Exponential Smoothing State Space Model Research Articles

Applying k‐nearest neighbors to time series forecasting: Two new approaches

AbstractThe k‐nearest neighbors algorithm is one of the prominent techniques used in classification and regression. Despite its simplicity, the k‐nearest neighbors has been successfully applied in time series forecasting. However, the selection of the number of neighbors and feature selection is a daunting task. In this paper, we introduce two methodologies for forecasting time series that we refer to as Classical Parameters Tuning in Weighted Nearest Neighbors and Fast Parameters Tuning in Weighted Nearest Neighbors. The first approach uses classical parameters tuning that compares the most recent subsequence with every possible subsequence from the past of the same length. The second approach reduces the neighbors' search set, which leads to significantly reduced grid size and hence a lower computational time. To tune the models' parameters, both methods implement an approach inspired by cross‐validation for weighted nearest neighbors. We evaluate the forecasting performance and accuracy of our models. Then, we compare them to other approaches, especially, Seasonal Autoregressive Integrated Moving Average, Holt Winters, and Exponential Smoothing State Space Model. Real data examples on retail and food services sales in the United States and milk production in the United Kingdom are analyzed to demonstrate the application and efficiency of the proposed approaches.

Towards cleaner air in Siliguri: A comprehensive study of PM2.5 and PM10 through advance computational forecasting models for effective environmental interventions

This research addresses the escalating concern of air pollution, primarily due to fine particulate matter (PM2.5) and coarse particulate matter (PM10), in Siliguri city, West Bengal, India. Using a comprehensive dataset of daily 24-h average concentrations from February 2018 to February 2023, procured from the Central Pollution Control Board, six advanced computational models i.e., Artificial Neural Networks (ANN), Autoregressive Integrated Moving Averages (ARIMA), Extreme Learning Machine (ELM), Exponential Smoothing State Space Models (ETS), Naïve, and Trigonometric Seasonality, Box-Cox Transformation, ARMA Errors, Trend, and Seasonality (TBATS) were rigorously tested for predicting particulate matter concentrations. Daily data from 2018 to 2021 was used for training and the remaining for testing. The models in the testing phase were evaluated using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) along with R2. In the testing phase, the TBATS model emerged as the most accurate with the lowest RMSE values of 8.11 for PM2.5 and 12.33 for PM10, followed by the ARIMA model with an RMSE of 10.72 for PM2.5 and 18.10 for PM10. The ETS model also demonstrated reliable performance. In addition, by using the advantages of the most effective models, namely ARIMA and TBATS, the research makes forecasts for PM2.5 and PM10 levels from 2023 to 2025, on a monthly basis. These findings are helpful for air quality management in Siliguri and underscore the importance of using advanced computational models for pollution forecasting, encouraging further research on hybrid models with meteorological parameters.

Seasonal Methods of Demand Forecasting in the Supply Chain as Support for the Company’s Sustainable Growth

Demand forecasting plays a key role in supply chain planning, management and its sustainable development, but it is a challenging process as demand depends on numerous, often unidentified or unknown factors that are seasonal in nature. Another problem is limited availability of information. Specifically, companies lacking modern IT systems are constrained to rely on historical sales observation as their sole source of information. This paper employs and contrasts a selection of mathematical models for short-term demand forecasting for products whose sales are characterized by high seasonal variations and a development trend. The aim of this publication is to demonstrate that even when only limited empirical data is available, while other factors influencing demand are unknown, it is possible to identify a time series that describes the sales of a product characterized by strong seasonal fluctuations and a trend, using selected mathematical methods. This study uses the seasonal ARIMA (autoregressive integrated moving average) model, ARIMA with Fourier terms model, ETS (exponential smoothing) model, and TBATS (Trigonometric Exponential Smoothing State Space Model with Box–Cox transformation, ARMA errors, Trend and Seasonal component). The models are presented as an alternative to popular machine learning models, which are more complicated to interpret, while their effectiveness is often similar. The selected methods were presented using a case study. The results obtained were compared and the best solution was identified, while emphasizing that each of the methods used could improve demand forecasting in the supply chain.

