Univariate Time Series Models Research Articles

Forecasting Volatility Returns of Oil Price Using Gene Expression Programming Approach

Abstract This study employs four (4) Generalized Autoregressive Conditional Heteroscedasticity (GARCH) variants namely GARCH (1, 1), Glosten–Jagannathan–Runkle (GJR), Auto Regressive Integrated Moving Average (ARIMA)-GARCH and ARIMA-GJR as benchmark models to assess the performance of a proposed novel Gene Expression Programming (GEP) based univariate time series modeling approach used to conduct ex ante oil price volatility forecasts. The report illustrates that the GEP model is more superior to any of the traditional models on issues relating to both loss functions applied. The GEP model is of a greater volatility forecasting precision at different forecast horizons, therefore. There is also the existence of evidence that GJR and ARIMA-GJR differ in their loss functions, the performance is nevertheless better than GARCH (1, 1) and ARIMA-GARCH. This study conducted herein achieves importance in literature by broadening the application of gene algorithms in finance and forecasting. It also solves the problem of high error associated with the use of GARCH related models in oil price volatility forecasting.

Forecasting the total electricity production in South Africa: Comparative analysis to improve the predictive modelling accuracy

Electricity plays an important role in the South African economy with the industrial sector consuming the highest proportion followed by the residential and mining sector. Besides the fact that electricity is considered as an important energy sources, an adequate supply of electricity remains an important factor that affects the development and economic growth of a country. Therefore, it becomes even more important to forecast the total electricity production in South Africa. It turns out that the comparison of the predictive performance of different forecasting methods is inevitable. Hybrid forecasting approaches, such as artificial neural network (ANN) based seasonal Autoregressive Integrated Moving Average (sARIMA) model, ANN based multiplicative Holt-Winters (HW) model, ANN based additive HW model, an adaptive neuro-fuzzy inference system (ANFIS) based sARIMA model, ANFIS based multiplicative HW model and ANFIS based additive HW model, are employed as some valuable alternatives compared with the conventional univariate time series models, such as sARIMA model and both multiplicative and additive HW models. The aim of this study is not only to provide evidence on the weakness of the univariate time series models, but also to show that hybrid forecasting method has the superior ability over the univariate time series models, with achieving a higher forecasting accuracy. In addition, random walk model is used as benchmark model, allowing for the fair competition. The results show that the hybrid model, ANN based on multiplicative HW model, is the most fitted for the total electricity production in South Africa. This study presents an empirical framework to guide the field of prediction research by providing a more comprehensive empirical investigation of the total electricity production forecasting by using various hybrid models.

A novel deseasonalized time series model with an improved seasonal estimate for groundwater level predictions

Abstract Groundwater level prediction and forecasting using univariate time series models are useful for effective groundwater management under data limiting conditions. The seasonal autoregressive integrated moving average (SARIMA) models are widely used for modeling groundwater level data as the groundwater level signals possess the seasonality pattern. Alternatively, deseasonalized autoregressive and moving average models (Ds-ARMA) can be modeled with deseasonalized groundwater level signals in which the seasonal component is estimated and removed from the raw groundwater level signals. The seasonal component is traditionally estimated by calculating long-term averaging values of the corresponding months in the year. This traditional way of estimating seasonal component may not be appropriate for non-stationary groundwater level signals. Thus, in this study, an improved way of estimating the seasonal component by adopting a 13-month moving average trend and corresponding confidence interval approach has been attempted. To test the proposed approach, two representative observation wells from Adyar basin, India were modeled by both traditional and proposed methods. It was observed from this study that the proposed model prediction performance was better than the traditional model's performance with R2 values of 0.82 and 0.93 for the corresponding wells' groundwater level data.

Modeling Short Run Relationship between Naira-USD Exchange Rate and Crude Oil Price in Nigeria

The vector auto-regressive (VAR) model is one of the most successful, flexible, and easy to use models for the analysis of multivariate time series. It is a natural extension of the univariate auto-regressive model to a dynamic multivariate time series.The VAR model has proven to be especially useful for describing the dynamic behavior of economic and financial time series and for forecasting. It often provides superior forecasts to those from univariate time series models. The data used are monthlyobservations from January 2006 to October 2016 of Nigeria Crude Oil price and Naira to the dollar exchange rate. The VAR model was employed for modelling the data. The unit root test reveals that all the series are non-stationary at the level and stationary at first difference. The co-integration relations among the series indices were identified by applying Johansen’s cointegration test. The result of Johansen’s test indicates no existence of co-integration relation between the variables. The final result shows that a vector autoregressive (VAR) model of lag three with no co-integration equations best fits the data.

