Improving the order selection of moving average time series model

2012 ◽  
Vol 5 (5) ◽  
Author(s):  
Ali Hussein Al-Marshadi
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Time Series Model ◽  
Order Selection ◽  
Selection Of

scholarly journals Justification of Wold’s Theorem and the Unbiasedness of a Stable Vector Autoregressive Time Series Model Forecasts

2017 ◽  
Vol 6 (2) ◽  
pp. 1
Author(s):  
Iberedem A. Iwok
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Autoregressive Process ◽  
Time Series Model ◽  
Average Process ◽  
Moving Average Process ◽  
Autoregressive Time Series ◽  
Vector Autoregressive ◽  
Vector Autoregressive Process ◽  
Vector Time Series

In this work, the multivariate analogue to the univariate Wold’s theorem for a purely non-deterministic stable vector time series process was presented and justified using the method of undetermined coefficients. By this method, a finite vector autoregressive process of order  [] was represented as an infinite vector moving average () process which was found to be the same as the Wold’s representation. Thus, obtaining the properties of a  process is equivalent to obtaining the properties of an infinite  process. The proof of the unbiasedness of forecasts followed immediately based on the fact that a stable VAR process can be represented as an infinite VEMA process.

scholarly journals Spatiotemporal characteristics and the epidemiology of tuberculosis from 2004 to 2017 in China by the nationwide surveillance system

2020 ◽  
Author(s):  
Zhongbao Zuo ◽  
Miaochan Wang ◽  
Huaizhong Cui ◽  
Ying Wang ◽  
Jing Wu ◽  
...  
Keyword(s):  
Time Series ◽  
Regression Analysis ◽  
Moving Average ◽  
Multivariate Time Series ◽  
Time Series Model ◽  
Joinpoint Regression ◽  
Sarima Model ◽  
Autoregressive Integrated Moving Average ◽  
Joinpoint Regression Analysis ◽  
Infectious Disease Reporting

Abstract Background The objective was to identify the Spatial-temporal characteristics and the epidemiology of tuberculosis in China from 2004 to 2017 with Joinpoint regression analysis, Seasonal Autoregressive integrated moving average (SARIMA) model, geographic cluster, and multivariate time series model. Methods The data of TB from January 2004 to December 2017 were obtained from the notifiable infectious disease reporting system supplied by the China CDC. Joinpoint regression analysis was used to observe the trend. The monthly incidence was predicted by the Seasonal autoregressive integrated moving average (SARIMA) model. Spatial autocorrelation analysis was performed to detect geographic clusters. A multivariate time series model was employed to analyze heterogeneous transmission. Results We included 13,991,850 TB cases from 2004 to 2017. The final selected model was the 0 Joinpoint model with an annual average percent change of -3.3. A seasonality was observed across the fourteen years, and the seasonal peaks were in January and March. The best SARIMA model was (0, 1, 1) X (0, 1, 1) 12 , with a minimum AIC (880.5) and SBC (886.4). The predicted value and the original incidence data of 2017 were well matched. The provinces with a high incidence were located in the northwest (Xinjiang, Tibet) and south (Guangxi, Guizhou, Hainan) of China. The autoregressive component had a leading role in the incidence of TB which accounted for 81.5% - 84.5% of the patients on average. The endemic component was about twice as large in the western provinces as the average while the spatial-temporal component was less important there. Most of the high incidences areas were mainly affected by the autoregressive component for the past fourteen years. Conclusion A significant decreasing trend was seen from 2004 to 2017. The seasonal peaks were in January and March every year. Obvious clusters were identified in Tibet and Xinjiang Province. A spatial heterogeneity in the component driving the transmission of TB was identified from the multivariate time series model. This suggested that targeted preventive efforts should be made in different provinces based on the main component contributing to the epidemics.