Time Series Forecasting of Hong Kong Inter-bank Offered Rate (HIBOR) using Exponential Smoothing State Space Model

Time Series Forecasting of Hong Kong Inter-bank Offered Rate (HIBOR) using Exponential Smoothing State Space Model

Forecasting daily admissions to an emergency department considering single and multiple seasonal patterns

When dealing with several years of daily data, such as the number of daily admissions to a hospital’s emergency department (ED), how complex does it get to forecast into the future? With that in mind, this study has two main goals: to explore the differences between several methodologies, considering both single and multiple-seasonal patterns; and to select the most suitable model for the administration of a Portuguese hospital to use while managing their ED. To that end, we first considered the data as a time series with a single weekly seasonal pattern. We then modelled the data using time series regression, linear regression with autoregressive integrated moving average (ARIMA) errors, seasonal ARIMA and exponential smoothing techniques. Second, the data was set to be a time series with weekly and annual seasonal patterns. Then, using Fourier terms, we applied time series regression, linear regression with ARIMA errors and trigonometric exponential smoothing state space models with Box–Cox transformation, ARMA errors, Trend and Seasonal components (TBATS) for the analysis. After selecting the best-fitting models using the Akaike Information Criteria (AIC) values, we forecasted into the future and compared the results using both training and test datasets’ root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) values. The time series regression model based on seasonal variables and a weekly seasonal pattern gives the best results. However, we decided to use linear regression with ARIMA errors, seasonal variables, and both weekly and annual seasonal patterns. This produces similar results but allows for the annual seasonality to be considered, which is useful when more data is added.

Forecasting admissions in psychiatric hospitals before and during Covid-19: a retrospective study with routine data

The COVID-19 pandemic has strong effects on most health care systems. Forecasting of admissions can help for the efficient organisation of hospital care. We aimed to forecast the number of admissions to psychiatric hospitals before and during the COVID-19 pandemic and we compared the performance of machine learning models and time series models. This would eventually allow to support timely resource allocation for optimal treatment of patients. We used admission data from 9 psychiatric hospitals in Germany between 2017 and 2020. We compared machine learning models with time series models in weekly, monthly and yearly forecasting before and during the COVID-19 pandemic. A total of 90,686 admissions were analysed. The models explained up to 90% of variance in hospital admissions in 2019 and 75% in 2020 with the effects of the COVID-19 pandemic. The best models substantially outperformed a one-step seasonal naïve forecast (seasonal mean absolute scaled error (sMASE) 2019: 0.59, 2020: 0.76). The best model in 2019 was a machine learning model (elastic net, mean absolute error (MAE): 7.25). The best model in 2020 was a time series model (exponential smoothing state space model with Box-Cox transformation, ARMA errors and trend and seasonal components, MAE: 10.44). Models forecasting admissions one week in advance did not perform better than monthly and yearly models in 2019 but they did in 2020. The most important features for the machine learning models were calendrical variables. Model performance did not vary much between different modelling approaches before the COVID-19 pandemic and established forecasts were substantially better than one-step seasonal naïve forecasts. However, weekly time series models adjusted quicker to the COVID-19 related shock effects. In practice, multiple individual forecast horizons could be used simultaneously, such as a yearly model to achieve early forecasts for a long planning period and weekly models to adjust quicker to sudden changes.

