Seasonal Time Series Forecasting Research Articles

A Bagging Ensemble Algorithm for Seasonal Time Series Forecasting

A Bagging Ensemble Algorithm for Seasonal Time Series Forecasting

An ensemble learning strategy for panel time series forecasting of excess mortality during the COVID-19 pandemic

Quantifying and analyzing excess mortality in crises such as the ongoing COVID-19 pandemic is crucial for policymakers. Traditional measures fail to take into account differences in the level, long-term secular trends, and seasonal patterns in all-cause mortality across countries and regions. This paper develops and empirically investigates the forecasting performance of a novel, flexible and dynamic ensemble learning with a model selection strategy (DELMS) for the seasonal time series forecasting of monthly respiratory disease death data across a pool of 61 heterogeneous countries. The strategy is based on a Bayesian model averaging (BMA) of heterogeneous time series methods involving both the selection of the subset of best forecasters (model confidence set), the identification of the best holdout period for each contributed model, and the determination of optimal weights using out-of-sample predictive accuracy. A model selection strategy is also developed to remove the outlier models and to combine the models with reasonable accuracy in the ensemble. The empirical outcomes of this large set of experiments show that the accuracy of the BMA approach is significantly improved with DELMS when selecting a flexible and dynamic holdout period and removing the outlier models. Additionally, the forecasts of respiratory disease deaths for each country are highly accurate and exhibit a high correlation (94%) with COVID-19 deaths in 2020.

Inventory Management and Demand Forecasting Improvement of a Forecasting Model Based on Artificial Neural Networks

Forecasting is predicting or estimating a future event or trend. Supply chains have been constantly growing in most countries ever since the industrial revolution of the 18th century. As the competitiveness between supply chains intensifies day by day, companies are shifting their focus to predictive analytics techniques to minimize costs and boost productivity and profits. Excessive inventory (overstock) and stock outs are very significant issues for suppliers. Excessive inventory levels can lead to loss of revenue because the company's capital is tied up in excess inventory. Excess inventory can also lead to increased storage, insurance costs and labor as well as lower and degraded quality based on the nature of the product. Shortages or out of stock can lead to lost sales and a decline in customer contentment and loyalty to the store. If clients are unable to find the right products on the shelves, they may switch to another vendor or purchase alternative items. Demand forecasting is valuable for planning, scheduling and improving the coordination of all supply chain activities. This paper discusses the use of neural networks for seasonal time series forecasting. Our objective is to evaluate the contribution of the correct choice of the transfer function by proposing a new form of the transfer function to improve the quality of the forecast.

A parallel-series hybridization of seasonal intelligent based statistical model for demand forecasting

PurposeThe purpose of this paper, because of the complexity of demand time series and the need to construct a more accurate hybrid model that can model all relationships in data, is to propose a parallel-series hybridization of seasonal neural networks and statistical models for demand time series forecasting.Design/methodology/approachThe main idea of proposed model is centered around combining parallel and series hybrid methodologies to use the benefit of unique advantages of both hybrid strategies as well as intelligent and classic seasonal time series models simultaneously for achieving results that are more accurate for the first time. In the proposed model, in contrast of traditional parallel and series hybrid strategies, it can be generally shown that the performance of the proposed model will not be worse than components.FindingsEmpirical results of forecasting two well-known seasonal time series data sets, including the total production value of the Taiwan machinery industry and the sales volume of soft drinks, indicate that the proposed model can effectively improve the forecasting accuracy achieved by either of their components used in isolation. In addition, the proposed model can achieve more accurate results than parallel and series hybrid model with same components. Therefore, the proposed model can be used as an appropriate alternative model for seasonal time series forecasting, especially when higher forecasting accuracy is needed.Originality/valueTo the best of the authors’ knowledge, the proposed model, for first time and in contrast of traditional parallel and series hybrid strategies, is developed.

Seasonal Time Series Forecasting by F1-Fuzzy Transform.

We present a new seasonal forecasting method based on F1-transform (fuzzy transform of order 1) applied on weather datasets. The objective of this research is to improve the performances of the fuzzy transform-based prediction method applied to seasonal time series. The time series’ trend is obtained via polynomial fitting: then, the dataset is partitioned in S seasonal subsets and the direct F1-transform components for each seasonal subset are calculated as well. The inverse F1-transforms are used to predict the value of the weather parameter in the future. We test our method on heat index datasets obtained from daily weather data measured from weather stations of the Campania Region (Italy) during the months of July and August from 2003 to 2017. We compare the results obtained with the statistics Autoregressive Integrated Moving Average (ARIMA), Automatic Design of Artificial Neural Networks (ADANN), and the seasonal F-transform methods, showing that the best results are just given by our approach.