Paygo for punctuality

2016 ◽  
Vol 28 (3) ◽  
pp. 265-298
Author(s):  
Luke Fowler
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Presidential Leadership ◽  
Mixed Effects ◽  
Time Series Model ◽  
Autoregressive Moving Average ◽  
Party Polarization ◽  
Budgeting Process

The federal budgeting process is wrought with conflict that makes it nearly impossible for the budget to be passed on time, or so it seems. One aspect overlooked is the effects of statutory Pay-As-You-Go (PAYGO) rules. The cursory evidence indicates PAYGO may be beneficial under certain circumstances. The analysis relies on an Autoregressive-Moving-Average (ARMA) time series model with data from appropriations bills signed into law from fiscal years 1994 to 2014. The findings indicate mixed effects for PAYGO statutes with a shorter budgeting timeline under the Budget Enforcement Act of 1990, but a longer timeline under the Statutory PAYGO Act of 2010. Additional findings suggest substantive relationships between the length of the budgeting process and party polarization, presidential leadership, and the economy.

scholarly journals Bootstrap Order Determination for ARMA Models: A Comparison between Different Model Selection Criteria

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Livio Fenga
Keyword(s):  
Selection Criteria ◽  
Moving Average ◽  
Information Criterion ◽  
Autoregressive Moving Average ◽  
Order Selection ◽  
Arma Models ◽  
Final Prediction Error ◽  
Novel Method ◽  
Order Determination ◽  
Selection Of

The present paper deals with the order selection of models of the class for autoregressive moving average. A novel method—previously designed to enhance the selection capabilities of the Akaike Information Criterion and successfully tested—is now extended to the other three popular selectors commonly used by both theoretical statisticians and practitioners. They are the final prediction error, the Bayesian information criterion, and the Hannan-Quinn information criterion which are employed in conjunction with a semiparametric bootstrap scheme of the type sieve.

scholarly journals Prediksi Pencurian Sepeda Motor Menggunakan Model Time Series (Studi Kasus: Polres Kotabumi Lampung Utara)

2020 ◽  
Vol 14 (3) ◽  
pp. 425-434
Author(s):  
MELI PRANATA ◽  
DIAN ANGGRAINI ◽  
Deden Makbuloh ◽  
Achi Rinaldi
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Arima Model ◽  
Time Series Model ◽  
Ar Model ◽  
Autoregressive Integrated Moving Average ◽  
Model Time Series

Tindak kriminal adalah kejahatan yang melanggar undang-undang suatu Negara atau melanggar norma yang berlaku dalam masyarakat. Pencurian merupakan salah satu bentuk dari perbuatan tindak kriminal. Dampak yang ditimbulkan dari adanya pencurian adalah perasaan kurang aman, takut, dan tenang. Salah satu model yang digunakan untuk memprediksi jumlah kasus pencurian yaitu model time series. Model time series adalah serangkaian nilai pengamatan yang diambil selama periode waktu tertentu. Pada umumnya, dalam interval-interval yang sama panjang, (Spuege & Stephens, 2004). Penelitian ini bertujuan memodelkan data tindak kriminal yang terjadi di Lampung Utara dengan model Autoregressive (AR), Moving Average (MA), dan Autoregressive Integrated Moving Average (ARIMA). Selanjutnya dari model terbaik akan digunakan untuk peramalan 6 bulan kedepan. Hasil penelitian model AR , model AR , model MA , ARIMA , dan model ARIMA . Model MA  memiliki koefisien parameter yang signifikan, memenuhi uji diagnostic tidak adanya residual pada model dan memiliki nilai RMSE dan AIC terkecil dengan nilai RMSE sebesar dan nilai AIC sebesar . Hasil prediksi model MA  untuk 6 bulan ke depan cenderung mendatar.

scholarly journals PENERAPAN METODE EXPONENTIAL SMOOTHING UNTUK PERAMALAN JUMLAH KLAIM DI BPJS KESEHATAN PAMEKASAN

2016 ◽  
Vol 2 (1) ◽  
pp. 46 ◽  
Author(s):  
Faisol Faisol ◽  
Sitti Aisah
Keyword(s):  
Time Series ◽  
Average Method ◽  
Moving Average ◽  
Exponential Smoothing ◽  
Time Series Model ◽  
Smoothing Method ◽  
Repair Procedure ◽  
Double Exponential Smoothing ◽  
Using Data ◽  
Exponential Smoothing Method