THE FORECASTING OF MONTHLY INFLATION IN YOGYAKARTA CITY USES AN EXPONENTIAL SMOOTHING-STATE SPACE MODEL

Yogyakarta is known as a student city, tourist city, and also a city of culture. Yogyakarta is an interesting tourist and cultural place with many beautiful tourist attractions in the city of Yogyakarta. Public transportation in the city of Yogyakarta is also varied, ranging from conventional and online-based. Access to the city of Yogyakarta varies, namely trains, buses, and planes. Thus, the economic growth in the city of Yogyakarta is getting better, this can be seen from the economic activity in the city of Yogyakarta which is getting busier. A good economy is usually always followed by stable inflation. This study aims to predict inflation in the future period using the Exponential Smoothing-State Space (ETS) model. Secondary monthly inflation data was obtained from BPS Yogyakarta City. From this research, the Exponential Smoothing-State Space Model / ETS (A, N, A) is obtained, which means that the monthly inflation data for the city of Yogyakarta does not contain trends, but contains additive seasonality and has additive errors. The results of this study indicate that inflation in the next three months is relatively stable, namely, the decline in inflation and the increase in inflation is still below 10%. Keywords: BPS Yogyakarta City, Monthly Inflation Forecasting, Exponential Smoothing-State Space ETS

Time-Series Analysis for the Number of Foot and Mouth Disease Outbreak Episodes in Cattle Farms in Thailand Using Data from 2010-2020.

Thailand is one of the countries where foot and mouth disease outbreaks have resulted in considerable economic losses. Forecasting is an important warning technique that can allow authorities to establish an FMD surveillance and control program. This study aimed to model and forecast the monthly number of FMD outbreak episodes (n-FMD episodes) in Thailand using the time-series methods, including seasonal autoregressive integrated moving average (SARIMA), error trend seasonality (ETS), neural network autoregression (NNAR), and Trigonometric Exponential smoothing state–space model with Box–Cox transformation, ARMA errors, Trend and Seasonal components (TBATS), and hybrid methods. These methods were applied to monthly n-FMD episodes (n = 1209) from January 2010 to December 2020. Results showed that the n-FMD episodes had a stable trend from 2010 to 2020, but they appeared to increase from 2014 to 2020. The outbreak episodes followed a seasonal pattern, with a predominant peak occurring from September to November annually. The single-technique methods yielded the best-fitting time-series models, including , , , and . Moreover, SARIMA-NNAR and NNAR-TBATS were the hybrid models that performed the best on the validation datasets. The models that incorporate seasonality and a non-linear trend performed better than others. The forecasts highlighted the rising trend of n-FMD episodes in Thailand, which shares borders with several FMD endemic countries in which cross-border trading of cattle is found common. Thus, control strategies and effective measures to prevent FMD outbreaks should be strengthened not only in Thailand but also in neighboring countries.

A Novel Approach to Modeling and Forecasting Cancer Incidence and Mortality Rates through Web Queries and Automated Forecasting Algorithms: Evidence from Romania.

Simple SummaryCancer remains a global burden, currently causing nearly one in six deaths worldwide. Accurate projections of cancer incidence and mortality are needed for effective and efficient policymaking, accurate resource allocation, and to assess the impact of newly introduced policies and measures. However, the COVID-19 pandemic disrupted public health systems and caused a significant number of cancers to remain undiagnosed, thus affecting the quality of official statistics and their usefulness for health studies. This paper addresses this issue by proposing novel cancer incidence/cancer mortality models based on population web-search habits and historical links with official health variables. The models are empirically estimated using data from one of the most vulnerable European Union (EU) members, Romania, a country that consistently reports lower survival rates than the EU average, and are further used to forecast cancer incidence and mortality rates in the country. Research findings have important policy implications, and the novel framework, owing to its generalizability, can be applied to the same task in other countries. Overall, the results indicate a continuation of the increasing trends in cancer incidence and mortality in Romania and thus underline the urgency to change the status quo in the Romanian public-health system.Cancer remains a leading cause of worldwide mortality and is a growing, multifaceted global burden. As a result, cancer prevention and cancer mortality reduction are counted among the most pressing public health issues of the twenty-first century. In turn, accurate projections of cancer incidence and mortality rates are paramount for robust policymaking, aimed at creating efficient and inclusive public health systems and also for establishing a baseline to assess the impact of newly introduced public health measures. Within the European Union (EU), Romania consistently reports higher mortality from all types of cancer than the EU average, caused by an inefficient and underfinanced public health system and lower economic development that in turn have created the phenomenon of “oncotourism”. This paper aims to develop novel cancer incidence/cancer mortality models based on historical links between incidence and mortality occurrence as reflected in official statistics and population web-search habits. Subsequently, it employs estimates of the web query index to produce forecasts of cancer incidence and mortality rates in Romania. Various statistical and machine-learning models—the autoregressive integrated moving average model (ARIMA), the Exponential Smoothing State Space Model with Box-Cox Transformation, ARMA Errors, Trend, and Seasonal Components (TBATS), and a feed-forward neural network nonlinear autoregression model, or NNAR—are estimated through automated algorithms to assess in-sample fit and out-of-sample forecasting accuracy for web-query volume data. Forecasts are produced with the overperforming model in the out-of-sample context (i.e., NNAR) and fed into the novel incidence/mortality models. Results indicate a continuation of the increasing trends in cancer incidence and mortality in Romania by 2026, with projected levels for the age-standardized total cancer incidence of 313.8 and the age-standardized mortality rate of 233.8 representing an increase of 2%, and, respectively, 3% relative to the 2019 levels. Research findings thus indicate that, under the no-change hypothesis, cancer will remain a significant burden in Romania and highlight the need and urgency to improve the status quo in the Romanian public health system.