Seasonal time series forecasting by the Walsh-transformation based technique

It is relatively well known that Walsh–Fourier analysis is capable of approximating functions by decomposing them into simple values: 1 and − 1. This method and its valuable characteristics however, are seldom applied in time series forecasting. Moreover, despite the promising applicability of the technique, there is gap in the scientific literature for a comprehensive and detailed introduction and application. Inspired by the results Stoffer (J Time Ser Anal 6:261–267, 1985, J Time Ser Anal 8:449–167, 1987, J Time Ser Anal 11:57–73, 1990, J Am Stat Assoc 86(414):461–479, 1991), Stoffer et al. (J Am Stat Assoc 83:954–963, 1988) and Basu et al. (Electr Power Energy Syst 13(4):193–200, 1991) in the current paper, we aim to describe the theory of Walsh–Fourier analysis, to introduce the so-called Walsh transformation based “row-wise” forecasting process—using the characteristics of the Walsh-matrix—for its application and to compare numerically in R-programming environment (RStudio) using the MComp test data set and the state-of-the-art methods (generic function forecast()) the following two approaches: As can be seen—based on our intentions—a significant advantage of the proposed forecasting process is that when forecasting more than one-step ahead it does not use previously forecasted values and, hence, does not accumulate inaccuracy, thus the forecasted results can be more proper compared to other mainstream techniques. Moreover, as show our numeric results the longer the horizon of forecasting, the more attractive relative accuracy achieved.

An Empirical Study of Error Evaluation in Trend and Seasonal Time Series Forecasting Based on SSA

SSA (Singular Spectrum Analysis) starts to become a popular method in decomposing time series into some separable and interpretable series. This study provides an error evaluation in the SSA-based model for trend and multiple seasonal time series forecasting. This error evaluation is obtained by means of a numerical study on the mean square error of the estimators and mean absolute percentage error of the forecast values. Four distinct types of data generating processes (DGP) with varying sample sizes are considered in this experimental study. The parameters are estimated from the component series of SSA. Each DGP is decomposed into trend, periodic and irregular components. All these components except the irregular one are fitted by appropriate deterministic function separately. Based on the numerical simulation results, the estimated parameters are closer to the true values as the sample size increases. As the illustrative example of the real data set implementation, we used the monthly atmospheric concentrations of CO2 from Moana Loa observatory for period January 1959 to June 1972. The proposed method produces better forecast values than the results of SSA-LRF (Linear Recurrent Formula) and TLSAR (Two Level Seasonal Autoregressive). The results encourage the improvement in the time series modeling on the more complex pattern.

Forecasting seasonal time series based on fuzzy techniques

This paper is devoted to a method for the forecasting of seasonal time series. The core of our approach is based on the fuzzy transform and fuzzy natural logic (FNL) techniques. Under the assumption that a time series can be additively decomposed into a trend-cycle, a seasonal component and an irregular fluctuation, the forecasting is a combination of individual forecasting of each of these constituents. More precisely, the trend-cycle and the seasonal component are predicted with the help of fuzzy transform, pattern recognition and fuzzy natural logic techniques. To model the irregular component, we apply the Box–Jenkins approach. In the paper, we compare the suggested method with two other well-known methods, namely STL (see [14]) and ARIMA ones.

A novel intelligent approach for state space evolving forecasting of seasonal time series

This paper proposes a new methodology for modelling based on an evolving Neuro-Fuzzy Takagi–Sugeno (NF-TS) network used for seasonal time series forecasting. The NF-TS considers the unobservable components extracted from the time series data to evolve, that is, to adapt and to adjust its structure, where the fuzzy rules number of this network can increase or decrease according to components behaviour. The method used to extract these components is a recursive version, proposed in this paper, based on the Spectral Singular Analysis (SSA) technique. The NF-TS network adopts the principle divide to conquer, where it divides a complex problem into subproblems easier to deal, forecasting separately each unobservable component, because they present dynamic behaviours that are simpler to forecast. The consequent propositions of fuzzy rules are linear state space models, where the states are the unobservable components data. When there are available observations from the time series, the training stage of NF-TS is performed, i.e., the NF-TS evolves its structure and adapts its parameters to carry out the mapping between the components data and the available sample of original time series. On the other hand, if this observation is not available, the network considers the forecasting stage, keeping its structure fixed and using the states of consequent fuzzy rules to feedback the unobservable components data to NF-TS. The NF-TS was evaluated and compared with other recent and traditional techniques for seasonal time series forecasting, obtaining competitive and advantageous results in relation to other papers. This paper also presents a case study about real-time detection of anomalies based on a patient electrocardiogram data.

