Multiplicative Seasonal Model Research Articles

Highly irregular serial correlation tests

Tests are developed for neglected serial correlation when the information matrix is repeatedly singular under the null hypothesis. Specifically, consideration is given to white noise against a multiplicative seasonal Ar model, and a local-level model against a nesting Ucarima one. The proposed tests, which involve higher-order derivatives, are asymptotically equivalent to the likelihood ratio test but only require estimation under the null. It is shown that the tests effectively check that certain autocorrelations of the observations are zero, so their asymptotic distribution is standard. Monte Carlo exercises examine finite sample size and power properties, with comparisons made to alternative approaches.

Prediction of reported monthly incidence of hepatitis B in Hainan Province of China based on SARIMA-BPNN model.

In recent years, the incidence of hepatitis B has been serious in Hainan Province of China. To construct a statistical model of the monthly incidence of hepatitis B in Hainan Province of China and predict the monthly incidence of hepatitis B in 2022. Simple central moving average method and seasonal index were used to analyze the trend and seasonal effects of monthly incidence of hepatitis B. Based on the time series of reported monthly incidence of hepatitis B in Hainan Province from 2017 to 2020, a multiplicative seasonal model (SARIMA), multiplicative seasonal model combined with error back propagation neural network model (SARIMA-BPNN), and a gray prediction model were constructed to fit the incidence, and the time series of monthly incidence of hepatitis B in 2021 was used to verify the accuracy of models. The lowest and highest monthly incidence of hepatitis B in Hainan Province were in February and August, respectively, and MAPE of SARIMA, SARIMA-BPNN, and gray prediction models were 0.089, 0.087, and 0.316, respectively. The best fitting model is the SARIMA-BPNN model. The predicted monthly incidence of hepatitis B in 2022 showed a downward trend, with the steepest decline in March, which indicates that the prevention and control of hepatitis B in Hainan Province is effective, and the study can provide scientific and reasonable suggestions for the prevention and control of hepatitis B in Hainan.

Prediction of women and Children's hospital outpatient numbers based on the autoregressive integrated moving average model

ObjectiveTo evaluate the predictive value of the autoregressive integrated moving average (ARIMA) product seasonal model for the daily outpatient volume of paediatric internal medicine departments in hospitals. MethodsThe daily outpatient volume of paediatric internal medicine recorded by the hospital information system of the Chengdu Women's and Children's Central Hospital from 1 January 2011 to 31 December 2020 was collected. Using the data from 1 January 2011 to 31 December 2019, the seasonal summation ARIMA model of the time product was established by fitting the tseries program in the R-3.6.3 software. The monthly outpatient volume from January to December 2020 was predicted, and the prediction effect was evaluated according to the mean absolute percentage error (MAPE) between the predicted value and the actual value. ResultsThe outpatient volume of paediatric internal medicine in the hospital from 2011 to 2019 showed an upward trend, with obvious seasonal fluctuations. The optimal model was the ARIMA model ([3,4], 1,2) × (1,1,0) 12, with an Akaike information criterion of 3116.656 and a Bayesian information criterion of 3217.412. The model's residual was a white noise sequence (x2 = 7.56, P = 0.819), and the MAPE between the predicted value and the actual value of the model was 9.56%. Within a 95% confidence interval of the predicted value, the prediction accuracy of the model was high. ConclusionThe ARIMA multiplicative seasonal model established in this study is suitable for the short-term prediction of the outpatient volume.

An Improved Energy Detection Scheme Based on Channel Prediction In CR Networks

Cognitive radio is considered as an intelligent wireless communication system proposed to improve the utilization of the radio electromagnetic spectrum. In CR technology the secondary users take the responsibility of dynamically sensing and accessing any unused channels in the spectrum allocated to the licensed users. As spectrum sensing consumes considerable energy, predictive methods for inferring the availability of spectrum holes can reduce energy consumption of the unlicensed users to only sense those channels which are likely to be idle. It also helps to improve the spectrum utilizations. Several prediction techniques have been used to predict spectrum utilization. However, most of current approaches do not consider seasonality in spectrum workload, for example most of the channels are busy during business hours in mobile phone bands. This paper; proposes a channel status predictor based on the multiplicative seasonal model called Holt-Winters’ method. The proposed prediction method has the ability to adapt with changes in trends and seasonal patterns of the sensing observations. Performance analysis and the accuracy of the channel status prediction schemes are investigated.

