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This study aimed to find a model to forecast monthly measles immunization coverage using Autoregressive Integrated Moving Average (ARIMA). The monthly registered data for measles immunization coverage from January 2014 to December 2018 were used for the development of the model. The best model with the smallest Normalized Bayesian Information Criterion (BIC) of 8.673 is ARIMA (0, 1, 0). ARIMA (0, 1, 0) was used to forecast the monthly measles immunization coverage for the next 36 months from January 2018 to December 2020. The results obtained prove that this model can be used for forecasting future immunization coverage and will help decision-makers to establish strategies, priorities, and proper use of immunization resources.

Measles is a highly contagious respiratory disease caused by a virus which belongs to the paramyxovirus family. It is an airborne disease which spreads quickly through the coughs and sneezes of infected people. It may also be spread through direct contact with the mouth or nasal secretions. Even though the safe and effective vaccine is available, it remains a notable cause of death among young children worldwide. In 2017, there were about 110,000 global deaths related to measles, and mostly in children under the age of five [

In the Philippines, Expanded Program on Immunization (EPI) was established in 1976, one dose of measles vaccine given at nine months of age has been included in the program, then later on introduced nationwide in 1983 [

This study aimed to propose a forecasting model for monthly measles infant immunization coverage. The forecasting result generated by the model can serve as the basis for preparing the accurate monthly volume of measles vaccine. By doing so, this will help to achieve a high level of coverage and improve measles immunization planning and program.

A time-series approach with autoregressive integrated moving average (ARIMA) modeling is used to provide a monthly forecast of immunization coverage with precision. It is a combination of three statistical models. It uses the Autoregressive, Integrated, and Moving Average (ARIMA) model for statistical information. ARIMA model is commonly used in analysis and forecasting. It is the most efficient forecasting technique in social science and used extensively for time series [

Several studies were conducted to forecast immunization coverage. Authors in [

The research methodology used in this study is summarized below. The study used monthly registered data for measles immunization coverage from January 2014 to December 2018 total time series 60 was taken from the City Health Office of Cabanatuan. ARIMA is used to uncover the measles immunization coverage trend and the development of the forecasting model using IBM SPSS.

The dataset for this study was obtained from Cabanatuan City Health Office, Immunization Department. The dataset consists of the number of infant per month receiving the measles immunization for 60 month period from January 2014 to December 2018 in Cabanatuan City, Nueva Ecija, Philippines.

Autoregressive Integrated Moving Average model is popular and widely used stochastic time series model. It is a combination of three statistical models. An ARIMA model is denoted as an ARIMA model (p, d, q), where p is the number of autoregressive terms, d is the degree of differencing involve, and q is the number of moving-average terms [

1) Model Identification. In this step, the order of respective time series model is determined, the order of differencing “d”, the order of AR process which is “p” and order of MA process is “q”. This mainly leads to the use of graphical procedures such as plotting the series, the ACF and PACF.

2) Estimation of Model Parameters. Involves the estimation of the parameters of the different models using previously available data and proceeds to the first selection of models using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values.

3) Diagnostic checks (model checking). This step determines whether the model(s) specified and estimated is valid. Thus, the residual values are normally distributed, no significant periodicity is present in the residual, and the residual series is uncorrelated. The process will start again if this step is not fulfilled.

4) Forecasting. In this step, the model is now ready to be tested on real data to forecast future values of immunization coverage.

This study applies Box-Jenkins methodology for the identification, estimation, diagnostic checking, and forecasting of the univariate time-series data on monthly measles immunization coverage. The graph of the raw data is shown in

The first stage in developing an ARIMA model is to determine if the series is stationary. The graph below (

(i.e., the mean of the series decreases as time increases). Also, there are some points in time where the variances are smaller and larger (i.e., the variances are not constant over time). Visually, both sequence charts show that the monthly measles immunization data is non-stationary.

Augmented Dickey-Fuller (ADF) test was conducted to test the hypothesis statistically that the natural log-transformed series has a unit root or not. The series is non-stationary if there is a unit root and the series is stationary if there is no unit root. Results of the ADF test is summarized in

Differencing the natural log-transformed series can transform the series from non-stationary series to stationary. The graph below shows that the “first difference of the log-transformed series” is stationary (

The ADF test for the first difference of the natural log-transformed data confirms that a stationary series can be achieved after the first differencing.

The ACF and PACF of the first difference natural log-transformed series are shown below. The height of bars in the ACF represents the autocorrelation coefficients. The two parallel lines represent the confidence interval. All bars fall inside the confidence interval, indicating that the autocorrelations are statistically non-significant at 5% level. This means that an ARIMA with Moving Average component of order 0 can be tentatively considered, that is, MA (0) (

The height of bars in the PACF represents the partial autocorrelation coefficients. Though the partial autocorrelation coefficients fall within the confidence level, that is, the partial autocorrelation coefficients are statistically nonsignificant at 5%, some are larger than the others. The PACF suggests an ARIMA model with AR of order 0 can be considered. AR of orders 1, 4, 8, and 9 can also

Test equation | T-value | p-value | Remarks |
---|---|---|---|

Intercept Only | −2.4495 | 0.1330 | There is a unit root. |

Trend and Intercept | −4.7055 | 0.0018 | There is no unit root |

No Constant, No Intercept | −0.5265 | 0.4845 | There is a unit root. |

Test equation | T-value | p-value | Remarks |
---|---|---|---|

Intercept Only | −9.2437 | 0.0000 | There is no unit root. |

Trend and Intercept | −9.2414 | 0.0000 | There is no unit root |

No Constant, No Intercept | −9.2900 | 0.0000 | There is no unit root. |

Note: No unit root indicates a stationary series. To be stationary, the three test equations should show no unit root.

be considered. In short, ARIMA with AR (0), AR (1), AR (4), AR (8), and AR (9) can be considered.