MATHEMATICAL MODELLING AS AN ELEMENT OF PLANNING RAIL TRANSPORT STRATEGIES

Effective planning and optimization of rail transport operations depends on effective and reliable forecasting of demand. The results of transport performance forecasts usually differ from measured values because the mathematical models used are inadequate. In response to this applicative need, we report the results of a study whose goal was to develop, on the basis of historical data, an effective mathematical model of rail passenger transport performance that would allow to make reliable forecasts of future demand for this service. Several models dedicated to this type of empirical data were proposed and selection criteria were established. The models used in the study are: the seasonal naive model, the Exponential Smoothing (ETS) model, the exponential smoothing state space model with Box–Cox transformation, ARMA errors, trigonometric trend and seasonal components (TBATS) model, and the AutoRegressive Integrated Moving Average (ARIMA) model. The proposed time series identification and forecasting methods are dedicated to the processing of time series data with trend and seasonality. Then, the best model was identified and its accuracy and effectiveness were assessed. It was noticed that investigated time series is characterized by strong seasonality and an upward trend. This information is important for planning a development strategy for rail passenger transport, because it shows that additional investments and engagement in the development of both transport infrastructure and superstructure are required to meet the existing demand. Finally, a forecast of transport performance in sequential periods of time was presented. Such forecast may significantly improve the system of scheduling train journeys and determining the level of demand for rolling stock depending on the season and the annual rise in passenger numbers, increasing the effectiveness of management of rail transport.

Comparison of ARIMA, ETS, NNAR, TBATS and hybrid models to forecast the second wave of COVID-19 hospitalizations in Italy

The coronavirus disease (COVID-19) is a severe, ongoing, novel pandemic that emerged in Wuhan, China, in December 2019. As of January 21, 2021, the virus had infected approximately 100 million people, causing over 2 million deaths. This article analyzed several time series forecasting methods to predict the spread of COVID-19 during the pandemic’s second wave in Italy (the period after October 13, 2020). The autoregressive moving average (ARIMA) model, innovations state space models for exponential smoothing (ETS), the neural network autoregression (NNAR) model, the trigonometric exponential smoothing state space model with Box–Cox transformation, ARMA errors, and trend and seasonal components (TBATS), and all of their feasible hybrid combinations were employed to forecast the number of patients hospitalized with mild symptoms and the number of patients hospitalized in the intensive care units (ICU). The data for the period February 21, 2020–October 13, 2020 were extracted from the website of the Italian Ministry of Health (www.salute.gov.it). The results showed that (i) hybrid models were better at capturing the linear, nonlinear, and seasonal pandemic patterns, significantly outperforming the respective single models for both time series, and (ii) the numbers of COVID-19-related hospitalizations of patients with mild symptoms and in the ICU were projected to increase rapidly from October 2020 to mid-November 2020. According to the estimations, the necessary ordinary and intensive care beds were expected to double in 10 days and to triple in approximately 20 days. These predictions were consistent with the observed trend, demonstrating that hybrid models may facilitate public health authorities’ decision-making, especially in the short-term.