The Offset Position Prediction of Light Buoy Based on Grey Optimization Multiplicative Seasonal Model

Light buoy is a navigation aid sign to guide ship navigation, which plays an important role in ensuring the safety of ship navigation. To predict the offset distance of light buoy and provide accurate position information of light buoy for ship navigation safety, and to solve the problem of low prediction accuracy caused by the excessive amplitude of initial training data in the traditional multiplicative seasonal model, a grey optimization multiplicative seasonal model is proposed. By analyzing the characteristics of the time series of the light buoy offset data, as well as the regularity and seasonal characteristics of the light buoy offset distance, an optimization model is established. Based on the real offset distance data of the 1 # light buoy in Meizhou Bay, the model is simulated, and the prediction accuracy of the model is evaluated by MAPE, RMSE, and the Monte Carlo sampling method. The results show that, compared to the traditional multiplicative seasonal model, the average absolute percentage error of the grey optimization multiplicative seasonal model is reduced by 6.66%, and the root mean square error is reduced by 2.96. It shows that the model can effectively deal with the problem that the error of the prediction results caused by the instability of the initial time series of the traditional multiplicative seasonal model is too large, which provides a new idea for the prediction of the offset distance of the light buoy and the navigation safety of the ship.

The Offset Azimuth Prediction of Light Buoy Based on Markov Chain Optimization Multiplicative Seasonal Model

Aimed at the problem of the large error caused by uncertain factors in the fitting process of the traditional multiplicative seasonal model, the advantages of the Markov chain in this study are applied to the multiplicative seasonal model to optimize the prediction results. Based on the residual value between the theoretical and actual values, the values of different intervals are divided into states. The transition probability matrix is established through different probabilities; then, the weighted sum of different prediction probabilities is carried out to select the optimal prediction state. The real number of Meizhou Bay portlight buoys is used to verify the prediction effect of the model, and MAE, MAPE, RMSE, RRMSE, SSE, R2 are used to calculate the error between the predicted value and the actual value. The results show that compared to the traditional multiplicative seasonal model and other prediction models, the prediction MAE of the MC-SARIMA model is decreased by 2.19003794, the MAPE is decreased by 0.66%, the RMSE is decreased by 2.092671823, the RRMSE is decreased by 0.006221352, the SSE is decreased by 404.0231931, and the R2 is increased by 0.224686247. It shows that the multiplicative seasonal model optimized by the Markov chain can predict the azimuth data of the light buoy more effectively than the traditional multiplicative seasonal model and other prediction models.

