Stationary Time Series Models Research Articles

Forecasting the United State Dollar(USD)/Bangladeshi Taka (BDT) exchange rate with deep learning models: Inclusion of macroeconomic factors influencing the currency exchange rates.

Forecasting a currency exchange rate is one of the most challenging tasks nowadays. Due to government monetary policy and some uncertain factors, such as political stability, it becomes difficult to correctly forecast the currency exchange rate. Previously, many investigations have been done to forecast the exchange rate of the United State Dollar(USD)/Bangladeshi Taka(BDT) using statistical time series models, machine learning models, and neural network models. But none of the previous methods considered the underlying macroeconomic factors of the two countries, such as GDP, import/export, government revenue, etc., for forecasting the USD/BDT exchange rate. We have included various time-sensitive macroeconomic features directly impacting the USD/BDT exchange rate to address this issue. These features will create a new dimension for researchers to predict and forecast the USD/BDT exchange rate. We have used various types of models for predicting and forecasting the USD/BDT exchange rate and found that Among all our models, Time Distributed MLP provides the best performance with an RMSE of 0.1984. Finally, we have proposed a pipeline for forecasting the USD/BDT exchange rate, which reduced the RMSE of Time Distributed MLP to 0.1900 and has proven effective in reducing the error of all our models.

Efficient Variational Bayes Learning of Graphical Models With Smooth Structural Changes.

Estimating a sequence of dynamic undirected graphical models, in which adjacent graphs share similar structures, is of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. Existing methods for learning dynamic graphical models require the tuning parameters that control the graph sparsity and the temporal smoothness to be selected via brute-force grid search. Furthermore, these methods are computationally burdensome with time complexity O(NP3) for P variables and N time points. As a remedy, we propose a low-complexity tuning-free Bayesian approach, named BASS. Specifically, we impose temporally dependent spike and slab priors on the graphs such that they are sparse and varying smoothly across time. An efficient variational inference algorithm based on natural gradients is then derived to learn the graph structures from the data in an automatic manner. Owing to the pseudo-likelihood and the mean-field approximation, the time complexity of BASS is only O(NP2). To cope with the local maxima problem of variational inference, we resort to simulated annealing and propose a method based on bootstrapping of the observations to generate the annealing noise. We provide numerical evidence that BASS outperforms existing methods on synthetic data in terms of structure estimation, while being more efficient especially when the dimension P becomes high. We further apply the approach to the stock return data of 78 banks from 2005 to 2013 and find that the number of edges in the financial network as a function of time contains three peaks, in coincidence with the 2008 global financial crisis and the two subsequent European debt crisis. On the other hand, by identifying the frequency-domain resemblance to the time-varying graphical models, we show that BASS can be extended to learning frequency-varying inverse spectral density matrices, and further yields graphical models for multivariate stationary time series. As an illustration, we analyze scalp EEG signals of patients at the early stages of Alzheimer's disease (AD) and show that the brain networks extracted by BASS can better distinguish between the patients and the healthy controls.

Extreme Rainfall Forecast and Flood Prediction in Equatorial Zone of West Africa: Port Harcourt, Nigeria in Focus

Purpose: Rainfall is the most important element of climate in the tropics, it dictate human outdoor activities, recharge underground water and streams, dictate agricultural calendar and many cultural activities. More recently the incidence of extreme rainfall leading to urban flood in the city of Port Harcourt is increasingly becoming a looming disaster. Despite the importance of rainfall in the tropic, the fact that it varies significantly is worrisome to both scholars and the stakeholders. This study focused on extreme rainfall forecast and flood prediction in equatorial zone of West Africa especially in a humid tropic environment like Port Harcourt.
 Methodology: Statistical Time Series Model performed very well in rainfall forecast, but did better in flood prediction. Secondary data extracted from Nigeria Meteorological Agency, Oshodi, Lagos form 100/3 of the agency record servers as main source of data for this work. Descriptive statistics and inferential statistics were used, among which are mean, standard deviation, and coefficient of variation; Pearson product moment correlation and structural time series model.
 Findings: The study discovered that rainfall distribution has reduced over the years, besides the dry spell in the month of August has deduced gradually but steadily over the years. It also shown that flood cannot occur in the first 6 months of the year. Rainfall distribution varies significantly over the climatic period.
 Conclusion: There is a significant variation in rainfall distribution over Port Harcourt. August dry spell is steadily disappearing, giving raise to excessive run-off that triggers flood during late September to October. Flood will likely occur whenever the forecasted rainfall exceeds the generated level output during the seasonal peak. Structural Time Series Model performed well in flood prediction than in rainfall forecast.
 Recommendations: Extreme RF forecast by the authorities should be taken serious by inhabitants and warning be given and adhered to by residences. Also, structural time series model should be used for long time forecast since it performed very well, but this should be done with large data.

