that occurred in the North Atlantic Oscillation (NAO) index between the 1960s to 1990s. By considering stochastic models, we show that the chance of extreme trends is determined by the variance of the trend process, which generally increases when there is more serial correlation in the index series. We find that the Coupled Model Intercomparison Project (CMIP5 + 6) historical simulations have very rarely (around 1 in 200 chance) simulated maximum trends greater than the observed maximum. Consistent with this, the NAO indices simulated by CMIP models were found to resemble white noise, with almost no serial correlation, in contrast to the observed NAO which exhibits year-to-year correlation. Stochastic model best fits to the observed NAO suggest an unlikely chance (around 1 in 20) for there to be maximum 31-year NAO trends as large as the maximum observed since 1860. This suggests that current climate models do not fully represent important aspects of the mechanism for low frequency variability of the NAO.

Stochastic Identification of Guided Wave Propagation under Ambient Temperature via Non-Stationary Time Series Models.

In the context of active-sensing guided-wave-based acousto-ultrasound structural health monitoring, environmental and operational variability poses a considerable challenge in the damage diagnosis process as they may mask the presence of damage. In this work, the stochastic nature of guided wave propagation due to the small temperature variation, naturally occurring in the ambient or environment, is rigorously investigated and modeled with the help of stochastic time-varying time series models, for the first time, with a system identification point of view. More specifically, the output-only recursive maximum likelihood time-varying auto-regressive model (RML-TAR) is employed to investigate the uncertainty in guided wave propagation by analyzing the time-varying model parameters. The steps and facets of the identification procedure are presented, and the obtained model is used for modeling the uncertainty of the time-varying model parameters that capture the underlying dynamics of the guided waves. The stochasticity inherent in the modal properties of the system, such as natural frequencies and damping ratios, is also analyzed with the help of the identified RML-TAR model. It is stressed that the narrow-band high-frequency actuation for guided wave propagation excites more than one frequency in the system. The values and the time evolution of those frequencies are analyzed, and the associated uncertainties are also investigated. In addition, a high-fidelity finite element (FE) model was established and Monte Carlo simulations on that FE model were carried out to understand the effect of small temperature perturbation on guided wave signals.

Multicopter Fault Detection and Identification via Data-Driven Statistical Learning Methods

This paper presents the introduction, investigation, and critical assessment of three data-driven methods for rotor failure detection and identification in a multicopter. These methods are based on aircraft attitude signals obtained from forward flight under turbulence and uncertainty. The knowledge-based method exploits the system rigid-body dynamics insight under the different rotor failures to construct a decision tree that detects and identifies the rotor failure simultaneously by how the roll, pitch, and yaw signals violate the statistical confidence limits immediately after failure. For the statistical time-series method, the development of stochastic time-series models and residual-based statistical hypothesis tests are discussed. Here, fault detection in the transient response is followed by identification after the signals reach a stationary state, after controller compensation, with the healthy and the different faulty models, respectively, in a two-step manner. The third method employs the healthy time-series model to extract a useful feature, which is the residual cross correlation, as an input to a neural network trained to achieve simultaneous rotor failure detection and identification. The time-series assisted neural network is capable of making decisions throughout the entire flight with an accuracy of 98.8%, with minimum computation time (less than 0.03 s) making it the best alternative for real-time monitoring.

A Stochastic Time-Series Model for Solar Irradiation

We propose a novel stochastic time series model able to explain the stylized features of daily irradation level data in 5 cities in Germany. The model is suitable for applications to risk management of photovoltaic power production in renewable energy markets. The suggested dynamics is a low order autoregressive time series with seasonal level given by an atmospheric clear-sky model. Moreover, we detect a skewness property in the residuals which we explain by a winter-summer regime switch. The stochastic variance is modelled by a seasonally varying GARCH-dynamics. The winter and summer standardized residuals are proposed to be a Gaussian mixture model to capture the bimodal distributions. We estimate the model on the observed data, and perform a validation study. An application to energy markets studying the production at risk for a PV-producer is presented.