An Optimal Forecasting Method of Passenger Traffic in Greek Coastal Shipping

Purpose: The main goal of this study is to exact an optimal forecasting method by answering the research question: which is the best model for capturing short-term seasonal components of passenger traffic in Greek coastal shipping? Design/methodology/approach: There are not a lot of scientific efforts in forecasting passenger traffic in Greece. In order to fill this gap, we tried to find an optimal forecasting method, by comparing Box-Jenkins ARIMA, smoothing and decomposition methods. As Greek coastal shipping consists of several concentrated submarkets (lines) we remained in fourteen popular itineraries (including total passenger traffic). Taking into consideration the high seasonality and no stationarity that characterizes those routes we limited our analysis to Winter’s triple exponential smoothing, to time series decomposition method, to simple seasonal model and to seasonal ARIMA models. Findings: The analysis results show that in fourteen popular coastal routes Winters’ multiplicative method, simple seasonal model and decomposition multiplicative trend and seasonal model have the best integration to the time series data. No coastal line led to better results by seasonal Box-Jenkins ARIMA models. Research limitations/implications: The results should be treated with caution since COVID-19 pandemic does not allow safe conclusions for the forecasting period 2020-2022 in GCS. However, the forecasting results of the first quarter of 2020, when pandemic had not fully prevailed, gave encouraging results with little deviations between predicted and actual values. Originality/value: Greek coastal shipping is one of the biggest in Europe serving a large number of passengers and having a large part of the total shipping fleet. It plays an important role for Greek economy and society, as it connects the majority of inhabited islands to mainland. The finding of an optimal forecasting method of passenger traffic is very significant for both business and government policy. Decisions on the number of routes served by shipping companies, on ships by coastal line (number and size), on companies' pricing policy, on public service obligations, on state port infrastructure policy and on the amount of state funding for barren lines are typical examples.

Selecting the Forecasting Model of Heat Energy Delivery

To solve the problems of saving thermal energy, instead of the currently used cumbersome methods or complex mathematical models, for example, in the form of partial differential equations, it is proposed to use simpler models of time series for the supply and production of thermal energy. The data of a specific heat supply organization on a city scale and the website of the Ministry of Energy of the Russian Federation were used as initial data. The proposed approach is based on a comparison of various mathematical models for predicting the production and supply of heat energy according to the criterion of adequacy (average relative error and coefficient of determination). The results of research carried out using the Matlab software package are presented. A substantiated comparison of the possibility of using different models is carried out. Models have been developed that take into account the seasonal component and higher accuracy. The possibility of using the following time series models is investigated: regression models with a seasonal component, triple exponential smoothing Holt–Winters, multiplicative seasonal autoregression model of the integrated moving average SARIMA (seasonal autoregression integrated moving average), and nonparametric model SSA (singular spectrum analysis). Multiplicative models containing a trend in the form of a linear or autoregression model with the calculation of the seasonality index, as well as additive models with a trend in the form of a linear or autoregression model with a seasonal component in the form of a Fourier series or sum of sines, were compared. In the Holt–Winters model, fminsearch, a function of the Matlab software package, was used to determine the tuning parameters. In the multiplicative SARIMA model, the orders of autoregression and moving average were fitted according to the autocorrelation and partial autocorrelation function. The nonparametric SSA model was used for comparison with the listed parametric models. An opportunity has been obtained to make reasonable forecasts of the production and supply of heat energy It is shown that the best results (average relative error 6.52%) were obtained using the SARIMA multiplicative model.

Exponential Smoothing on Modeling and Forecasting Multiple Seasonal Time Series: An Overview

This paper presents the development process of the exponential smoothing (ES) model, starts with the traditional ES model and then focuses to the multiple seasonal ES model. This paper describes and visualizes the existing multiple seasonal ES models for the purpose of finding guidance for further development. Though some progress and development have been made in this field, the best fit for many possible cases is still needed. Finally, the paper is concluded with comments regarding possible direction of future research.

Box–Jenkins multiplicative ARIMA modeling for prediction of solar radiation: a case study

This study deals with stochastic modeling of solar radiation in all sky conditions and presents an effort to predict and analyze the future trends of monthly insolation based on time series analysis. Multiplicative seasonal autoregressive integrated moving average (ARIMA) model, using Box–Jenkins approach, has been utilized for simulating monthly average insolation data retrieved from NASA POWER (Prediction of Worldwide Energy Resource) data over the study area. The satellite dataset for a period of 34 years has been analyzed for modeling monthly average insolation. The insolation data time series examined by differencing and autocorrelation functions clearly indicates the existence of seasonality. Various multiplicative seasonal ARIMA models developed were validated by assessing various estimation parameters and their performance was evaluated by utilizing different selection measure criterion. The ARIMA (1, 0, 1) × (0, 1, 1)12, possessing minimum value of these criteria, was identified as the most adequate model. Forecasting of insolation was performed through selected models at 95% confidence interval. Results also reveal that ARIMA (1, 0, 1) × (0, 1, 2)12 produces minimum mean percentage error (MPE) in the forecast. As the difference in MPE for ARIMA (1, 0, 1) × (0, 1, 1)12 and ARIMA (1, 0, 1) × (0, 1, 2)12 is marginal (i.e., 0.004), the two models present minimal differences in estimated values and are therefore, reckoned as adequate for forecasting solar radiation.

