On the Noninvertible Moving Average Time Series with Infinite Variance

1993 ◽  
Vol 9 (4) ◽  
pp. 680-685 ◽  
Author(s):  
Ngai Hang Chan
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Moving Average ◽  
Infinite Variance ◽  
Average Model ◽  
Initial Value ◽  
Least Squares Estimate ◽  
Moving Average Model ◽  
Heavy Tailed ◽  
Stable Index

The limiting distribution of the least squares estimate of the derived process of a noninvertible and nearly noninvertible moving average model with infinite variance innovations is established as a functional of a Lévy process. The form of the limiting law depends on the initial value of the innovation and the stable index α. This result enables one to perform asymptotic testing for the presence of a unit root for a noninvertible moving average model through the constructed derived process under the null hypothesis. It provides not only a parallel analog of its autoregressive counterparts, but also a useful alternative to determine “over-differencing” for time series that exhibit heavy-tailed phenomena.

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 Examination of Temperature Variability over Lahore (Pakistan) and Dhaka (Bangladesh): A Comparative Study

2020 ◽  
Vol 10 (4) ◽  
pp. 46-50
Author(s):  
Khadija Shakrullah ◽  
Safdar Ali Shirazi ◽  
Sajjad Hussain Sajjad ◽  
Zartab Jahan
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Temperature Variability ◽  
Series Data ◽  
Maximum Temperature ◽  
Average Model ◽  
Temperature Variations ◽  
Moving Average Model ◽  
Mega Cities

Lahore and Dhaka are rapid expanding and over populated cities of South Asia located in Pakistan andBangladesh respectively. The present study focuses on the evaluation of temperature variability in comparison of bothcities. This study primarily aims at the assessment and examination of temperature variations in both mega cities ofSouth Asia which are seasonal as well as the annual. The time series data were analysed by using statistical techniquesAutoregressive Moving Average Model (ARMA) and Autoregressive Integrated Average Model (ARIMA). The resultsreveal that the minimum temperature is increasing much faster than that of the maximum temperature of both cities.However, the temperature rise(in maximum and minimum) has been observed highest during the spring seasons in bothcities.

Modeling and Forecasting Sales Data by Time Series Analysis

1981 ◽  
Vol 18 (1) ◽  
pp. 94-100 ◽  
Author(s):  
S. G. Kapoor ◽  
P. Madhok ◽  
S. M. Wu
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Time Series Modeling ◽  
Average Model ◽  
Sales Data ◽  
Autoregressive Moving Average Model ◽  
Deterministic Function ◽  
Modeling And Forecasting ◽  
Moving Average Model

Time series modeling technique is used to model a series of sales data in which seasonality causes distinct spike peaks. The analysis of actual sales data shows that the seasonality in the data can be approximated by a deterministic function and the stochastic component is a sixth-order autoregressive moving average model. Use of the combined deterministic and stochastic models to derive the minimum mean squared forecast yields reliable results.

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.

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