Forecasting the Remittances of the Overseas Filipino Workers in the Philippines

Merry Christ E. Manayaga; Roel F. Ceballos

arxiv: 1906.10422 · v1 · pith:EYTAY3JEnew · submitted 2019-06-25 · 📊 stat.AP · econ.EM

Forecasting the Remittances of the Overseas Filipino Workers in the Philippines

Merry Christ E. Manayaga , Roel F. Ceballos This is my paper

Pith reviewed 2026-05-25 16:10 UTC · model grok-4.3

classification 📊 stat.AP econ.EM

keywords SARIMAtime series forecastingremittancesOFWPhilippinesBox-Jenkinsseasonal modelstationarity

0 comments

The pith

SARIMA (2,1,0)x(0,0,2)_12 is an appropriate model for monthly overseas Filipino worker remittances in the Philippines.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper applies the Box-Jenkins approach to identify a time series model for monthly remittances sent by overseas Filipino workers. The authors use 108 observations from official central bank data, split into 96 for fitting and 12 for evaluation, confirm stationarity via ACF, PACF, and the Augmented Dickey-Fuller test, detect seasonality, and select the final SARIMA specification. They verify the model through residual plots, the Ljung-Box test showing no remaining correlation, and the Shapiro-Wilk test indicating Gaussian white noise errors. A reader would care because remittances form a large share of Philippine foreign exchange inflows, so forecasts from a validated model could inform economic planning if the structure persists.

Core claim

The study establishes that the SARIMA (2,1,0)x(0,0,2)_12 model is appropriate for the monthly OFW remittance series, as the data exhibit stationarity after first differencing and a seasonal component at lag 12, the residuals show no significant spikes in ACF or PACF and pass the Ljung-Box test, the forecast errors are consistent with Gaussian white noise by the Shapiro-Wilk test, and the model produces usable forecasts for 2018 and 2019.

What carries the argument

The SARIMA (2,1,0)x(0,0,2)_12 model, which combines non-seasonal autoregressive terms of order 2 with first differencing and seasonal moving-average terms of order 2 at period 12 to capture both trend and annual seasonal dependence in the remittance series.

Load-bearing premise

The 108 monthly observations are sufficient and representative, and the stationarity confirmed by the ADF test on the training sample generalizes to the process that will generate future remittances.

What would settle it

If the actual 2018-2019 remittance values produce forecast errors that fail the Ljung-Box test for uncorrelated residuals or the Shapiro-Wilk test for normality, the claim that SARIMA (2,1,0)x(0,0,2)_12 is appropriate would be falsified.

Figures

Figures reproduced from arXiv: 1906.10422 by Merry Christ E. Manayaga, Roel F. Ceballos.

**Figure 3.** Figure 3: Plot of the Transformed series [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Plot of the Differenced and Transformed Series [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: shows that the ACF of the differenced series have improved since it shows a damped sinusoidal pattern. The slowly decaying pattern is no longer present [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: Residual Plots for Final Model [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: shows the ACF and PACF plot of residuals. Although there are few lags that touch the limit, all of the lags are within the acceptable limit. This means that the residuals are uncorrelated [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: ACF and PACF Plots of Forecast errors spikes in the both the ACF and PACF plots. Therefore, the forecast errors behave like a white noise process. Furthermore, the mean absolute percentage error was found to be 4.1% which implies that the one-step ahead forecast is accurate [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

read the original abstract

This study aims to find a Box-Jenkins time series model for the monthly OFW's remittance in the Philippines. Forecasts of OFW's remittance for the years 2018 and 2019 will be generated using the appropriate time series model. The data were retrieved from the official website of Bangko Sentral ng Pilipinas. There are 108 observations, 96 of which were used in model building and the remaining 12 observations were used in forecast evaluation. ACF and PACF were used to examine the stationarity of the series. Augmented Dickey Fuller test was used to confirm the stationarity of the series. The data was found to have a seasonal component, thus, seasonality has been considered in the final model which is SARIMA (2,1,0)x(0,0,2)_12. There are no significant spikes in the ACF and PACF of residuals of the final model and the L-jung Box Q* test confirms further that the residuals of the model are uncorrelated. Also, based on the result of the Shapiro-Wilk test for the forecast errors, the forecast errors can be considered a Gaussian white noise. Considering the results of diagnostic checking and forecast evaluation, SARIMA (2,1,0)x(0,0,2)_12 is an appropriate model for the series. All necessary computations were done using the R statistical software.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Routine SARIMA fit on Philippine remittances that follows textbook steps but rests on a thin sample and reports no actual test numbers.

