Multiplicative Seasonal ARIMA Research Articles

Time series analysis on precipitation with missing data using stochastic SARIMA

This paper presents an application of the Box-Jenkins methodology for modeling the precipitation in Iran. Linear stochastic model known as multiplicative seasonal ARIMA was used to model the monthly precipitation data for 44 years. Missing data occurred in between for 34 months for some reason. To fill the gap a SARIMA model was fitted based on the first 180 available observations and the missing observations were substituted by the forecasts for the next 34 months. Then a SARIMA model was fitted for the full data. The result showed that the fitted model represent the full data well.

Effects of catastrophic financial loss on suicide risk: evidence from Korean stock market crash in October 2008.

PurposeThe negative effect of catastrophic financial loss on suicide risk is widely perceived but hardly studied in-depth because of various difficulties in designing studies. We empirically investigated the effect utilizing the stock market crash event in October 2008 in South Korea.MethodsWe extracted stock market investor data from Korea Exchanges, and mortality data from Microdata Integrated Service of individuals aged 30–60 years. We calculated age-standardized monthly suicide rate per 100,000 persons according to sex and age, and developed intervention analysis with multiplicative seasonal ARIMA model to isolate the effect of the stock market crash on suicide rate.ResultsMore than 11% of people aged 30–60 years were directly investing in stocks during stock market crash. In October 2008, both KOSPI and KOSDAQ indexes dropped by 22.67% and 30.14%, respectively. In November 2008, the suicide rate in males 30–60 years increased by > 40% compared to the expected levels if there had been no market crash, and in females aged 30–40 and 40–50 years, it increased by 101.84% and 74.81%, respectively. The effect appeared to persist in males, whereas it degenerated with time in females during our sampling period. Suicide was more pronounced in younger age groups and females.ConclusionIn this first in-depth study, the effect of catastrophic financial loss negatively affects suicide risk for an extended period, indicating health and financial authorities should provide a long-term financial and psychological support for people with extreme financial loss.

A comprehensive research on exponential smoothing methods in modeling and forecasting cellular traffic

SummaryTraffic prediction based on time series analysis methods that are low‐cost and low computational complexity can offer more efficient resource management and better QoS. Although exponential smoothing is such a kind of method, there is a lack of application in cellular networks and data traffic research, especially with the robust development of mobile Internet applications nowadays. Therefore, this study provides a comprehensive research on cellular network traffic prediction using exponential smoothing methods. More cases of traffic including voice and data in different time granularities as well as different domains compared with other studies are considered. Besides, more exponential smoothing methods are simultaneously investigated for different cases of traffic. Our multiple case study approach leads to a more convincing result of choosing the best fit model. Data collected from real commercial cellular networks is used for experiments to make the results more practical and persuasively. In our experiment method, the model has the lowest RMSE value is chosen among three types of method. The experiment results show that exponential smoothing methods outperform multiplicative seasonal ARIMA, which is slower and more complex in computation in all cases, so they should be recommended for traffic prediction.

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.

Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics.

Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1) model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1)), and the Modified Grey Model using Fourier Series (FGM(1,1)), in addition to a multiplicative seasonal ARIMA(1,0,1)(1,1,0)4 model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1) model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends.

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.

Time-Series Approaches for Forecasting the Number of Hospital Daily Discharged Inpatients.

For hospitals where decisions regarding acceptable rates of elective admissions are made in advance based on expected available bed capacity and emergency requests, accurate predictions of inpatient bed capacity are especially useful for capacity reservation purposes. As given, the remaining unoccupied beds at the end of each day, bed capacity of the next day can be obtained by examining the forecasts of the number of discharged patients during the next day. The features of fluctuations in daily discharges like trend, seasonal cycles, special-day effects, and autocorrelation complicate decision optimizing, while time-series models can capture these features well. This research compares three models: a model combining seasonal regression and ARIMA, a multiplicative seasonal ARIMA (MSARIMA) model, and a combinatorial model based on MSARIMA and weighted Markov Chain models in generating forecasts of daily discharges. The models are applied to three years of discharge data of an entire hospital. Several performance measures like the direction of the symmetry value, normalized mean squared error, and mean absolute percentage error are utilized to capture the under- and overprediction in model selection. The findings indicate that daily discharges can be forecast by using the proposed models. A number of important practical implications are discussed, such as the use of accurate forecasts in discharge planning, admission scheduling, and capacity reservation.