Predictive Performance of Alternative Inflation Forecasting Models: New International Evidence

Inflation rate and its volatility have been at a subdued level for most industrialized and emerging countries since the mid-1990s. The objective of this study is to evaluate the predictive performance of three alternative inflation forecasting models -- univariate time-series (ARIMA) model, Phillips curve model, and naïve model -- for a selected number of inflation-targeting countries and non-inflation targeting countries over the period 1998-2015, a unique period marked by relatively low and stable inflation rate. It is found that out-of-sample inflation forecasts generated by ARIMA model are more accurate than those generated by the other two forecasting models for the majority of these countries. This study concludes, that during the period of low inflation rate, the central bank should weigh inflation forecasts obtained from a simple time-series model, such as ARIMA model, more heavily in its decisionmaking process.

A Review on Short-Term Prediction of Air Pollutant Concentrations

In the attempt to increase the production of the industrial sector to accommodate human needs; motor vehicles and power plants have led to the decline of air quality. The tremendous decline of air pollution levels can adversely affect human health, especially children, those elderly, as well as patients suffering from asthma and respiratory problems. As such, the air pollution modelling appears to be an important tool to help the local authorities in giving early warning, apart from functioning as a guide to develop policies in near future. Hence, in order to predict the concentration of air pollutants that involves multiple parameters, both artificial neural network (ANN) and principal component regression (PCR) have been widely used, in comparison to classical multivariate time series. Besides, this paper also presents comprehensive literature on univariate time series modelling. Overall, the classical multivariate time series modelling has to be further investigated so as to overcome the limitations of ANN and PCR, including univariate time series methods in short-term prediction of air pollutant concentrations.

Spatio-temporal heterogeneity of malaria morbidity in Ghana: Analysis of routine health facility data.

BackgroundMalaria incidence is largely influenced by vector abundance. Among the many interconnected factors relating to malaria transmission, weather conditions such as rainfall and temperature are known to create suitable environmental conditions that sustain reproduction and propagation of anopheles mosquitoes and malaria parasites. In Ghana, climatic conditions vary across the country. Understanding the heterogeneity of malaria morbidity using data sourced from a recently setup data repository for routine health facility data could support planning.MethodsMonthly aggregated confirmed uncomplicated malaria cases from the District Health Information Management System and average monthly rainfall and temperature records obtained from the Ghana Meteorological Agency from 2008 to 2016 were analysed. Univariate time series models were fitted to the malaria, rainfall and temperature data series. After pre-whitening the morbidity data, cross correlation analyses were performed. Subsequently, transfer function models were developed for the relationship between malaria morbidity and rainfall and temperature.ResultsMalaria morbidity patterns vary across zones. In the Guinea savannah, morbidity peaks once in the year and twice in both the Transitional forest and Coastal savannah, following similar patterns of rainfall at the zonal level. While the effects of rainfall on malaria morbidity are delayed by a month in the Guinea savannah and Transitional Forest zones those of temperature are delayed by two months in the Transitional forest zone. In the Coastal savannah however, incidence of malaria is significantly associated with two months lead in rainfall and temperature.ConclusionData captured on the District Health Information Management System has been used to demonstrate heterogeneity in the dynamics of malaria morbidity across the country. Timing of these variations could guide the deployment of interventions such as indoor residual spraying, Seasonal Malaria Chemoprevention or vaccines to optimise effectiveness on zonal basis.

Using Univariate Time Series Models to Forecast Unemployment Rates: Evidence from State of Maine

Unemployment rate has been always one of the major issues that policy makers deal with. Having a future forecast of unemployment rate can really help policy makers in making right decision. Forecasting is a process that determines what will happen to the desired variable in future, which involves lots of uncertainties and risks, by studying and analyzing the past and the present. This paper uses ARIMA models to constructing a time series model based on historical data and then projecting it to the future to have a forecast on unemployment rate in the state of Maine. ARIMA models have the advantage of relatively low research costs compared to other econometric models and also a good efficiency in short-term forecasting. The time interval for the data is 1996M1-2015M4 and the data are taken from the “Center for Workforce Research and Information” website

Time-trend analysis and developing a forecasting model for the prevalence of multiple sclerosis in Kohgiluyeh and Boyer-Ahmad Province, southwest of Iran