Seasonal time-series modeling and forecasting of monthly mean temperature for decision making in the Kurdistan Region of Iraq

A generalized structural time-series modeling framework was used to analyze the monthly records of mean temperature, one of the most important environmental parameters, using classical stochastic processes. In this article we are using the SARIMA Box–Jenkins model and obtain a medium-term (10 years) forecast of the mean temperature in Erbil. A prediction of the monthly mean temperature during the past 287 months ((Formula presented.)24 years) using the SARIMA(0,1,2)(0,1,1)12 model predicts that the average temperature in the governorate of Erbil, Iraq, will be stable for the next 10 years. The evaluation of prediction accuracy shows that our model performs equally well when applying it to different periods of time for which data is available. The method used here could easily be applied by the decision makers responsible for providing water and electricity in the Kurdistan Region.

Short-term load forecasting method based on fuzzy time series, seasonality and long memory process

Seasonal Auto Regressive Fractionally Integrated Moving Average (SARFIMA) is a well-known model for forecasting of seasonal time series that follow a long memory process. However, to better boost the accuracy of forecasts inside such data for nonlinear problem, in this study, a combination of Fuzzy Time Series (FTS) with SARFIMA is proposed. To build the proposed model, certain parameters requires to be estimated. Therefore, a reliable Evolutionary Algorithm namely Particle Swarm Optimization (PSO) is employed. As a case study, a seasonal long memory time series, i.e., short term load consumption historical data, is selected. In fact, Short Term Load Forecasting (STLF) plays a key role in energy management systems (EMS) and in the decision making process of every power supply organization. In order to evaluate the proposed method, some experiments, using eight datasets of half-hourly load data from England and France for the year 2005 and four data sets of hourly load data from Malaysia for the year 2007, are designed. Although the focus of this research is STLF, six other seasonal long memory time series from several interesting case studies are employed to better evaluate the performance of the proposed method. The results are compared with some novel FTS methods and new state-of-the-art forecasting methods. The analysis of the results indicates that the proposed method presents higher accuracy than its counterparts, representing an efficient hybrid method for load forecasting problems.

A NEW APPROACH BASED ON OPTIMIZATION OF RATIO FOR SEASONAL FUZZY TIME SERIES

In recent years, many studies have been done on forecasting fuzzy time series. First-order fuzzy time series forecasting methods with first-order lagged variables and high-order fuzzy time series forecasting methods with consecutive lagged variables constitute the considerable part of these studies. However, these methods are not effective in forecasting fuzzy time series which contain seasonal structures. In this respect, it would be more appropriate to use methods that consider the seasonal relations in seasonal fuzzy time series forecasting. Although seasonal fuzzy time series forecasting methods exist in literature, these methods use equal interval lengths in partition of the universe of discourse. This situation incapacitates the performance of the method in forecasting time series including seasonality and trend. In this study, a new fuzzy time series forecasting method in which intervals constituting partition of the universe of discourse increase in time at a rate that obtained based on optimization was proposed. The proposed method was applied to two real time series and obtained results were compared with other methods and the superior performance of the proposed method was proved.

Least square support vector machines as an alternative method in seasonal time series forecasting

The least square support vector machines (LSSSVM) model is a novel forecasting approach and has been successfully used to solve time series problems. However, the applications of LSSVM model in a seasonal time series forecasting has not been widely investigated. This study aims at developing a LSSVM model to forecast seasonal time series data. To assess the effectiveness of this model, the airline passenger series exhibits nonlinear behaviour and shows multiplicative seasonal behaviour was applied. In order to obtain the optimal model parameters of the LSSVM, a grid search algorithm and cross-validation method were employed. In this study, seasonal autoregressive integrated moving average (SARIMA) and artificial neural network (ANN) models are employed for forecasting the same data sets. Empirical results indicate that the LSSVM yields well forecasting performances. Thus, the LSSVM model provides a promising alternative for seasonal time series forecasting.

Modelling trigonometric seasonal components for monthly economic time series

The basic structural time series model has been designed for the modelling and forecasting of seasonal economic time series. In this article, we explore a generalization of the basic structural time series model in which the time-varying trigonometric terms associated with different seasonal frequencies have different variances for their disturbances. The contribution of the article is two-fold. The first aim is to investigate the dynamic properties of this frequency-specific Basic Structural Model (BSM). The second aim is to relate the model to a comparable generalized version of the Airline model developed at the US Census Bureau. By adopting a quadratic distance metric based on the restricted reduced form moving-average representation of the models, we conclude that the generalized models have properties that are close to each other compared to their default counterparts. In some settings, the distance between the models is almost zero so that the models can be regarded as observationally equivalent. An extensive empirical study on disaggregated monthly shipment and foreign trade series illustrates the improvements of the frequency-specific extension and investigates the relations between the two classes of models.