Copula ARMA-GARCH modelling of spatially and temporally correlated time series data for transportation planning use

Time series analysis has been used extensively in transport research in various areas, such as traffic management and transport planning. Time-series data may contain temporal and spatial correlations. Temporal correlation refers to the dependency of observations on time, while spatial correlation refers to the dependence of observations on space. Although there is a substantial amount of literature on statistical models that modelled temporal correlation of transport time-series data, there are few studies that accommodate both temporal and spatial correlations. In cases where more than one time-series dataset is collected from different locations, each observation can depend on its previous values and observations from other locations. Transport-related time-series data (e.g., traffic volumes, travel times, etc.) may exhibit nonlinear spatial correlation within the transport network. However, existing statistical time series models that consider spatial correlation, such as vector auto-regression (VAR) models, are limited to linear spatial correlation functions with a time-invariance assumption. This study introduces a copula time series model capable of modelling correlations between variables through time and space. Temporal correlations are modelled by an autoregressive moving average-generalised autoregressive conditional heteroskedasticity (ARMA-GARCH) model, where the conditional mean is predicted based on past values and errors, and conditional variance is predicted based on past residuals and conditional variances. This enables the model to describe heteroscedastic data. The spatial correlation is modelled with a copula model, which has the flexibility to model different types of correlations, such as nonlinear, tailed and asymmetric correlations. We illustrate the statistical properties of our approach where the performance of the copula ARMA-GARCH model is compared with the VAR model based on mean absolute percentage error (MAPE) and root mean square error (RMSE) values of model predictions on synthesised data. We then demonstrate practical implementations of these models examined in two case studies with traffic count data collected from four main arterial roads in Sydney.

Análisis estadístico y modelo de pronóstico SARIMA aplicado al consumo de energía eléctrica en instalaciones universitarias

Analyzing the energy consumption behavior in buildings is essential for implementing energy-saving and efficient energy use measures without losing attention to the comfort inside the buildings. In this study, a statistical analysis and time series forecast of the energy situation of a group of buildings in a university academic unit in Mexico City was conducted. Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used for the forecast with electrical energy consumption data from 55 months. Training and test partitions were created with these data to generate two SARIMA models. The results showed a strong dependence on the school cycle of electricity consumption, in addition to a shift in the cycle in the first year of the study. The mean absolute percentage error (MAPE) for the training partitions created shows that the best fit is provided by the SARIMA (3,1,1) (1,0,0)12 model for the 48-month separation. In comparison, the SARIMA (2,1,2) (1,0,0)12 model does so for the 43-month test partition. The confidence intervals for the 7- and 12-month forecast are less wide for the SARIMA (3,1,1) (1,0,0)12 model than for the SARIMA (2,1,2) (1,0,0)12 model. Statistical analysis and time series modeling allows a better understanding of the building stock's energy performance and strengthens the energy audit to design or implement energy saving or efficient energy use measures.

Are Twitter sentiments during COVID-19 pandemic a critical determinant to predict stock market movements? A machine learning approach

The problem of stock market prediction is a challenging task owing to its complex nature and the numerous indirect factors at play. The sentiments regarding socio-political issues such as wars and pandemics can affect stock prices. The spread of the COVID-19 pandemic continues to take a toll on the economy and fluctuations in sentiment of the concerns about the health impacts of the disease can be captured from the microblogging platform, Twitter. We examined how these sentiments during the Covid-19 pandemic and the health impacts arising from the disease along with other macroeconomic indicators provide useful information to predict the stock indices in a more accurate manner. We developed a machine learning model namely, long-short term memory (LSTM) networks to predict the impact of the Covid-19 induced sentiments on the stock values of different sectors in the United States and India. We did the same predictions using the timeseries statistical models such as autoregressive moving average model and the linear regression model. We then compared the performance of the LSTM and the timeseries statistical models to find that the machine learning model has produced more accurate predictions of the stock indices. The performance of the models across the sectors and between the United States and India are compared to draw economic inferences.