Performance comparison of filtering methods on modelling and forecasting the total precipitation amount: a case study for Muğla in Turkey

Abstract Condensed water vapor in the atmosphere is observed as precipitation whenever moist air rises sufficiently enough to produce saturation, condensation, and the growth of precipitation particles. It is hard to measure the amount and concentration of total precipitation over time due to the changes in the amount of precipitation and the variability of climate. As a result of these, the modelling and forecasting of precipitation amount is challenging. For this reason, this study compares forecasting performances of different methods on monthly precipitation series with covariates including the temperature, relative humidity, and cloudiness of Muğla region, Turkey. To accomplish this, the performance of multiple linear regression, the state space model (SSM) via Kalman Filter, a hybrid model integrating the logistic regression and SSM models, the seasonal autoregressive integrated moving average (SARIMA), exponential smoothing with state space model (ETS), exponential smoothing state space model with Box-Cox transformation-ARMA errors-trend and seasonal components (TBATS), feed-forward neural network (NNETAR) and Prophet models are all compared. This comparison has yet to be undertaken in the literature. The empirical findings overwhelmingly support the SSM when modelling and forecasting the monthly total precipitation amount of the Muğla region, encouraging the time-varying coefficients extensions of the precipitation model.

Forecasting mortality rates with the penalized exponential smoothing state space model

It is well known that accurate forecasts of mortality rates are essential to various demographic research like population projection, and the pricing of insurance products such as pensions and annuities. Recent studies suggest that mortality rates of multivariate ages are usually not leading indicators in mortality forecasting. Therefore, multivariate stochastic mortality models including the classic Lee–Carter may not necessarily lead to more accurate forecasts, compared with sophisticated univariate counterparties like the exponential smoothing state space (ETS) model. Despite its improved forecasting accuracy, the original ETS model cannot ensure the age-coherence of forecast mortality rates. By introducing an effective penalty scheme, we propose a penalized ETS model to significantly overcome this problem, with discussions on related technical issues including the reduction of parameter dimensionality and the selection of tuning parameter. Empirical results based on mortality rates of the Australian males and females suggest that the proposed model consistently outperforms the Lee–Carter and original ETS models. Robust conclusions are drawn when various forecasting scenarios are considered. Long-term forecasting analyses up to 2050 comparing the three models are further performed. To illustrate its usefulness in practice, an application to price fixed-term annuities with the penalized ETS model is demonstrated.

Improving the precision of modeling the incidence of hemorrhagic fever with renal syndrome in mainland China with an ensemble machine learning approach.

Hemorrhagic fever with renal syndrome (HFRS), one of the main public health concerns in mainland China, is a group of clinically similar diseases caused by hantaviruses. Statistical approaches have always been leveraged to forecast the future incidence rates of certain infectious diseases to effectively control their prevalence and outbreak potential. Compared to the use of one base model, model stacking can often produce better forecasting results. In this study, we fitted the monthly reported cases of HFRS in mainland China with a model stacking approach and compared its forecasting performance with those of five base models. We fitted the monthly reported cases of HFRS ranging from January 2004 to June 2019 in mainland China with an autoregressive integrated moving average (ARIMA) model; the Holt-Winter (HW) method, seasonal decomposition of the time series by LOESS (STL); a neural network autoregressive (NNAR) model; and an exponential smoothing state space model with a Box-Cox transformation; ARMA errors; and trend and seasonal components (TBATS), and we combined the forecasting results with the inverse rank approach. The forecasting performance was estimated based on several accuracy criteria for model prediction, including the mean absolute percentage error (MAPE), root-mean-squared error (RMSE) and mean absolute error (MAE). There was a slight downward trend and obvious seasonal periodicity inherent in the time series data for HFRS in mainland China. The model stacking method was selected as the best approach with the best performance in terms of both fitting (RMSE 128.19, MAE 85.63, MAPE 8.18) and prediction (RMSE 151.86, MAE 118.28, MAPE 13.16). The results showed that model stacking by using the optimal mean forecasting weight of the five abovementioned models achieved the best performance in terms of predicting HFRS one year into the future. This study has corroborated the conclusion that model stacking is an easy way to enhance prediction accuracy when modeling HFRS.

