Seasonal Time Series Models Research Articles

Analysis of Philip Morris International’s ‘aspirational’ target for its 2025 cigarette shipments

BackgroundPhilip Morris International (PMI) claims to be transforming and has committed to a ‘smoke-free’ future. In 2020, it announced an ‘aspirational’ target for reduced cigarette shipments by 2025.MethodsPMI cigarette shipment...

Forecasting cauliflower prices in Nepal: a comparative analysis using seasonal time series and nonlinear models

Forecasting cauliflower prices in Nepal: a comparative analysis using seasonal time series and nonlinear models

Local and global trend Bayesian exponential smoothing models

This paper describes a family of seasonal and non-seasonal time series models that can be viewed as generalisations of additive and multiplicative exponential smoothing models to model series that grow faster than linear but slower than exponential. Their development is motivated by fast-growing, volatile time series. In particular, our models have a global trend that can smoothly change from additive to multiplicative and is combined with a linear local trend. Seasonality, when used, is multiplicative in our models, and the error is always additive but heteroscedastic and can grow through a parameter sigma. We leverage state-of-the-art Bayesian fitting techniques to fit these models accurately, which are more complex and flexible than standard exponential smoothing models. When applied to the M3 competition data set, our models outperform the best algorithms in the competition and other benchmarks, thus achieving, to the best of our knowledge, the best results of per-series univariate methods on this dataset in the literature. An open-source software package of our method is available.

Yellow River Water and Sand Monitoring Data Model based on SARIMAX Rediction

With the evolution of history, the problems faced by the Yellow River Basin have been an important research topic in hydrology. In this paper, for the problems in the monitoring of water and sand in the Yellow River, a seasonal time series model of the monitoring data is established based on the time series prediction model, and the CUSUM algorithm is used to test the model. First, the data are processed to calculate the spearman correlation for each pair of categories. Then, for analyzing the description of single dimensional data, data descriptive analysis was used. Next, the data were forecasted using a seasonal time series forecasting model. Finally, the seasonal time series prediction model was used to predict water fluxes and solved using double interpolation to obtain the predicted effect plots for the next ten years. The proposed model is close to the reality, can reasonably solve the proposed problem, and is characterized by high practicality and high efficiency of the algorithm.

Approximating the ARL of Changes in the Mean of a Seasonal Time Series Model with Exponential White Noise Running on a CUSUM Control Chart

Control charts comprise an excellent statistical process control tool for monitoring industrial processes. Especially, the CUSUM control chart is very sensitive to small-to-moderate process parameter changes. The proposed approach utilizes the numerical integral equation (NIE) method to approximate the average run length (ARL) of changes in the mean of a seasonal time series model with underlying exponential white noise running on a CUSUM control chart. This was achieved by solving a system of linear equations and integration through partitioning and summation using the area under the curve of a function obtained by applying the Gauss-Legendre quadrature. A numerical study was conducted to compare the capabilities of the ARL derivations obtained using the NIE method and explicit formulas to detect changes in the mean of a long-memory model with exponential white noise running on a CUSUM control chart. The results reveal that the performances of both were comparable in terms of the accuracy percentage, which was greater than 95%, meaning that the ARL values were highly consistent. Thus, the NIE method can be used to validate ARL results for this situation.

Probabilistic Intraday Wastewater Treatment Plant Inflow Forecast Utilizing Rain Forecast Data and Sewer Network Sensor Data

AbstractForecasting of wastewater treatment plant inflow dynamics constitutes an enabler technology for wastewater treatment process optimization using model predictive control. However, accurate inflow prediction is still challenging, especially for strong rainfall events, where complex system dynamics and missing information on future rainfall represent limiting factors. We propose a seasonal probabilistic time series model for modeling the short‐term wastewater inflow accurately while providing quantification of forecast uncertainty. To ensure suitability for practical implementation, the unconstrained parameters of the predictive distribution are modeled as linear functions of the input variables in the framework of Generalized Additive Models for Location Scale and Shape. Non‐linear effects are approximated by Rectified Linear Units, accounting for buffering within the sewer network and flow‐dependent catchment response time. In addition to water level measurements from within the sewer network and rain rate measurements, rain forecasts are incorporated as exogenous regressors, where historical rain forecasts are used for model calibration. The model performance is evaluated on historical data from a German wastewater treatment plant using deterministic and probabilistic scoring rules. We benchmark against an autoregressive time series model and a long short‐term memory artificial neural network. Our results show that the proposed model unites the benefits of high prediction accuracy of the neural network and enhanced intelligibility of the autoregressive model, but accurate real‐time rain forecasts are mandatory for successful real‐world implementation.