Forecasting seasonal time series with computational intelligence: On recent methods and the potential of their combinations

Accurate time series forecasting is a key issue to support individual and organizational decision making. In this paper, we introduce novel methods for multi-step seasonal time series forecasting. All the presented methods stem from computational intelligence techniques: evolutionary artificial neural networks, support vector machines and genuine linguistic fuzzy rules. Performance of the suggested methods is experimentally justified on seasonal time series from distinct domains on three forecasting horizons. The most important contribution is the introduction of a new hybrid combination using linguistic fuzzy rules and the other computational intelligence methods. This hybrid combination presents competitive forecasts, when compared with the popular ARIMA method. Moreover, such hybrid model is more easy to interpret by decision-makers when modeling trended series.

Combining seasonal ARIMA models with computational intelligence techniques for time series forecasting

Seasonal autoregressive integrated moving average (SARIMA) models form one of the most popular and widely used seasonal time series models over the past three decades. However, in several researches it has been argued that they have two basic limitations that detract from their popularity for seasonal time series forecasting tasks. SARIMA models assume that future values of a time series have a linear relationship with current and past values as well as with white noise; therefore, approximations by SARIMA models may not be adequate for complex nonlinear problems. In addition, SARIMA models require a large amount of historical data to produce desired results. However, in real situations, due to uncertainty resulting from the integral environment and rapid development of new technology, future situations must be forecasted using small data sets over a short span of time. Using hybrid models or combining several models has become a common practice to overcome the limitations of single models and improve forecasting accuracy. In this paper, a new hybrid model, which combines the seasonal autoregressive integrated moving average (SARIMA) and computational intelligence techniques such as artificial neural networks and fuzzy models for seasonal time series forecasting is proposed. In the proposed model, these two techniques are applied to simultaneously overcome the linear and data limitations of SARIMA models and yield more accurate results. Empirical results of forecasting two well-known seasonal time series data sets indicate that the proposed model exhibits effectively improved forecasting accuracy, so that it can be used as an appropriate seasonal time series model.

Forecasting intraday time series with multiple seasonal cycles using parsimonious seasonal exponential smoothing

This paper concerns the forecasting of seasonal intraday time series that exhibit repeating intraweek and intraday cycles. A recently proposed exponential smoothing method involves smoothing a different intraday cycle for each distinct type of day of the week. Similar days are allocated identical intraday cycles. A limitation is that the method allows only whole days to be treated as identical. We introduce a new exponential smoothing formulation that allows parts of different days of the week to be treated as identical. The result is a method that involves the smoothing and initialisation of fewer terms. We evaluate forecasting up to a day ahead using two empirical studies. For electricity load data, the new method compares well with a range of alternatives. The second study involves a series of arrivals at a call centre that is open for a shorter duration at the weekends than on weekdays. Among the variety of methods considered, the new method is the only one that can model in a satisfactory way in this situation, where the number of periods on each day of the week is not the same.

Average Power Function of Noise and Its Applications in Seasonal Time Series Modeling and Forecasting

This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.

Seasonal Time Series Data Forecasting by Using Neural Networks Multiscale Autoregressive Model

Problem statement: The aim of this research was to study further some latest progress of wavelet transform for time series forecasting, particularly about Neural Networks Multiscale Autoregressive (NN-MAR). Approach: There were three main issues that be considered further in this research. The first was some properties of scale and wavelet coefficients from Maximal Overlap Discrete Wavelet Transform (MODWT) decomposition, particularly at seasonal time series data. The second focused on the development of model building procedures of NN-MAR based on the properties of scale and wavelet coefficients. Then, the third was empirical study about the implementation of the proposed procedure and comparison study about the forecast accuracy of NN-MAR to other forecasting models. Results: The results showed that MODWT at seasonal time series data also has seasonal pattern for scale coefficient, whereas the wavelet coefficients are stationer. The result of model building procedure development yielded a new proposed procedure of NN-MAR model for seasonal time series forecasting. In general, this procedure accommodated input lags of scale and wavelet coefficients and other additional seasonal lags. In addition, the result showed that the proposed procedure works well for determining the best NN-MAR model for seasonal time series forecasting. Conclusion: The comparison study of forecast accuracy showed that the NN-MAR model yields better forecast than MAR and ARIMA models.

Long-Term Forecasting by Wavelet-Based Filter Bank Selections and Its Application

Long-term forecasting of seasonal time series is critical in many applications such as planning business strategies and resolving possible problems of a business company. Unlike the traditional approach that depends solely on dynamic models, Li and Hinich (2002) introduced a combination of stochastic dynamic modeling with filter bank approach for forecasting seasonal patterns using highly coherent(High-C) waveforms. We modify the filter selection and forecasting procedure on wavelet domain to be more feasible and compare the resulting predictor with one that obtained from the wavelet variance estimation method. An improvement over other seasonal pattern extraction and forecasting methods based on such as wavelet scalogram, Holt-Winters, and seasonal autoregressive integrated moving average(SARIMA) is shown in terms of the prediction error. The performance of the proposed method is illustrated by a simulation study and an application to the real stock price data.