scholarly journals Determining the Pension Benefit Obligation of a Defined Benefit Plan: Applying a Multivariate ARIMA Stochastic Model

2022 ◽  
Vol 17 (4) ◽  
pp. 145
Author(s):  
Jeffrey Tim Query ◽  
Evaristo Diz
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Pension Benefit ◽  
Defined Benefit ◽  
Data Set ◽  
Autoregressive Integrated Moving Average ◽  
Statistical Estimates ◽  
Moving Average Model ◽  
Series Type ◽  
Sample Time

<p>In this study we examine the robustness of fit for a multivariate and an autoregressive integrated moving average model to a data sample time series type.  The sample is a recurrent actuarial data set for a 10-year horizon.  We utilize this methodology to contrast with stochastic models to make projections beyond the data horizon. Our key results suggest that both types of models are useful for making predictions of actuarial liability levels given by PBO Projected Benefit Obligations on and off the horizon of the sample time series.  As we have seen in prior research, the use of multivariate models for control and auditing purposes is widely recommended.  Fast and reliable statistical estimates are desirable in all cases, whether for audit purposes or to verify and validate miscellaneous actuarial results.</p>

scholarly journals Forecasting GDP Movements in Nepal Using Autoregressive Integrated Moving Average (ARIMA) Modelling Process

2019 ◽  
Vol 4 (2) ◽  
pp. 1-20
Author(s):  
Surya Bahadur Rana
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Arima Model ◽  
Data Set ◽  
Autoregressive Integrated Moving Average ◽  
Sample Data ◽  
Moving Average Model ◽  
Annual Time Series ◽  
Annual Time ◽  
Modelling Process

This study attempts to test the ARIMA model and forecast annual time series of GDP in Nepal from mid-July, 1960 to mid-July, 2018. The annual time series on GDP used in this study consists of total 59 observations. Out of them, three years’ data from mid-July 2016 to mid-July 2018 have been used for in-sample forecasting and evaluation. The study uses univariate Box-Jenkins ARIMA modelling process to identify the best fitted model that describes the sample data set. The study examines a number of ARIMA family models and recommends ARIMA (0,1,2) as the most appropriate model that best describes the annual GDP series of the sampled period. The ARIMA (0, 1, 2) model incorporates zero lag order for autoregression, integrated with 2 lag order for moving average model using first difference operator. The ARIMA model forecasts documented in this study are not significantly different from actual because the actual annual GDP series observed in forecast period fall within 95 per cent confidence interval of estimates. Hence, ARIMA (0,1,2) model can best capture the GDP movement in Nepal for the sample period.

scholarly journals Studying monthly rainfall over Dibrugarh, Assam: Use of SARIMA approach

MAUSAM ◽  
2021 ◽  
Vol 68 (2) ◽  
pp. 349-356
Author(s):  
J. HAZARIKA ◽  
B. PATHAK ◽  
A. N. PATOWARY
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Demand Management ◽  
Arima Model ◽  
Monthly Rainfall ◽  
Series Data ◽  
Data Set ◽  
Modeling And Forecasting ◽  
Moving Average Model

Perceptive the rainfall pattern is tough for the solution of several regional environmental issues of water resources management, with implications for agriculture, climate change, and natural calamity such as floods and droughts. Statistical computing, modeling and forecasting data are key instruments for studying these patterns. The study of time series analysis and forecasting has become a major tool in different applications in hydrology and environmental fields. Among the most effective approaches for analyzing time series data is the ARIMA (Autoregressive Integrated Moving Average) model introduced by Box and Jenkins. In this study, an attempt has been made to use Box-Jenkins methodology to build ARIMA model for monthly rainfall data taken from Dibrugarh for the period of 1980- 2014 with a total of 420 points.  We investigated and found that ARIMA (0, 0, 0) (0, 1, 1)12 model is suitable for the given data set. As such this model can be used to forecast the pattern of monthly rainfall for the upcoming years, which can help the decision makers to establish priorities in terms of agricultural, flood, water demand management etc.  

scholarly journals The Impact of Lengths of Time Series on the Accuracy of the ARIMA Forecasting