Short-term and seasonal time series models for online marketing campaigns

Marketing companies use the market response to price products, determine advertising expenditures, forecast sales or prepare and test the effectiveness of various marketing plans and campaigns. Predictions of future traffic for online marketing campaigns can be based on data analysis and market response models. Mathematical models have become the main tools for marketing decision-making. The main goal of this paper is to describe and show how to use behavioral modelling of potential customers in online marketing campaigns. In addition to the basic ARMA model for short-term website traffic forecasting, we evaluate the TBATS and Prophet models. Both models comprehensively capture seasonal and holiday fluctuations. More specifically we show how time series modelling can be incorporated into the evaluation of online marketing campaign traffic forecasts for marketing agency clients.

Analysis of Blood Collection of National Blood Transfusion Service, Sri Lanka

Background and Objectives: Blood transfusion is a widely accepted treatment modality in modern medical practice and it has no substitute. Therefore, blood is a scarce resource, and proper management of bloodstock is essential. Transfusion service is responsible to maintain an adequate blood stock to ensure the supply of blood for hospitals while minimizing blood wastage due to postexpiry. To achieve efficient bloodstock management, the pattern of blood collection should be identified. This study was designed to establish a time series model for monthly blood collection of Sri Lanka. Methods: Data on monthly blood collection of Sri Lanka were collected from the year 2010 to 2020 and time series models were developed using “R” statistical software. Results: Time series data clearly exhibited an increasing trend with seasonality in blood collection. Therefore, seasonal time series models were fitted and the best seasonal autoregressive integrated moving average (ARIMA) model was selected as ARIMA (0, 1, 1) (0, 1, 2) (12) which showed the lowest Akaike information criteria value. Conclusion: It is suitable for forecasting the monthly blood collection.

Applying seasonal time series modeling to forecast marine fishery landings for six species in the Colombian Pacific Ocean

Marine fisheries are keystone components of the industrial and social development of countries. Management of marine resources requires forecasting skills to support best decisions for the sustainability of fishery resources and food security under different environmental, social and political scenarios. In this study, we aimed at forecasting the landings of six marine fish species in the Colombian Pacific Ocean (CPO) from 2020 to 2024, using monthly time series from 2012 to 2020 provided by SEPEC (Servicio Estadístico Pesquero Colombiano), the Colombian governmental authority in charge of aquaculture and fisheries. These forecasts consisted of building, fitting and evaluating SARIMA models (Seasonal Autoregressive Integrated Moving Average), since all of the time series were non-stationary. We focused on evaluating the average percent change of landings between the historical and the forecast periods exclusively on peak landing months. The main results suggested that the landings of the Yellowfin tuna (Thunnus albacores) will decrease by 14% until 2024, those of the Skipjack tuna (Katsunowus pelamis) by 20% until 2022, and those of the Spotted snapper (Lutjanus peru) by 28% until 2023. The forecast landings of the Cachema weakfish (Cynoscion phoxocephalus) and the Red snapper (Lutjanus peru) showed constant increases until 2024, by 1.5 and 0.85 tons per year on average respectively, and those of the Pink grouper (Hyporthodus acanthistius) showed no trends until 2024. These results are the first approach to a multi-species forecast of marine fishery landings in the Colombian Pacific Ocean using a SARIMA model, and their implications must be carefully interpreted for decision making towards the sustainability of fishery resources.

Sudan Load Forecast for Period 2017 – 2066 Using Seasonal Time Series Model

The importance of this paper is the use of seasonal time series models (some seasonal models of Box & Jenkins) to predict electricity consumption in Sudan National Grid, making it easier to estimate consumption, and provide accurate indicators for planners to develop appropriate future plans in electricity sector. The objective of this paper is to forecast the electric load consumption using different model.