ObjectiveThis study was designed and implemented to assess the current situation and to estimate the time trend of multiple sclerosis (MS), as well as to explain potential factors associated with such a trend. MethodsThis longitudinal study was carried out based on analysis of the data from the monitoring and treatment surveillance system for 421 patients with MS in Kohgiluyeh and Boyer-Ahmad Province, Iran, from 1990 to 2015. To this end, curve estimation approach was used to investigate the changes in prevalence and incidence of the disease, and univariate time series model analysis was applied in order to estimate the disease incidence in the next 10 years. ResultsThe mean and standard deviation of age were 29.78 and 8.5 years at the time of diagnosis, and the mean and 95% confidence interval of age were 29.18 (28.86–30.77) and 29.68 (28.06–31.30) at the time of diagnosis for women and men, respectively. The sex ratio (males to females) was estimated as 3.3, and the prevalence of the disease was estimated as 60.14 in 100,000 people. The diagram of the 35-year trend of the disease indicated three distinct patterns with a tendency to increase in recent years. ConclusionThe prevalence and incidence trend of the disease in the study population is consistent with regional and global changes. Climatic and environmental factors such as extreme weather changes, dust particles, expansion of the application of new industrial materials, and regional wars with potential use of banned weapons are among the issues that may, in part, be able to justify the global and regional changes of the disease. Predictive models indicate a growing trend of the disease, highlighting the need for more regular monitoring of the disease trend in upcoming years.

A new bivariate integer-valued GARCH model allowing for negative cross-correlation

Univariate integer-valued time series models, including integer-valued autoregressive (INAR) models and integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, have been well studied in the literature, but there is little progress in multivariate models. Although some multivariate INAR models were proposed, they do not provide enough flexibility in modeling count data, such as volatility of numbers of stock transactions. Then, a bivariate Poisson INGARCH model was suggested by Liu (Some models for time series of counts, Dissertations, Columbia University, 2012), but it can only deal with positive cross-correlation between two components. To remedy this defect, we propose a new bivariate Poisson INGARCH model, which is more flexible and allows for positive or negative cross-correlation. Stationarity and ergodicity of the new process are established. The maximum likelihood method is used to estimate the unknown parameters, and consistency and asymptotic normality for estimators are given. A simulation study is given to evaluate the estimators for parameters of interest. Real and artificial data examples are illustrated to demonstrate good performances of the proposed model relative to the existing model.

Forecasting stream flow using hybrid neuro-wavelet technique

Precise and timely predictions of high and low flow events at any watershed location can provide stakeholders the information required to make strategic, informed decisions. Specifically, soft computing models have become popular in last few decades because of their ability of offering effective solutions for modeling and analyzing the behavior of complex dynamical systems along with simulating and forecasting hydrological applications. Artificial neural networks (ANN) have gained significant attention for forecasting stream flows in last two decades. Phase lag nevertheless is the common problem noticed in most of the studies that used univariate time series modeling. This technical issue must be resolved if such tools are to be transferred into an operational settings. This study explores the potential benefits of applying a phase lag correction procedure to neural network stream flow forecasting models by combining wavelet transform with ANN at four stations from Krishna and Narmada basins in India.

Incorporating Relevant Multivariate Information for Characterizing Half-Life with an Application to Purchasing Power Parity

Half-lives are summary measures of persistence, and are usually characterized from impulse response functions (IRFs) of univariate time series models. Two issues which occur with half-life characterization in multivariate time series are IRFs become conditional on specific shocks and are often also not uniquely identified. I introduce an approach for characterizing the half-life in multivariate time series models which circumvents both issues. An empirical application suggests the half-life of the real exchange rate estimated from multivariate models is generally longer relative to univariate models.

Forecasting electric vehicles sales with univariate and multivariate time series models: The case of China.

The market demand for electric vehicles (EVs) has increased in recent years. Suitable models are necessary to understand and forecast EV sales. This study presents a singular spectrum analysis (SSA) as a univariate time-series model and vector autoregressive model (VAR) as a multivariate model. Empirical results suggest that SSA satisfactorily indicates the evolving trend and provides reasonable results. The VAR model, which comprised exogenous parameters related to the market on a monthly basis, can significantly improve the prediction accuracy. The EV sales in China, which are categorized into battery and plug-in EVs, are predicted in both short term (up to December 2017) and long term (up to 2020), as statistical proofs of the growth of the Chinese EV industry.

Measuring uncertainty of traffic volume on motorway concessions: a time-series analysis

Abstract This paper presents a method to build up a confidence interval for the evolution of traffic in motorway concessions, based on a univariate time-series model. The main advantage of this method, compared to traditional traffic models, is that it allows to avoid the error in the prediction of the explanatory variables. The results obtained show that the use of a time-series model represents a feasible alternative to assess traffic uncertainty in existing concessions, when long series of traffic data are available.

Out-of-sample forecasting of the Canadian unemployment rates using univariate models

ABSTRACTThis article investigates the out-of-sample forecasting performance of some linear and nonlinear univariate time series models on the monthly seasonally adjusted Canadian unemployment rates during the 1980–2013 period. The findings reveal that nonlinear time series models better capture the asymmetry present in the unemployment rate series at short and long forecast horizons.