Distribution of residual autocorrelations for multiplicative seasonal ARMA models with uncorrelated but nonindependent error terms

In this paper, we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving‐average models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption on the error terms in order to extend the range of applications of the seasonal autoregressive moving‐average models. We study the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations under weak assumptions on noise. We establish the asymptotic behavior of the proposed statistics. A set of Monte Carlo experiments and an application to monthly mean total sunspot number are presented.

A comparison of Process Capability Measures for Seasonal and Non-Seasonal Autoregressive Auto-Correlated Data

The process capability indices give a measure of how a process suits within the specification limits. Traditionally, the main assumptions are used in calculating these indices that the measurements for the specified characteristic are independent and normally distributed. In this paper we investigated the distributional properties in terms of Bias, MSE and empirical distribution for the sample version of the most common three process capability measures namely; when the process data are autocorrelated following seasonal or non-seasonal first-order autoregressive process. We have found that the characteristics of those estimators are negatively affected by the autocorrelation data, especially for the multiplicative seasonal AR model. Besides, we found that the empirical distributions of the three sample capability measures are positively skewed and leptokurtic, a fact which is true when the data are independent and normal.

Modelling Electricity Demand in Sudan Using Multiplicative Seasonal ARIMA and HOLT-WINTERS

Reliable forecast of energy demand represents a starting point in policy development and improvement of production and distribution facilities. This paper predicts the electricity demand in Sudan during the period from January 2006 to December 2016. For the purposes of these forecasts, multiplicative seasonal ARIMA and Holt-Winters models were used. The results show that the Holt-Winters exponential smoothing method, as opposed to one. An autoregressive model has been included in both the standard and the seasonal Holt-Winters methods to model the residuals and thus improve the forecast accuracy.

Multivariate portmanteau tests for weak multiplicative seasonal VARMA models

Numerous multivariate time series encountered in real applications display seasonal behavior. In this paper we consider portmanteau tests for testing the adequacy of structural multiplicative seasonal vector autoregressive moving-average (SVARMA) models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak SVARMA). We study the asymptotic distributions of residual autocorrelations at seasonal lags of multiple of the length of the seasonal period under weak assumptions on the noise. We deduce the asymptotic distribution of the proposed multivariate portmanteau statistics, which can be quite different from the usual chi-squared approximation used under independent and identically distributed (iid) assumptions on the noise. A set of Monte Carlo experiments and an application of U.S. monthly housing starts and housing sold are presented.

FORECASTING ONE-DECADE AHEAD MINIMUM TEMPERATURE AND RELATIVE HUMDITY FOR WATER RESOURCES MANAGEMENT IN LOWER NIGER

Water availability is highly influenced by variability of weather parameters. Minimum temperature and relative humidity are important parameters that have been sidelined in many water resources management projects. In this study, Autoregressive Integrated Moving Average (ARIMA) models were identified and diagnosed in order to forecast mini-mum temperature and relative humidity of the study area. The findings of the study show that minimum temperature was high during dry season, when relative humidity was low. Furthermore, the multiplicative seasonal models best fit mini-mum temperature and relative humidity represented as ARIMA (5, 1, 0)(2, 0, 0)12 and ARIMA (1, 0, 0)(2, 0, 0)12 respec-tively. While, a ten-year forecast derived from the models would be useful for effective planning and acquisition of water resources projects in the study area.