Multiplicative seasonal ARIMA modelling of monthly stream flows of Choriti river

The multiplicative seasonal ARIMA (p,d,q) × (P,D,Q) s models of different orders were tried for modelling of monthly inflow of Choriti river of Konkan region of Maharashtra, based on 20 years data. The parameters of seasonal ARIMA models were estimated by fitting ARIMA models to differenced series (d=0 and D=1) at different lags. The goodness of fit of models was tested by Box-Pierce Portmanteau lack of fit test and comparison of historical and forecasted monthly inflows. The forecasted performance of the model was evaluated by using goodness of fit tests. Lower values of root mean squared error; mean relative error and integral square error for multiplicative seasonal ARIMA (0,0,1) × (0,1,1) 12 model indicated closer agreement between forested and historical monthly inflow series.

A Multiplicative Seasonal ARIMA/GARCH Model in EVN Traffic Prediction

This paper highlights the statistical procedure used in developing models that have the ability of capturing and forecasting the traffic of mobile communication network operating in Vietnam. To build such models, we follow Box-Jenkins method to construct a multiplicative seasonal ARIMA model to represent the mean component using the past values of traffic, then incorporate a GARCH model to represent its volatility. The traffic is collected from EVN Telecom mobile communication network. Diagnostic tests and examination of forecast accuracy measures indicate that the multiplicative seasonal ARIMA/GARCH model, i.e. ARIMA (1, 0, 1) × (0, 1, 1)24/GARCH (1, 1) shows a good estimation when dealing with volatility clustering in the data series. This model can be considered to be a flexible model to capture well the characteristics of EVN traffic series and give reasonable forecasting results. Moreover, in such situations that the volatility is not necessary to be taken into account, i.e. short-term prediction, the multiplicative seasonal ARIMA/GARCH model still acts well with the GARCH parameters adjusted to GARCH (0, 0).

Model of multiple seasonal autoregressive integrated moving average model and its application in prediction of the hand-foot-mouth disease incidence in Changsha

To establish multiple seasonal autoregressive integrated moving average model (ARIMA) according to the hand-foot-mouth disease incidence in Changsha, and to explore the feasibility of the multiple seasonal ARIMA in predicting the hand-foot-mouth disease incidence. EVIEWS 6.0 was used to establish multiple seasonal ARIMA according to the hand-foot- mouth disease incidence from May 2008 to August 2013 in Changsha, and the data of the hand- foot-mouth disease incidence from September 2013 to February 2014 were served as the examined samples of the multiple seasonal ARIMA, then the errors were compared between the forecasted incidence and the real value. Finally, the incidence of hand-foot-mouth disease from March 2014 to August 2014 was predicted by the model. After the data sequence was handled by smooth sequence, model identification and model diagnosis, the multiple seasonal ARIMA (1, 0, 1)×(0, 1, 1)12 was established. The R2 value of the model fitting degree was 0.81, the root mean square prediction error was 8.29 and the mean absolute error was 5.83. The multiple seasonal ARIMA is a good prediction model, and the fitting degree is good. It can provide reference for the prevention and control work in hand-foot-mouth disease.

Forecast Performance of Multiplicative Seasonal Arima Model: an Application to Naira/Us Dollar Exchange Rate

Seasonality accounts majorly for quarterly and monthly movements in macro-economics and time series and in modelling such patterns to have a forecasting robustness, precision and reliability have been steadily increased in recent years but no consensus has been reached as to which model yields the appropriate description. However, this research seeks to address the robustness and accuracy of seasonal ARIMA model of Naira/Dollar exchange rate using a monthly data for the period of Jan 1994 to July 2013. The series was subjected to a time plot revealing seasonal patterns and upward trend. Both behaviours were taken into account by moving average and seasonal moving average, where little or fewer months of data were used to estimate the local level and trend and also few seasons of data were averaged over to estimate the seasonal patterns. The proposed model shows predictive power, robustness and precision which was revealed by the normality of data and residual analysis. The estimated forecast values from our proposed model are more realistic and closely reflect in the current economic reality in two countries as indicated by the forecast measurement criteria.