Investigating the impact of global market trends and market interaction on the Indian stock market through statistical time series modeling

In today’s age, Stock Market is considered to be one of the most thrilling and challenging financial activities. Due to globalization, it can easily be said that the fluctuations seen in the stock market are the result of the flow of information. In order to get this information, one way is to get the stock prices of another market across the globe. With the advancement in global trades and interdependency of various markets, it can easily be concluded that there would be a great degree of interrelation between the national market and the global. This understanding of inter relation between national and global markets plays an important role in pricing, forecasting, and equivocation activities. In order to predict the Indian market the information is gathered overnight in other stock markets such as NYSE (New York Stock Exchange), LSE (London Stock Exchange), and All ordinates. (Australian all Ordinaries) can be taken into consideration. The opening value of the Indian market can be predicted considering the closing values of mentioned stock markets. The proposed work empirically investigates how Indian National Stock Exchange (NSE) gets affected by other global stock markets. The proposed work does a comprehensive analysis in order to understand the co-movement and exchange of information from NYSE, LSE, and All Ordinates to the NSE. We found a strong correlation between these stock markets during our study period and we can easily conclude that using this correlation we can predict the value of NSE based on the index of other stock markets i.e. NYSE, LSE, and All ordinates.

Bootstrapping a powerful mixed portmanteau test for time series

A new portmanteau test statistic is proposed for detecting nonlinearity in time series data. The new portmanteau statistic is calculated from the log of the determinant of a matrix comprised of the autocorrelations and cross-correlations of the residuals and squared residuals of a fitted time series. The asymptotic distribution of the proposed test statistic is derived as a linear combination of chi-square distributed random variables and can be approximated by a gamma distribution. A bootstrapping approach is shown to be robust when distributional assumptions are relaxed. The efficacy of the statistic is studied against linear and nonlinear dependency structures of some stationary time series models. It is shown that the new test can provide higher power than other tests in many situations. We demonstrate the advantages of the proposed test by investigating linear and nonlinear effects in an economic series and two environmental time series.

Comparison of Active COVID-19 Cases Per Population Using Time-Series Models

This research explored the precision of diverse time-series models for COVID-19 epidemic detection in all the thirty-six different states and the Federal Capital Territory (FCT) in Nigeria with the maximum count of daily cumulative of confirmed, recovered and death cases as of 4 November 2020 of COVID-19 and populace of each state. A 14-multi step ahead forecast system for active coronavirus cases was built, analyzed and compared for six (6) different deep learning-stimulated and statistical time-series models using two openly accessible datasets. The results obtained showed that based on RMSE metric, ARIMA model obtained the best values for four of the states (0.002537, 0.001969.12E-058, 5.36E-05 values for Lagos, FCT, Edo and Delta states respectively). While no method is all-encompassing for predicting daily active coronavirus cases for different states in Nigeria, ARIMA model obtains the highest-ranking prediction performance and attained a good position results in other states.

The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series

This paper is an introduction to the new package in R called [smoots](https://CRAN.R-project.org/package=smoots) (smoothing time series), developed for data-driven local polynomial smoothing of trend-stationary time series. Functions for data-driven estimation of the first and second derivatives of the trend are also built-in. It is first applied to monthly changes of the global temperature. The quarterly US-GDP series shows that this package can also be well applied to a semiparametric multiplicative component model for non-negative time series via the log-transformation. Furthermore, we introduced a semiparametric Log-GARCH and a semiparametric Log-ACD model, which can be easily estimated by the smoots package. Of course, this package applies to suitable time series from any other research area. The smoots package also provides a useful tool for teaching time series analysis, because many practical time series follow an additive or a multiplicative component model.

Supervised learning using routine surveillance data improves outbreak detection of Salmonella and Campylobacter infections in Germany.

The early detection of infectious disease outbreaks is a crucial task to protect population health. To this end, public health surveillance systems have been established to systematically collect and analyse infectious disease data. A variety of statistical tools are available, which detect potential outbreaks as abberations from an expected endemic level using these data. Here, we present supervised hidden Markov models for disease outbreak detection, which use reported outbreaks that are routinely collected in the German infectious disease surveillance system and have not been leveraged so far. This allows to directly integrate labeled outbreak data in a statistical time series model for outbreak detection. We evaluate our model using real Salmonella and Campylobacter data, as well as simulations. The proposed supervised learning approach performs substantially better than unsupervised learning and on par with or better than a state-of-the-art approach, which is applied in multiple European countries including Germany.