read the letter

The paper fits SARIMA(2,1,0)x(0,0,2)_12 to monthly OFW remittance data and concludes the model is appropriate after standard diagnostics and a 12-month hold-out check. That is the whole contribution in one sentence. It splits 108 observations into 96 for fitting and 12 for evaluation, runs ACF/PACF and ADF on the training window, then checks residuals with Ljung-Box and Shapiro-Wilk. The hold-out step keeps the fitting from being fully circular, which is the one thing done correctly. Everything else is standard Box-Jenkins practice applied to one narrow series. The method, the model class, and the diagnostic sequence have been documented for decades, so nothing here is new. The data come from the central bank website and the computations are done in R, which is fine but adds no technical advance. The soft spot is exactly the one the stress-test note flags. Ninety-six monthly points give only eight full seasonal cycles, which is marginal for pinning down seasonal orders. If the series has any break or if the seasonal integration order is off, the claim that the model is appropriate does not hold. The abstract lists the tests but supplies none of the actual statistics or forecast error numbers, so a reader cannot verify whether the residuals really are white noise or how large the forecast errors are. This work is for a Philippine policy office that needs a quick remittance projection and is willing to accept the model on the authors' word. A reader looking for methodological insight or robust evidence will get nothing. I would not send it to referees. The sample is too small and the result too routine to justify the time.

Referee Report

4 major / 2 minor

Summary. The manuscript applies the Box-Jenkins methodology to monthly OFW remittance data (108 observations total). It identifies SARIMA(2,1,0)x(0,0,2)_12 on the first 96 observations after ACF/PACF inspection and ADF confirmation of stationarity, validates residuals via Ljung-Box and ACF/PACF plots, and evaluates the 12-month hold-out forecasts with the Shapiro-Wilk test on errors, concluding that the model is appropriate.

Significance. If the unreported diagnostics are in fact supportive, the work supplies a straightforward, seasonally adjusted forecasting model for an economically important series. The explicit use of a 12-observation hold-out set for forecast evaluation is a methodological strength that reduces circularity risk.

major comments (4)

[Abstract and Results] Abstract and Results section: the claim that the ADF test 'confirms the stationarity of the series' is load-bearing for the choice of d=1, yet no test statistic, p-value, or lag specification is supplied, so the justification for first differencing cannot be verified.
[Abstract and Results] Abstract and Results section: the statements that 'there are no significant spikes in the ACF and PACF of residuals' and that the Ljung-Box Q* test 'confirms' uncorrelated residuals are central to the appropriateness conclusion, but no numerical Q* value, p-value, or lag count is reported.
[Abstract and Results] Abstract and Results section: the Shapiro-Wilk test is said to show that forecast errors are Gaussian white noise, yet neither the test statistic nor its p-value is given; likewise, no forecast accuracy metrics (RMSE, MAPE, or similar) are supplied for the 12-observation hold-out, preventing assessment of predictive performance.
[Model identification] Model identification: with only 96 observations (eight seasonal cycles), the selection of the seasonal MA order (0,0,2)_12 rests on limited data; the manuscript should quantify the uncertainty of this identification (e.g., via information criteria or sensitivity checks) because a modest change in D or Q would alter the central claim.

minor comments (2)

[Abstract] Abstract: 'L-jung Box' should read 'Ljung-Box'.
[Abstract] Abstract: the final sentence repeats the conclusion already stated; a single concise statement would improve clarity.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the careful review and constructive suggestions. We address each major comment below and will revise the manuscript to incorporate the requested diagnostic details and robustness checks.

read point-by-point responses

Referee: [Abstract and Results] Abstract and Results section: the claim that the ADF test 'confirms the stationarity of the series' is load-bearing for the choice of d=1, yet no test statistic, p-value, or lag specification is supplied, so the justification for first differencing cannot be verified.

Authors: We agree that the specific ADF results should have been reported. The revised manuscript will include the ADF test statistic, p-value, and lag order used after first differencing to confirm stationarity. revision: yes
Referee: [Abstract and Results] Abstract and Results section: the statements that 'there are no significant spikes in the ACF and PACF of residuals' and that the Ljung-Box Q* test 'confirms' uncorrelated residuals are central to the appropriateness conclusion, but no numerical Q* value, p-value, or lag count is reported.