Hierarchical mortality forecasting with EVT tails: An application to solvency capital requirement

In this paper, we propose a new framework to coherently produce probabilistic mortality forecasts by exploiting techniques in seasonal time-series models, extreme value theory (EVT), and hierarchical forecast reconciliation. In a hierarchical setting, coherent forecasts are those forecasts that add up in a manner consistent with the aggregation structure of the collection of time series. We are amongst the first to model and analyze U.S. monthly death data during the period from 1968–2019 to explore the seasonality and the age–gender dependence structure of mortality. Our results indicate that incorporating EVT and hierarchical forecast reconciliation greatly improves the overall forecast accuracy, which has important implications for life insurers in terms of rate making, reserve setting, and capital adequacy compliance. Using the solvency capital requirement (SCR) under Solvency II as an example, we show that the SCR calculated by our approach is considerably higher than those calculated by alternative models, suggesting that failing to account for extreme mortality risk and mortality dependence in the hierarchy can result in significantly underfunded problems for life insurers. We also find that our model can yield death forecasts that are largely consistent with actual observations in most of months in 2021 when death tolls surged due to COVID-19. This provides additional evidence of the effectiveness of our model for practical uses.

Assessment of indoor radon concentration and time-series analysis of gamma dose rate in three thermal spas from Portugal

This work is a follow-up study on the exposure to indoor radon levels in Portuguese thermal spas. The previous research involved 16 thermal spas, where radon measurements in air and thermal mineral water were performed twice a year, from 2012 to 2016. These studies revealed concerning radon concentrations both in air and water. Therefore, a follow-up study on long-term radon measurements was conducted to estimate the year-round average radon exposure. The closer the long-term measurement is to 365 days, the more representative it will be of annual average radon levels. Continuous measurements over 1 year for the indoor radon levels are now presented for three of the 16 previously studied thermal spas, together with a time-series analysis of the gamma dose rates registered within the facilities of these thermal spas (TS). An attempt to identify possible patterns in the variation of gamma dose rates was made. Hourly gamma dose rates were modelled and forecasted using the Box–Jenkins seasonal time series models (SARIMA). The results showed that between December 2018 and November 2019, the indoor radon concentration varied from 202 to 1941 Bq/m3 (TS1), from 52 to 191 Bq/m3 (TS2), and from 937 to 1750 Bq/m3 (TS3). Approximately 60% of the obtained values for radon concentration in the indoor air exceed the reference level of 300 Bq/m3. Gamma dose rates were continuously measured with GAMMA SCOUT® detectors for hourly readings (µSv/h) between 83 and 229 days. On average, the results are similar in all considered locations and range between 0.169 and 0.264 µSv/h, although variations are different in winter and summer. The calculated effective doses ranged between 3.49 and 18.65 mSv/year (TS1), between 1.37 and 2.53 mSv/year (TS2), and between 13.89 and 22.97 mSv/year (TS3). For occupational exposure purposes, workers would be classified as category A in nine locations (out of 20), as the exposure is liable to exceed an effective dose of 6 mSv/year. For the time-series analysis, the obtained models captured the dynamics of the time series data and produced short-term forecasts. Their accuracies have been quantified by minimizing the root mean square error, the mean absolute error due to the actual forecast, and the mean absolute scaled error. The current results corroborate the conclusions of previous research and give continuous data on occupational exposure to radon for three Portuguese thermal spas. For TS1 and TS3, the indoor radon levels are much higher than the reference level. Under this circumstance, mitigation measures must be implemented to reduce the radon levels accordingly with the Euratom Directive 2013/59 and the Decree-Law No. 108/2018. In general, the gamma dose rates were below 1 μSv/h and, therefore, the contribution to the annual effective dose is not significant. Nevertheless, the variation of the gamma dose rates showed a coherent behavior with the radon progeny build up in closed spaces, as when the considered facilities were closed for certain periods. The time series analysis made it possible to fit some models to the gamma dose rate variation, and although the produced models cannot forecast exact gamma dose rates, they can provide valuable information to build sound planning and decision-making strategies in occupational exposure.

Seasonal count time series

Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This article uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model constructed here permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference are explored. The article first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.