Time series model is the model used to predict the future using past data, one example of a time series model is exponential smoothing. Exponential smoothing method is a repair procedure performed continuously at forecasting the most recent data. In this study the exponential smoothing method is applied to predict the number of claims in the health BPJS Pamekasan using data from the period January 2014 to December 2015, the measures used to obtain the output of this research there are four stages, namely 1) the identification of data, 2) Modeling, 3) forecasting, 4) Evaluation of forecasting results with RMSE and MAPE. Based on the research methodology, the result for the period 25 = 833.828, the 26 = 800.256, period 27 = 766.684, a period of 28 = 733.113, period 29 = 699.541, and the period of 30 = 655, 970. Value for RMSE = 98.865 and MAPE = 7.002, In this case the moving average method is also used to compare the results of forecasting with double exponential smoothing method. Forecasting results for the period 25 = 899.208, the 26 = 885, 792, 27 = 872.375 period, a period of 28 = 858.958, period 29 = 845.542, and the period of 30 = 832.125. Value for RMSE = 101.131 and MAPE = 7.756. Both methods together - both have very good performance because the value of MAPE is below 10%, but the method of exponential smoothing has a value of RMSE and MAPE are smaller than the moving average method.

scholarly journals Spatiotemporal characteristics and the epidemiology of tuberculosis from 2004 to 2017 in China by the nationwide surveillance system

2020 ◽  
Author(s):  
Zhongbao Zuo ◽  
Miaochan Wang ◽  
Huaizhong Cui ◽  
Ying Wang ◽  
Jing Wu ◽  
...  
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Multivariate Time Series ◽  
Time Series Model ◽  
Joinpoint Regression ◽  
Sarima Model ◽  
Autoregressive Integrated Moving Average ◽  
The Past ◽  
Leading Role ◽  
Joinpoint Regression Analysis

Abstract Background China has always been one of the countries with the most serious Tuberculosis epidemic in the world. Our study was to observe the Spatial-temporal characteristics and the epidemiology of Tuberculosis in China from 2004 to 2017 with Joinpoint regression analysis, Seasonal Autoregressive integrated moving average (SARIMA) model, geographic cluster, and multivariate time series model.Methods The data of TB from January 2004 to December 2017 were obtained from the notifiable infectious disease reporting system supplied by the Chinese Center for Disease Control and Prevention. The incidence trend of TB was observed by the Joinpoint regression analysis. The Seasonal autoregressive integrated moving average (SARIMA) model was used to predict the monthly incidence. Geographic clusters was employed to analyze the spatial autocorrelation. The relative importance component of TB was detected by the multivariate time series model. Results We included 13,991,850 TB cases from January 2004 to December 2017, with a yearly average morbidity of 999,417 cases. The final selected model was the 0 Joinpoint model (P=0.0001) with an annual average percent change (AAPC) of -3.3 (95% CI: -4.3 to -2.2, P<0.001). A seasonality was observed across the fourteen years, and the seasonal peaks were in January and March every year. The best SARIMA model was (0, 1, 1) X (0, 1, 1)12 which can be written as (1-B) (1-B12) Xt = (1-0.42349B) (1-0.43338B12) εt, with a minimum AIC (880.5) and SBC (886.4). The predicted value and the original incidence data of 2017 were well matched. The MSE, RMSE, MAE, and MAPE of the modelling performance were 201.76, 14.2, 8.4 and 0.06, respectively. The provinces with a high incidence were located in the northwest (Xinjiang, Tibet) and south (Guangxi, Guizhou, Hainan) of China. The hotspot of TB transmission was mainly located at southern region of China from 2004 to 2008, including Hainan, Guangxi, Guizhou, and Chongqing, which disappeared in the later years. The autoregressive component had a leading role in the incidence of TB which accounted for 81.5% - 84.5% of the patients on average. The endemic component was about twice as large in the western provinces as the average while the spatial-temporal component was less important there. Most of the high incidences (>70 cases per 100,000) were influenced by the autoregressive component for the past fourteen years. Conclusion In a word, China still has a high TB incidence. However, the incidence rate of TB was significantly decreasing from 2004 to 2017 in China. Seasonal peaks were in January and March every year. Obvious geographical clusters were observed in Tibet and Xinjiang Province. The relative importance component of TB driving transmission was distinguished from the multivariate time series model. For every provinces over the past fourteen years, the autoregressive component played a leading role in the incidence of TB which need us to enhance the early protective implementation.

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