On bayesian inference for almost periodic in mean autoregressive models

The goal of the paper is to discuss Bayesian estimation of a class of univariate time-series models being able to represent complicated patterns of “cyclical” fluctuations in mean function. We highlight problems that arise in Bayesian estimation of parametric time-series model using the Flexible Fourier Form of Gallant (1981). We demonstrate that the resulting posterior is likely to be highly multimodal, therefore standard Markov Chain Monte Carlo (MCMC in short) methods might fail to explore the whole posterior, especially when the modes are separated. We show that the multimodality is actually an issue using the exact solution (i.e. an analytical marginal posterior) in an approximate model. We address that problem using two essential steps. Firstly, we integrate the posterior with respect to amplitude parameters, which can be carried out analytically. Secondly, we propose a non-parametrically motivated proposal for the frequency parameters. This allows for construction of an improved MCMC sampler that effectively explores the space of all the model parameters, with the amplitudes sampled by the direct approach outside the MCMC chain. We illustrate the problem using simulations and demonstrate our solution using two real-data examples.

Forecasting traffic time series with multivariate predicting method

Scalar time series considered in most studies may be not sufficient to reconstruct the dynamics, while using multivariate time series may demonstrate great advantages over scalar time series if they are available. Multivariate time series are available in the traffic system and we intend to examine the issue for the real data in the traffic system. In this paper, we propose the multivariate predicting method and discuss the prediction performance of multivariate time series by comparison with univariate time series and K-nearest neighbor (KNN) nonparametric regression model. The three kinds of forecast accuracy measure for multivariate predicting method are smaller than those for the other two methods in all cases, which suggest the predicting results for traffic time series by multivariate predicting method are better and more accurate than those based on univariate time series and KNN model. It demonstrates that the proposed multivariate predicting method is more successful in predicting the traffic time series than univariate predicting method and KNN method. The multivariate predicting method has a broad application prospect on prediction because of its advantage on recovering the dynamics of nonlinear system.

Adaptive spectral estimation for nonstationary multivariate time series

Following the nonstationary univariate time series model of Rosen et al. (2012), we propose an adaptive estimation of time-varying spectra and cross-spectra for analyzing possibly nonstationary multivariate time series. Under the Bayesian framework, the estimation is implemented by smoothing stochastic approximation Monte Carlo (SSAMC) methods. We show by simulation study that the proposed method achieves good performance for time series whether changing abruptly or smoothly. The superiority to the other existing methods is also investigated. An application to longitudinal vibration data of the containership provides a wave-approach angle range, which should be recommended when sailing under a harsh sea condition.

Some stylised facts about the exchange rate behaviour of Central European currencies

The paper investigates developments of exchange rate time series of Central European currencies and tries to find evidence of some stylised facts. Statistical methods and an econometric approach to the univariate time series modelling of high-frequency data, i.e., daily, are used. The main conclusions are as follows: (1) All the CE nominal exchange time series are not stationary: nevertheless, stationarity of all the return time series was confirmed. (2) Volatility clustering was proven and the GARCH modelling approach was successfully applied, including asymmetric modelling of volatility. (3) The more flexible an exchange rate regime is, the more volatile the respective currency. This is true for both nominal and real exchange rates. While nominal volatility is lower than real volatility in a system of fixed or less flexible exchange rates, the opposite is true for flexible systems: exchange rate volatility is higher in nominal terms than in real terms.

Short- and Mid-Term Forecasting of Baseload Electricity Prices in the U.K.: The Impact of Intra-Day Price Relationships and Market Fundamentals

In this paper we investigate whether considering the fine structure of half-hourly electricity prices, the market closing prices of fundamentals (natural gas, coal and ${\rm CO}_{2}$ ) and the system-wide demand can lead to significantly more accurate short- and mid-term forecasts of APX U.K. baseload prices. We evaluate the predictive accuracy of a number of univariate and multivariate time series models over a three-year out-of-sample forecasting period and compare it against that of a benchmark autoregressive model. We find that in the short-term, up to a few business days ahead, a disaggregated model which independently predicts the intra-day prices and then takes their average to yield baseload price forecasts is the best performer. However, in the mid-term, factor models which explore the correlation structure of intra-day prices lead to significantly (as measured by the Diebold-Mariano test) better baseload price forecasts. At the same time, we observe that the inclusion of fundamental variables—especially natural gas prices (in the short-term) and coal prices (in the mid-term)—provides significant gains. The ${\rm CO}_{2}$ prices, on the other hand, generally do not improve the price forecasts at all, at least in the time period considered in this study (April 2009–December 2013).