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

Time series modelling of temperatures: an example from Kefalonia

This paper analyses monthly maximum and minimum temperatures from the Greek island of Kefalonia. The data are from the first decade of the twenty-first century and are analysed using a multiplicative seasonal ARIMA model which allows a simple interpretation in terms of adjusting exponentially moving averages of past values. A component decomposition of the data using this model reveals that there has been essentially no trend movement but that the seasonal patterns slowly evolve over time, with the amplitude of the seasonal cycle of maximum temperatures being over 3 ∘C greater than that for minimum temperatures. There appears to have been a break in the mechanism generating the two series in 2011, probably a consequence of shifting the location of the measuring equipment. Copyright © 2013 Royal Meteorological Society

A novel hybridization of echo state networks and multiplicative seasonal ARIMA model for mobile communication traffic series forecasting

For mobile communication traffic series, an accurate multistep prediction result plays an important role in network management, capacity planning, traffic congestion control, channel equalization, etc. A novel time series forecasting based on echo state networks and multiplicative seasonal ARIMA model are proposed for this multiperiodic, nonstationary, mobile communication traffic series. Motivated by the fact that the real traffic series exhibits periodicities at the cycle of 6, 12, and 24 h, as well as 1 week, we isolate most of mentioned above features for each cell and integrate all the wavelet multiresolution sublayers into two parts for consideration of alleviating the accumulated error. On seasonal characters, multiplicative seasonal ARIMA model is to predict the seasonal part, and echo state networks are to deal with the smooth part because of its prominent approximation capabilities and convenience. Experimental results on real traffic dataset show that proposed method performs well on the prediction accuracy.

A Multiplicative Seasonal Arima Model for Nigerian Unemployment Rates

Time series analysis of Nigerian Unemployment Rates is done. The data used is monthly from 1948 to 2008. The time plot reveals a slightly positive trend with no clear seasonality. A multiplicative seasonal model is suggestive given seasonality that typically tends to increase with time. Seasonal differencing once produced a series with no trend nor discernible stationarity. A non-seasonal differencing of the seasonal differences yielded a series with no trend but with a correlogram revealing stationarity of order 12, a nonseasonal autoregressive component of order 3 and a seasonal moving average component of order 1. A multiplicative seasonal autoregressive integrated moving average (ARIMA) model, (3, 1, 0)x(0, 1, 1)12, is fitted to the series. It has been shown to be adequate.

계절 ARIMA 모형을 이용한 제주공항 여객 수요예측 및 효율적 운영에 관한 연구

This research is to find out the method appropriate for the forecasting of passennger demand using seasonal ARIMA model and efficient operation in Jeju National Airport. Time series monthly data for the investigation were collected ranging from January 2003 to December 2011. A total of 108 observations were used for data analysis. Research findings showed that the multiplicative seasonal ARIMA(0.1.2)(0.1.1)12 model is appropriate model. The number of passengers in Jeju National Airport will continue to rise, it was expected to surpass 20 million people.

계절 아리마 모형을 이용한 관광객 예측 -경북 영덕지역을 대상으로-

The study uses a seasonal ARIMA model to forecast the number of tourists of Yeongdeok in an uni-variable time series. The monthly data for time series were collected ranging from 2006 to 2011 with some variation between on-season and off-season tourists in Yeongdeok county. A total of 72 observations were used for data analysis. The forecast multiplicative seasonal ARIMA(1,0,0)<TEX>$(0,1,1)_{12}$</TEX> model was found the most appropriate one. Results showed that the number of tourists was 10,974 thousands in 2012 and 13,465 thousands in 2013, It was suggested that the grasping forecast model is very important in respect of how experts in tourism development in Yeongdeok county, policy makers or planners would establish strategies to allocate service in Yeongdeok tourist destination and provide tourism facilities efficiently.