Non-Stationary Time Series Model for Station-Based Subway Ridership During COVID-19 Pandemic: Case Study of New York City.

The COVID-19 pandemic in 2020 has caused sudden shocks in transportation systems, specifically the subway ridership patterns in New York City (NYC), U.S. Understanding the temporal pattern of subway ridership through statistical models is crucial during such shocks. However, many existing statistical frameworks may not be a good fit to analyze the ridership data sets during the pandemic, since some of the modeling assumptions might be violated during this time. In this paper, utilizing change point detection procedures, a piecewise stationary time series model is proposed to capture the nonstationary structure of subway ridership. Specifically, the model consists of several independent station based autoregressive integrated moving average (ARIMA) models concatenated together at certain time points. Further, data-driven algorithms are utilized to detect the changes of ridership patterns as well as to estimate the model parameters before and during the COVID-19 pandemic. The data sets of focus are daily ridership of subway stations in NYC for randomly selected stations. Fitting the proposed model to these data sets enhances understanding of ridership changes during external shocks, both in relation to mean (average) changes and the temporal correlations.

Near-term forecasting of companion animal tick paralysis incidence: An iterative ensemble model.

Tick paralysis resulting from bites from Ixodes holocyclus and I. cornuatus is one of the leading causes of emergency veterinary admissions for companion animals in Australia, often resulting in death if left untreated. Availability of timely information on periods of increased risk can help modulate behaviors that reduce exposures to ticks and improve awareness of owners for the need of lifesaving preventative ectoparasite treatment. Improved awareness of clinicians and pet owners about temporal changes in tick paralysis risk can be assisted by ecological forecasting frameworks that integrate environmental information into statistical time series models. Using an 11-year time series of tick paralysis cases from veterinary clinics in one of Australia's hotspots for the paralysis tick Ixodes holocyclus, we asked whether an ensemble model could accurately forecast clinical caseloads over near-term horizons. We fit a series of statistical time series (ARIMA, GARCH) and generative models (Prophet, Generalised Additive Model) using environmental variables as predictors, and then combined forecasts into a weighted ensemble to minimise prediction interval error. Our results indicate that variables related to temperature anomalies, levels of vegetation moisture and the Southern Oscillation Index can be useful for predicting tick paralysis admissions. Our model forecasted tick paralysis cases with exceptional accuracy while preserving epidemiological interpretability, outperforming a field-leading benchmark Exponential Smoothing model by reducing both point and prediction interval errors. Using online particle filtering to assimilate new observations and adjust forecast distributions when new data became available, our model adapted to changing temporal conditions and provided further reduced forecast errors. We expect our model pipeline to act as a platform for developing early warning systems that can notify clinicians and pet owners about heightened risks of environmentally driven veterinary conditions.

Confidence Regions for Parameters in Stationary Time Series Models With Gaussian Noise

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical likelihood ratio is obtained which is shown to be asymptotically chi-square distributed. It can be used to construct confidence regions. By adding pseudo samples, we simultaneously eliminate the non-definition of the original empirical likelihood and enhance the coverage probability. Finite sample properties of the empirical likelihood confidence regions are explored through Monte Carlo simulation, and some real data applications are carried out.

Investigating seasonal patterns in enteric infections: a systematic review of time series methods.

Foodborne and waterborne gastrointestinal infections and their associated outbreaks are preventable, yet still result in significant morbidity, mortality and revenue loss. Many enteric infections demonstrate seasonality, or annual systematic periodic fluctuations in incidence, associated with climatic and environmental factors. Public health professionals use statistical methods and time series models to describe, compare, explain and predict seasonal patterns. However, descriptions and estimates of seasonal features, such as peak timing, depend on how researchers define seasonality for research purposes and how they apply time series methods. In this review, we outline the advantages and limitations of common methods for estimating seasonal peak timing. We provide recommendations improving reporting requirements for disease surveillance systems. Greater attention to how seasonality is defined, modelled, interpreted and reported is necessary to promote reproducible research and strengthen proactive and targeted public health policies, intervention strategies and preparedness plans to dampen the intensity and impacts of seasonal illnesses.