Based on the results of the ACF and PACF, the following ARIMA Models can be considered:

ARIMA Model 1: ARIMA (0, 1, 0)

ARIMA Model 2: ARIMA (1, 1, 0)

ARIMA Model 3: ARIMA (4, 1, 0)

ARIMA Model 4: ARIMA (8, 1, 0)

ARIMA Model 5: ARIMA (9, 1, 0)

After the estimation of the parameters, the Root Mean Square Errors (RMSE) and Normalized BIC are summarized as shown in

Using the Normalized BIC as the basis for the selection of the best ARIMA Model, model #1, the ARIMA (0, 1, 0), emerged as the best model with the smallest Normalized BIC of 8.673. The estimates of the model parameters generated by the IBM SPSS Forecasting module are presented below. In equation form, the ARIMA (0, 1, 0) can be written as: DLog(Immunization) = −0.009 (

Shapiro-Wilk test was used to test if the “residuals” of the ARIMA (0, 1, 0) is normally distributed. Shapiro-Wilk statistic is statistically nonsignificant (SW = 0.973, df = 59, p = 0.219), indicating that the residuals have no departure from normality.

The Ljung-Box Q was used to test the absence of autocorrelations as a whole. The Ljung-Box Q is statistically nonsignificant (Ljung-Box Q = 13.778, p = 0.743), indicating the absence of autocorrelations. The bars of the PACF and ACF plots are within the 95% confidence limits, indicating the absence of autocorrelations (

Models | RMSE | Normalized BIC |
---|---|---|

1. ARIMA (0, 1, 0) | 73.857 | 8.673 |

2. ARIMA (1, 1, 0) | 72.569 | 8.707 |

3. ARIMA (4, 1, 0) | 72.240 | 8.909 |

4. ARIMA (8, 1, 0) | 71.272 | 8.938 |

5. ARIMA (9, 1, 0) | 68.517 | 9.145 |

ARIMA (0, 1, 0) was used to forecast the monthly measles immunization coverage for the next 36 months from January 2018 to December 2020.

equation.

In this study, the ARIMA model was developed to forecast monthly measles immunization for the next 36 months from January 2019 to December 2021. The monthly registered data for measles immunization coverage from January 2014 to December 2018 were used for the development of the model. The best model

Year | Lo 95 | Hi 95 |
---|---|---|

Jan 2019 | 174.02 | 461.98 |

Feb 2019 | 114.38 | 521.62 |

Mar 2019 | 68.61 | 567.39 |

Apr 2019 | 30.03 | 605.97 |

May 2019 | −3.96 | 639.96 |

Jun 2019 | −34.69 | 670.69 |

Jul 2019 | −62.94 | 698.94 |

Aug 2019 | −89.25 | 725.25 |

Sep 2019 | −113.95 | 749.95 |

Oct 2019 | −137.32 | 773.32 |

Nov 2019 | −159.54 | 795.54 |

Dec 2019 | −180.77 | 816.77 |

Jan 2020 | −201.14 | 837.14 |

Feb 2020 | −220.74 | 856.74 |

Mar 2020 | −239.64 | 875.64 |

Apr 2020 | −257.93 | 893.93 |

May 2020 | −275.66 | 911.66 |

Jun 2020 | −292.87 | 928.87 |

Jul 2020 | −309.61 | 945.61 |

Aug 2020 | −325.91 | 961.91 |

Sep 2020 | −341.81 | 977.81 |

Oct 2020 | −357.34 | 993.34 |

Nov 2020 | −372.52 | 1008.52 |

Dec 2020 | −387.37 | 1023.37 |

Jan 2021 | −401.92 | 1037.92 |

Feb 2021 | −416.17 | 1052.17 |

Mar 2021 | −430.16 | 1066.16 |

Apr 2021 | −443.89 | 1079.89 |

May 2021 | −457.37 | 1093.37 |

Jun 2021 | −470.63 | 1106.63 |

Jul 2021 | −483.66 | 1119.66 |

Aug 2021 | −496.49 | 1132.49 |

Sep 2021 | −509.12 | 1145.12 |

Oct 2021 | −521.56 | 1157.56 |

Nov 2021 | −533.82 | 1169.82 |

Dec 2021 | −545.90 | 1181.90 |

with the smallest Normalized BIC of 8.673 is ARIMA (0, 1, 0). The results obtained prove that this model can be used for forecasting future immunization coverage and will help decision-makers to establish strategies, priorities, and proper use of immunization resources in Cabanatuan City. As future work, the researcher will develop other models by using the neural network approach to compare it with the ARIMA model.

The authors declare no conflicts of interest regarding the publication of this paper.

Alegado, R.T. and Tumibay, G.M. (2019) Forecasting Measles Immunization Coverage Using ARIMA Model. Journal of Computer and Communications, 7, 157-168. https://doi.org/10.4236/jcc.2019.710015