Forecasting of Tourist Arrivals Using Subset, Multiplicative or Additive Seasonal ARIMA Model

Most of Seasonal Autoregressive Integrated Moving Average (SARIMA) models that used for forecasting seasonal time series are multiplicative SARIMA models. These models assume that there is a significant parameter as a result of multiplication between non-seasonal and seasonal parameters without testing by certain statistical test. Moreover, most popular statistical software such as MINITAB and SPSS only has facility to fit multiplicative models. The aim of this research is to propose a new procedure for indentifying the most appropriate order of SARIMA model whether it involves subset, multiplicative or additive order. In particular, the study examined whether a multiplicative parameter existed in the SARIMA model. Data about the number of tourist arrivals to Bali, Indonesia, were used as a case study. The model identification step to determine the order of ARIMA model was done by using MINITAB program, and the model estimation step used SAS program to test whether the model consisted of subset, multiplicative or additive order. Modeling of the data yielded an additive SARIMA model is the best model for forecasting the number of tourist arrivals to Bali. The comparison evaluation showed that additive SARIMA model yielded more accurate forecasted values at out-sample datasets than multiplicative SARIMA model. This study is valuable contribution to the Box-Jenkins procedure particularly at the model identification and estimation steps in SARIMA models. Further work involving multiple seasonal ARIMA models, such as short term load data forecasting in certain countries, may provide further insights regarding the subset, multiplicative or additive orders. Keywords: SARIMA; subset; multiplicative; additive; tourist arrivals 2010 Mathematics Subject Classification 62M10; 62P20.

Time Series Forecasting by using Seasonal Autoregressive Integrated Moving Average: Subset, Multiplicative or Additive Model

Problem statement: Most of Seasonal Autoregressive Integrated Moving Average (SARIMA) models that used for forecasting seasonal time series are multiplicative SARIMA models. These models assume that there is a significant parameter as a result of multiplication between nonseasonal and seasonal parameters without testing by certain statistical test. Moreover, most popular statistical software such as MINITAB and SPSS only has facility to fit a multiplicative model. The aim of this research is to propose a new procedure for indentifying the most appropriate order of SARIMA model whether it involves subset, multiplicative or additive order. In particular, the study examined whether a multiplicative parameter existed in the SARIMA model. Approach: Theoretical derivation about Autocorrelation (ACF) and Partial Autocorrelation (PACF) functions from subset, multiplicative and additive SARIMA model was firstly discussed and then R program was used to create the graphics of these theoretical ACF and PACF. Then, two monthly datasets were used as case studies, i.e. the international airline passenger data and series about the number of tourist arrivals to Bali, Indonesia. The model identification step to determine the order of ARIMA model was done by using MINITAB program and the model estimation step used SAS program to test whether the model consisted of subset, multiplicative or additive order. Results: The theoretical ACF and PACF showed that subset, multiplicative and additive SARIMA models have different patterns, especially at the lag as a result of multiplication between non-seasonal and seasonal lags. Modeling of the airline data yielded a subset SARIMA model as the best model, whereas an additive SARIMA model is the best model for forecasting the number of tourist arrivals to Bali. Conclusion: Both of case studies showed that a multiplicative SARIMA model was not the best model for forecasting these data. The comparison evaluation showed that subset and additive SARIMA models gave more accurate forecasted values at out-sample datasets than multiplicative SARIMA model for airline and tourist arrivals datasets respectively. This study is valuable contribution to the Box-Jenkins procedure particularly at the model identification and estimation steps in SARIMA model. Further work involving multiple seasonal ARIMA models, such as short term load data forecasting in certain countries, may provide further insights regarding the subset, multiplicative or additive orders.

Univariate forecasting of day-ahead hourly electricity demand in the northern grid of India

Short-term electricity demand forecasts (minutes to several hours ahead) have become increasingly important since the rise of the competitive energy markets. The issue is particularly important for India as it has recently set up a power exchange (PX), which has been operating on day-ahead hourly basis. In this study, an attempt has been made to forecast day-ahead hourly demand of electricity in the northern grid of India using univariate time-series forecasting techniques namely multiplicative seasonal ARIMA and Holt-Winters multiplicative exponential smoothing (ES). In-sample forecasts reveal that ARIMA models, except in one case, outperform ES models in terms of lower RMSE, MAE and MAPE criteria. We may conclude that linear time-series models works well to explain day-ahead hourly demand forecasts in the northern grid of India. The findings of the study will immensely help the players in the upcoming power market in India.