Comparison of Active COVID-19 Cases per Population Using Time-Series Models

This research explored the precision of diverse time-series models for COVID-19 epidemic detection in all the thirty-six different states and the Federal Capital Territory (FCT) in Nigeria with the maximum count of daily cumulative of confirmed, recovered and death cases as of 4 November 2020 of COVID-19 and populace of each state. A 14-multi step ahead forecast system for active coronavirus cases was built, analyzed and compared for six (6) different deep learning-stimulated and statistical time-series models using two openly accessible datasets. The results obtained showed that based on RMSE metric, ARIMA model obtained the best values for four of the states (0.002537, 0.001969.12E-058, 5.36E-05 values for Lagos, FCT, Edo and Delta states respectively). While no method is all-encompassing for predicting daily active coronavirus cases for different states in Nigeria, ARIMA model obtains the highest-ranking prediction performance and attained a good position results in other states.

Model-based ensembles: Lessons learned from retrospective analysis of COVID-19 infection forecasts across 10 countries

Mathematical models of different types and data intensities are highly used by researchers, epidemiologists, and national authorities to explore the inherently unpredictable progression of COVID-19, including the effects of different non-pharmaceutical interventions. Regardless of model complexity, forecasts of future COVID-19 infections, deaths and hospitalization are associated with large uncertainties, and critically depend on the quality of the training data, and in particular how well the recorded national or regional numbers of infections, deaths and recoveries reflect the the actual situation. In turn, this depends on, e.g., local test and abatement strategies, treatment capacities and available technologies. Other influencing factors including temperature and humidity, which are suggested by several authors to affect the spread of COVID-19 in some countries, are generally only considered by the most complex models and further serve to inflate the uncertainty. Here we use comparative and retrospective analyses to illuminate the aggregated effect of these systematic biases on ensemble-based model forecasts. We compare the actual progression of active infections across ten of the most affected countries in the world until late November 2020 with “re-forecasts” produced by two of the most commonly used model types: (i) a compartment-type, susceptible–infected–removed (SIR) model; and (ii) a statistical (Holt-Winters) time series model. We specifically examine the sensitivity of the model parameters, estimated systematically from different subsets of the data and thereby different time windows, to illustrate the associated implications for short- to medium-term forecasting and for probabilistic projections based on (single) model ensembles as inspired by, e.g., weather forecasting and climate research. Our findings portray considerable variations in forecasting skill in between the ten countries and demonstrate that individual model predictions are highly sensitive to parameter assumptions. Significant skill is generally only confirmed for short-term forecasts (up to a few weeks) with some variation across locations and periods.

Exponential tilted likelihood for stationary time series models

Depending on the asymptotical independence of periodograms, exponential tilted (ET) likelihood, as an effective nonparametric statistical method, is developed to deal with time series in this paper. Similar to empirical likelihood (EL), it still suffers from two drawbacks: the non-definition problem of the likelihood function and the under-coverage probability of confidence region. To overcome these two problems, we further proposed the adjusted ET (AET) likelihood. With a specific adjustment level, our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method. In addition, due to the good performance of ET under moment model misspecification [Schennach, S. M. (2007). Point estimation with exponentially tilted empirical likelihood. The Annals of Statistics, 35(2), 634–672. https://doi.org/10.1214/009053606000001208], we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1). The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation. A real data set is analyzed for illustration purpose.

지수평활법과 ARIMA를 이용한 전남 김 위판가격 예측모형 비교

This study conducted a price forecast of major Purple laver production areas, Jeollanam-do, in South Korea. Based on the reasoning that price forecast of Purple laver production regions could assist in controlling supply and demand, through the Exponential smoothing technique(Single exponential smoothing, Holt-Winters Additive and Multiplicative, Exponential smoothing method) and Auto regressive integrated moving average model(ARIMA), Purple laver producer price of Jeollanam-do, the largest wet Purple laver producing area, has been predicted. Moreover, the accuracy and stability of the relevant forecasting model have been reviewed through the Historical simulation method. Concerning Jeollanam-do Purple laver producer price forecast results, among the total models adopted through the utilization of the Historical simulation method, the Simple exponential smoothing with DRIFT forecast model, which uses a DRIFT forecast, was ultimately selected after going through stationary Time series and forecast model accuracy tests.

SACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier

In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.