2019 ◽  
Vol 4 (3) ◽  
pp. 58
Author(s):  
Lu Qin ◽  
Kyle Shanks ◽  
Glenn Allen Phillips ◽  
Daphne Bernard
Keyword(s):  
Time Series ◽  
Historical Data ◽  
Moving Average ◽  
Arima Model ◽  
Forecasting Accuracy ◽  
Autoregressive Integrated Moving Average ◽  
Enrollment Forecasting ◽  
Moving Average Model ◽  
The Impact ◽  
Practical Impact

The Autoregressive Integrated Moving Average model (ARIMA) is a popular time-series model used to predict future trends in economics, energy markets, and stock markets. It has not been widely applied to enrollment forecasting in higher education. The accuracy of the ARIMA model heavily relies on the length of time series. Researchers and practitioners often utilize the most recent - to -years of historical data to predict future enrollment; however, the accuracy of enrollment projection under different lengths of time series has never been investigated and compared. A simulation and an empirical study were conducted to thoroughly investigate the accuracy of ARIMA forecasting under four different lengths of time series. When the ARIMA model completely captured the historical changing trajectories, it provided the most accurate predictions of student enrollment with 20-years of historical data and had the lowest forecasting accuracy with the shortest time series. The results of this paper contribute as a reference to studies in the enrollment projection and time-series forecasting. It provides a practical impact on enrollment strategies, budges plans, and financial aid policies at colleges and institutions across countries.

scholarly journals Predicting the detection of leprosy in a hyperendemic area of Brazil: Using time series analysis

2021 ◽  
Vol 0 ◽  
pp. 1-9
Author(s):  
Vera Gregório ◽  
Dinilson Pedroza ◽  
Celivane Barbosa ◽  
Gilberto Bezerra ◽  
Ulisses Montarroyos ◽  
...  
Keyword(s):  
Time Series ◽  
Information System ◽  
Moving Average ◽  
Northeastern Brazil ◽  
Average Model ◽  
Detection Rates ◽  
Autoregressive Integrated Moving Average ◽  
Notifiable Diseases ◽  
Hyperendemic Area ◽  
Moving Average Model

Background: Brazil has the second highest prevalence of leprosy worldwide. Autoregressive integrated moving average models are useful tools in surveillance systems because they provide reliable forecasts from epidemiological time series. Aim: To evaluate the temporal patterns of leprosy detection from 2001 to 2015 and forecast for 2020 in a hyperendemic area in northeastern Brazil. Methods: A cross-sectional study was conducted using monthly leprosy detection from the Brazil information system for notifiable diseases. The Box–Jenkins method was applied to fit a seasonal autoregressive integrated moving average model. Forecasting models (95% prediction interval) were developed to predict leprosy detection for 2020. Results: A total of 44,578 cases were registered with a mean of 247.7 cases per month. The best-fitted model to make forecasts was the seasonal autoregressive integrated moving average ((1,1,1); (1,1,1)). It was predicted 0.32 cases/100,000 inhabitants to January of 2016 and 0.38 cases/100,000 inhabitants to December of 2020. Limitations: This study used secondary data from Brazil information system for notifiable diseases; hence, leprosy data may be underreported. Conclusion: The forecast for leprosy detection rate for December 2020 was < 1 case/100,000 inhabitants. Seasonal autoregressive integrated moving average model has been shown to be appropriate and could be used to forecast leprosy detection rates. Thus, this strategy can be used to facilitate prevention and elimination programmes.

scholarly journals Predictability of Scrub Typhus Incidences Time Series in Thailand

2021 ◽  
Vol 5 (1) ◽  
pp. 44
Author(s):  
Valeria Bondarenko ◽  
Pierre Mazzega ◽  
Claire Lajaunie
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Scrub Typhus ◽  
Moving Average ◽  
Public Health Problem ◽  
Reference Level ◽  
Autoregressive Integrated Moving Average ◽  
Incidence Data ◽  
Motion Models ◽  
Moving Average Model