An adaptive cumulative sum method for monitoring integer-valued time-series data

In this paper, we propose an adaptive CUSUM monitoring method for detecting step and linear trend changes in count-data time-series. The data is represented using a seasonal INGARCH time series model and an exponential smoother is used to estimate level or trend changes in the data in the cumulative-sum (CUSUM) detector. In a simulation study, the proposed approach is compared to existing CUSUM approaches that are tuned for a specific shift size and the ability of the methods to detect step shifts and linear trends is investigated. The application of the proposed method in public health surveillance is demonstrated using a real infectious disease count data set.

Testing for the expected number of exceedances in strongly dependent seasonal time series

We consider seasonal time series models with a strongly dependent residual process. The question of testing for a change in the expected number of exceedances is addressed. Based on a functional limit theorem for seasonal empirical processes, a test of the null hypothesis of no change is proposed. The method is applied to daily temperature series at various locations in Switzerland. The test reveals interesting differences in the effect of global warming on seasonal temperature exceedances.

Seasonal functional autoregressive models

Functional autoregressive models are popular for functional time series analysis, but the standard formulation fails to address seasonal behaviour in functional time series data. To overcome this shortcoming, we introduce seasonal functional autoregressive time series models. For the model of order one, we derive sufficient stationarity conditions and limiting behaviour, and provide estimation and prediction methods. Moreover, we consider a portmanteau test for testing the adequacy of this model, and we derive its asymptotic distribution. The merits of this model are demonstrated using simulation studies and via an application to hourly pedestrian counts.

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.

Seasonality analysis of the tomato monthly price and its forecasting using seasonal time series models (SARIMA)

The aim of this research is to analysis the tomato monthly prices in Baghdad province for the period (Jan 2010- Dec 2015) by using seasonal time series (SARIMA) to detect seasonal variations to be excluded from the time series. The research problem is summarized by existing seasonality phenomenon in tomato monthly prices which will be reflected on the short-term planning progress. The results showed that the appropriate and efficiency model for representing time series data for tomato monthly prices was the SARIMA model (0,1,2)(1,1,0)12. Also the results of tomato monthly prices forecasting showed a harmonic direction with the same original time series. From the obtained results, the tomato monthly prices confirm the nature of the prevailing pattern in that the tomato production was affected by the season to a large extent, as the results concluded that there is a secular trend in increasing monthly prices of tomato for the period (Jan 2016-Dec 2020), which confirmed the rise in monthly prices during the forecast period. The research recommends the need to prevent imports especially at peak time (time of crop availability in local markets), and legislating laws to protect the domestic product , in addition to taxation of imported products.

THE TIPLING RIVER FLOW ANALYSIS TO ASSESS MICRO HYDRO POWER AND DIVERSION BASED IRRIGATION POTENTIAL

Micro hydropower projects and diversion based irrigation projects are dependent on the amount of water flowing in the river of concern. Analyses of historical River Flow information are crucial to understand its pattern, frequency and predictability. Statistical analysis is the basis for a better scientific comprehension of the river flow system. Based on this information designing of such projects as well as making management plans for any future eventualities are possible. In this paper historical discharge information for a period of 19 years is collected and analyzed. Based on the water level and volume of discharge information of the river for the year 1995, various stage discharge rating curves are prepared. The best fitted curve is used for the estimation of the discharge for the remaining years where only the stage information is available. Daily discharge hydrographs for 19 years is prepared along with annual discharge computation for each of the 19 years of observation period. Preparation of flow duration curve helped to understand what is to be expected minimum from the river and what could be the most risky situation for a river project in this river and make necessary allowances for designing such project. Finally seasonal and monthly time series models are prepared so that the future discharge could be scientifically forecasted for predicting the future of such projects.

PM2.5 Analysis and Prediction Based on Seasonal Time Series Model

The PM2.5 data in Hefei area from 2014 to 2018 were collected through the website of meteorological bureau, and the data were analyzed and modeled with the help of statistical analysis software SPSS and EVIEWS. Firstly, the annual and seasonal distribution characteristics and trend of PM2.5 data in Hefei area during the past five years were analyzed. It was concluded that the distribution of PM2.5 had periodic characteristics, and the air quality in summer was the best and that in winter was the worst. According to the results of statistical analysis, PM2.5 data had seasonal characteristics. On this basis, the Holt-Winters additive model and SARIMA model in seasonal time series model were selected to model and predict. The prediction values of the two models were compared with the real values. The results showed that the prediction accuracy of the Holt-Winters additive model was slightly higher than that of the SARIMA model.