Forecasting COVID-19 impact on RWI/ISL container throughput index by using SARIMA models

ABSTRACT Maritime operators are facing their biggest challenge called Coronavirus (COVID-19) since the 2008 financial crisis. As part of the measures taken by the countries against the virus, the domino effect started with the breaks in the interconnected supply chain, like the spider web. The main purpose of this study is modeling the Institute of Shipping Economics and Logistics (ISL) and the Leibniz-Institut für Wirtschaftsforschung (RWI) Container Throughput Index with the time series, to reveal the relationship between the short-term forecast results and the COVID-19 seen in the first months of 2020. The deep effect of COVID-19 on maritime trade is investigated by forecasting the RWI/ISL Container Throughput Index in 89 major international container ports, including and excluding seasonal variations. The modeling process of the Seasonal Autoregressive Integrated Moving Average (SARIMA) and Exponential Smoothing State Space Model (ETS) is explained. To evaluate SARIMA and ETS models’ performance, information criteria, and error measurements are calculated and compared. SARIMA model is found as more suitable model than ETS forecasting seasonally and working-day adjusted and original RWI/ISL. The results indicated that the SARIMA model is suitable and efficient for the forecasting of RWI/ISL. Three months’ forecasting results are showed that the decrease will continue.

Forecasting COVID-19 confirmed cases, deaths and recoveries: Revisiting established time series modeling through novel applications for the USA and Italy.

The novel coronavirus (COVID-19) is an emergent disease that initially had no historical data to guide scientists on predicting/ forecasting its global or national impact over time. The ability to predict the progress of this pandemic has been crucial for decision making aimed at fighting this pandemic and controlling its spread. In this work we considered four different statistical/time series models that are readily available from the ‘forecast’ package in R. We performed novel applications with these models, forecasting the number of infected cases (confirmed cases and similarly the number of deaths and recovery) along with the corresponding 90% prediction interval to estimate uncertainty around pointwise forecasts. Since the future may not repeat the past for this pandemic, no prediction model is certain. However, any prediction tool with acceptable prediction performance (or prediction error) could still be very useful for public-health planning to handle spread of the pandemic, and could policy decision-making and facilitate transition to normality. These four models were applied to publicly available data of the COVID-19 pandemic for both the USA and Italy. We observed that all models reasonably predicted the future numbers of confirmed cases, deaths, and recoveries of COVID-19. However, for the majority of the analyses, the time series model with autoregressive integrated moving average (ARIMA) and cubic smoothing spline models both had smaller prediction errors and narrower prediction intervals, compared to the Holt and Trigonometric Exponential smoothing state space model with Box-Cox transformation (TBATS) models. Therefore, the former two models were preferable to the latter models. Given similarities in performance of the models in the USA and Italy, the corresponding prediction tools can be applied to other countries grappling with the COVID-19 pandemic, and to any pandemics that can occur in future.

Outlier Detection in Data Streams — A Comparative Study of Selected Methods

Outlier detection is an increasingly important and intensively developing area of research. This paper focuses on the problem of outlier detection in data streams. It presents a performance comparison of selected statistical algorithms: AutoRegressive Integrated Moving Average (ARIMA), Exponential Smoothing State Space Model (ETS), Seasonal Hybrid Extreme Studentized Deviation (SHESD), Non-parametric methodology (NMV), and Chen-Liu method (CHL). Based on four data streams from the Kaggle Repository and DataHub Repository, the study provides results concerning the number of outliers detected by each algorithm and the algorithms’ operation times. The experiments were performed on data streams of different lengths (from a few hundred to 1200 records), characterized by the presence of different types of outliers.