Scrub typhus, an infectious disease caused by a bacterium transmitted by “chigger” mites, constitutes a public health problem in Thailand. Predicting epidemic peaks would allow implementing preventive measures locally. This study analyses the predictability of the time series of incidence of scrub typhus aggregated at the provincial level. After stationarizing the time series, the evaluation of the Hurst exponents indicates the provinces where the epidemiological dynamics present a long memory and are predictable. The predictive performances of ARIMA (autoregressive integrated moving average model), ARFIMA (autoregressive fractionally integrated moving average) and fractional Brownian motion models are evaluated. The results constitute the reference level for the predictability of the incidence data of this zoonosis.

scholarly journals Analysis and Prediction of Hydraulic Support Load Based on Time Series Data Modeling

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yi-Hui Pang ◽  
Hong-Bo Wang ◽  
Jian-Jian Zhao ◽  
De-Yong Shang
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Arima Model ◽  
Sliding Window ◽  
Series Data ◽  
Average Model ◽  
Hydraulic Support ◽  
Autoregressive Integrated Moving Average ◽  
Moving Average Model

Hydraulic support plays a key role in ground control of longwall mining. The smart prediction methods of support load are important for achieving intelligent mining. In this paper, the hydraulic support load data is decomposed into trend term, cycle term, and residual term, and it is found that the data has clear trend and period features, which can be called time series data. Based on the autoregression theory and weighted moving average method, the time series model is built to analyze the load data and predict its evolution trend, and the prediction accuracy of the sliding window model, ARIMA (Autoregressive Integrated Moving Average) model, and SARIMA (Seasonal Autoregressive Integrated Moving Average) model to the hydraulic support load under different parameters are evaluated, respectively. The results of single-point and multipoint prediction test with various sliding window values indicate that the sliding window method has no advantage in predicting the trend of the support load. The ARIMA model shows a better short-term trend prediction than the sliding window model. To some extent, increasing the length of the autoregressive term can improve the long-term prediction accuracy of the model, but it also increases the sensitivity of the model to support load fluctuation, and it is still difficult to predict the load trend in one support cycle. The SARIMA model has better prediction results than the sliding window model and the ARIMA model, which reveals the load evolution trend accurately during the whole support cycle. However, there are many external factors affecting the support load, such as overburden properties, hydraulic support moving speed, and worker’s operation. The smarter model of SARIMA considering these factors should be developed to be more suitable in predicting the hydraulic support load.

scholarly journals Forecasting cotton lint exports in Nigeria using the autoregressive integrated moving average model

2021 ◽  
Vol 19 (1) ◽  
pp. 150-162
Author(s):  
A.S. Akenbor ◽  
P.I. Nwandu
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Series Data ◽  
Cotton Lint ◽  
Colonial Era ◽  
Autoregressive Integrated Moving Average ◽  
Post Colonial ◽  
Moving Average Model ◽  
Oil Sector

Nigeria was a major global exporter of cotton lint to international market during the colonial and post-colonial era till late 70s when the  country fully embraced oil exports to the detriment of the non-oil sector, cotton lint exports inclusive. However, Nigeria is gradually emphasizing agricultural exports again to earn huge foreign exchange, the oil sector having left the country in economic crises. This study utilized time series model particularly, Autoregressive Integrated Moving Average (ARIMA) to make forecasting of cotton lint exports in Nigeria by using 46 yearly observations (1970-2015). The model went through series of investigative and diagnostic tests in order to observe the usefulness of the model. The fitting of the selected ARIMA (2,1,2) model to the time series data, means fitting ARIMA (2,1,2) model of one first order difference. Smaller RMSE, MAE as well as Theil Inequality coefficient are actually preferred and justified that ARIMA (2,1,2) model was justified as adequate for the forecasting of cotton lint exports in Nigeria with AIC value of 20.96771, SIC value of 21.04881, MAPE value of 6751.231, RMSE of 93303.67 and R2 of 0.330951. A thirty-year period ahead of cotton lint exports is predicted. The observations signify a rising trend in exports hence; it will be available especially in the future for foreign trade in the next thirty years. The outcome from the study is valuable for trade organisations and investors in assessing the precariousness of the market structure.

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