Effectiveness Of Time Series Models In Predicting The Rate Of Electrical Energy Supplying The City Of Dohuk

This paper deal with using time series models to study and analysis the monthly data on a rate of Electrical Power in Dohuk city for the period (2000-2013), estimating models,and The last twelve, which represents 2014 for the purposes of comparison with the predictions obtained. The results of application show that the proper and efficiency model for representing time series data are the multiplicative seasonal model of order : ARMA(2,1)×SARMA(0,1)12 . According to estimation results of this model done forecasting to monthly rate of electrics capacity for year ahead from the period Jan. 2014 to Dec. 2014, these values show a harmonic direction with the same original time series. I've used Minitab and SPSS programs in the statistical aspect.

Application of R-based multiple seasonal ARIMA model, in predicting the incidence of hand, foot and mouth disease in Shaanxi province

To apply the ' auto-regressive integrated moving average product seasonal model' in predicting the number of hand, foot and mouth disease in Shaanxi province. In Shaanxi province, the trend of hand, foot and mouth disease was analyzed and tested, under the use of R software, between January 2009 and June 2015. Multiple seasonal ARIMA model was then fitted under time series to predict the number of hand, foot and mouth disease in 2016 and 2017. Seasonal effect was seen in hand, foot and mouth disease in Shaanxi province. A multiple seasonal ARIMA (2,1,0)×(1,1,0)12 was established, with the equation as (1 -B)(1 -B12)Ln (Xt) =((1-1.000B)/(1-0.532B-0.363B(2))*(1-0.644B12-0.454B12(2)))*Epsilont. The mean of absolute error and the relative error were 531.535 and 0.114, respectively when compared to the simulated number of patients from Jun to Dec in 2015. RESULTS under the prediction of multiple seasonal ARIMA model showed that the numbers of patients in both 2016 and 2017 were similar to that of 2015 in Shaanxi province. Multiple seasonal ARIMA (2,1,0)×(1,1,0)12 model could be used to successfully predict the incidence of hand, foot and mouth disease in Shaanxi province.

Electricity Load Forecasting using Hybrid of Multiplicative Double Seasonal Exponential Smoothing Model with Artificial Neural Network

Electricity load forecasting often has many properties such as the nonlinearity, double seasonal cycles, and others those may be obstacles for the accuracy of forecasting using some classical statistical models. Many papers in this field have proposed using double seasonal (DS) exponential smoothing model to forecast. These papers indicated that electricity load forecasting using DS exponential smoothing model has better fit. Using artificial neural network (ANN) as a modern approach may be used for superior fitted forecasting, since this approach can deal with the non-linearity components of load data. The purpose of this paper is to improve the electricity load forecasting by building the hybrid model that includes a double seasonal exponential smoothing with an artificial neural network. This hybrid model will study the double seasonal effects and non-linearity components together based on the electricity load data. The strategy of building this hybrid model is by entering ANN output as an input in double seasonal exponential smoothing model. The data sets are taken from three stations with different electricity load characteristics such as a residential, industrial and city center. The electricity load testing forecast of DS exponential smoothing-ANN hybrid model gave the most minimum mean absolute percentage error (MAPE) measurement comparing with the electricity load testing forecasts of DS exponential smoothing and ANN for all electricity load data sets. In conclusion, DS exponential smoothing-ANN hybrid model are the most fitted for every electricity load data which contains the double seasonal effects and non-linearity components.

Application of multiple seasonal ARIMA model in forecasting incidence of HFMD in Wuhan, China

Application of multiple seasonal ARIMA model in forecasting incidence of HFMD in Wuhan, China

Predicting the sales volume of the medical product by triple exponential smoothing method.

This paper deals with the treatment of trend seasonality of time series by using the method of exponential smoothing, indeed the triple exponential method (Winter's Method) which includes two procedures of analysis, the first one is (multiplicative seasonal model) and second (additive seasonal model), we conclude the forecasting for future data for multiplicative model is better than additive model by using many criterions .MAD, MAPE, MSE.