Creatinine Fluctuations Forecast Cross-Harvest Kidney Function Decline Among Sugarcane Workers in Guatemala

BackgroundChronic kidney disease of unknown origin (CKDu) is an epidemic that disproportionately affects young agriculture workers in hot regions. It has been hypothesized that repeated acute kidney injury (AKI) may play a role in the development of disease.MethodsLatent class mixed models were used to identify groups of Guatemalan sugarcane harvesters based on their daily changes in creatinine over 6 consecutive days in 2018. Exponential smoothing state space models were used to forecast end-of-season creatinine between the identified groups. Percent change in estimated glomerular filtration rate (eGFR) across the harvest was compared between groups.ResultsTwenty-nine percent (n = 30) of the 103 workers experienced repeated severe fluctuations in creatinine across shift. The model with multiplicative error, multiplicative trend, and multiplicative seasonality was able to accurately forecast end-of-season creatinine in the severe group (mean percentage error [MPE]: −4.7%). eGFR of workers in the severe group on average decreased 20% across season compared to 11% decline for those in the moderate group (95% confidence interval for difference: −17% to 0%).ConclusionsDaily fluctuations in creatinine can be used to forecast end-of-season creatinine in sugarcane harvesters. Workers who experience repeat severe daily fluctuations in creatinine, on average, experience a greater reduction in kidney function across the season.

A Two-Population Extension of the Exponential Smoothing State Space Model with a Smoothing Penalisation Scheme

The joint modelling of mortality rates for multiple populations has gained increasing popularity in areas such as government planning and insurance pricing. Sub-groups of a population often preserve similar mortality features with short-term deviations from the common trend. Recent studies indicate that the exponential smoothing state space (ETS) model can produce outstanding prediction performance, while it fails to guarantee the consistency across neighbouring ages. Apart from that, single-population models such as the famous Lee-Carter (LC) may produce divergent forecasts between different populations in the long run and thus lack the property of the so-called coherence. This study extends the original ETS model to a two-population version (2-ETS) and imposes a smoothing penalisation scheme to reduce inconsistency of forecasts across adjacent ages. The exponential smoothing parameters in the 2-ETS model are fitted by a Fourier functional form to reduce dimensionality and thus improve estimation efficiency. We evaluate the performance of the proposed model via an empirical study using Australian female and male population data. Our results demonstrate the superiority of the 2-ETS model over the LC and ETS as well as two multi-population methods - the augmented common factor model (LL) and coherent functional data model (CFDM) regarding forecast accuracy and coherence.

Ranking of Univariate Forecasting Techniques for Seasonal Time Series using Analytical Hierarchy Process

The choice of a suitable forecasting method carries noteworthy significance for organisations in adequately accomplishing their business targets. The selection of forecasting method becomes more sophisticated when there is a significant impact of seasonality on the business of an organisation. To deal with the situation of selecting the most relevant forecasting method for seasonal data, this paper proposes a framework using analytical hierarchy process (AHP) to rank various forecasting techniques for long time series. Accuracy measures namely Theil's U, mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) are used as AHP criteria for performance measurement of various univariate time series methods such as naive + season level trend (SLT), error, trend, seasonal (ETS), seasonal autoregressive moving average (SARIMA), exponential smoothing state space model with Box-Cox transformation (BATS) and trigonometric exponential smoothing state space model with Box-Cox transformation (TBATS) for seasonal data. The proposed framework is validated through real-time data provided by a public sector company in India. Ranking obtained from the developed AHP framework suggests that SARIMA is ranked top amongst all the techniques for short-term forecasting of seasonal data.