Authors: We will add the Ljung-Box Q* statistic, its p-value, and the lag count to the revised Results section to fully document the residual diagnostics. revision: yes
Referee: [Abstract and Results] Abstract and Results section: the Shapiro-Wilk test is said to show that forecast errors are Gaussian white noise, yet neither the test statistic nor its p-value is given; likewise, no forecast accuracy metrics (RMSE, MAPE, or similar) are supplied for the 12-observation hold-out, preventing assessment of predictive performance.

Authors: We acknowledge these omissions. The revision will report the Shapiro-Wilk statistic and p-value together with RMSE and MAPE (and any other relevant accuracy measures) for the 12-month hold-out forecasts. revision: yes
Referee: [Model identification] Model identification: with only 96 observations (eight seasonal cycles), the selection of the seasonal MA order (0,0,2)_12 rests on limited data; the manuscript should quantify the uncertainty of this identification (e.g., via information criteria or sensitivity checks) because a modest change in D or Q would alter the central claim.

Authors: We agree that quantifying selection uncertainty strengthens the analysis. The revised manuscript will include AIC/BIC comparisons across plausible seasonal orders (including alternatives to Q=2) to support the chosen specification. revision: yes

Circularity Check

0 steps flagged

No circularity: standard Box-Jenkins identification and hold-out evaluation

full rationale

The paper applies conventional SARIMA order selection via ACF/PACF and ADF on the 96-observation training window, followed by residual diagnostics (ACF/PACF, Ljung-Box) and forecast evaluation on an independent 12-observation hold-out. No self-definitional reductions, no fitted inputs relabeled as predictions, and no load-bearing self-citations appear. The appropriateness claim is supported by separate diagnostic and out-of-sample checks rather than tautological construction from the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the remittance series is generated by a linear SARIMA process whose parameters can be identified from 96 observations; no new entities are postulated.

free parameters (1)

SARIMA orders (p,d,q)x(P,D,Q)_s
The specific orders (2,1,0)x(0,0,2)12 were selected from ACF/PACF plots and tests performed on the training sample.

axioms (1)

domain assumption After first regular differencing the series is stationary and can be represented by a linear combination of past values and white-noise errors.
This is the core modeling assumption of the Box-Jenkins SARIMA framework invoked throughout the abstract.

pith-pipeline@v0.9.0 · 5785 in / 1276 out tokens · 40850 ms · 2026-05-25T16:10:06.865749+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages

[1]

It is either sent through formal and informal channels

INTRODUCTION Remittance is the money sent by migrant workers to their home countries. It is either sent through formal and informal channels. In some countries, remittance s make up a decent p ortion of their GDP (Mohapatra and Ratha, 2010). Remittances play a huge role in the economy of developing countries like the Philippines for it can help alleviate ...

work page 2010
[2]

It starts with Model Identification then followed by Model Estimation and Diagnostic Checking

METHODS Montgomery, Jennings and Kulahci (2008), proposed the three iterative steps for Box -Jenkins forecasting method. It starts with Model Identification then followed by Model Estimation and Diagnostic Checking. An additional step called Model Evaluation is also suggested by several authors in order t o assess the validity of the model. Thus, putting ...

work page 2008
[3]

There were 96 data points from the year 2009 to 2016

RESULTS Figure 1 shows the time series plot of monthly remittance from sea -based and land-based OFW. There were 96 data points from the year 2009 to 2016. The highest point recorded was the latest remittance which is in December 2016. The remittance in January 2009 was the lowest in the given data. An upward trend is obviously present when observing the ...

work page 2009
[4]

From the first plot (Residual vs. Time), it is evident that there is no correlation among the residuals since the residuals International Journal of Statistics and Economics 41 are randomly positioned about the area of the plot. Also, there are no obvious patterns or systematic trends in the second plot (Residual vs. Fitted). The residual does not drift f...

work page 2017
[5]

 Remittances of OFW in the Philippines exhibits trend and seasonal components

CONCLUSION AND RECOMMENDATION The following conclusions and recommendations are made as a result of the study.  Remittances of OFW in the Philippines exhibits trend and seasonal components. The peak occurs on the month of December of every year.  Furthermore, the forecast errors should be normally distributed so that it can be considered Gaussian white ...

work page
[6]

REFERENCES Box, G. J. (2008). Time series analysis: forecasting and control. Hoboken: John Wiley & Sons, Inc. de Vera, B. O. (2018, October 08). Growth in OFW remittances in 2016 seen slowest in 10 years. Philippine Daily Inquirer. Dickey, D. F. (1979 ). Distribution of the estimators for autoregressive tiem series with a unit root. Journal of the America...

work page 2008

[1] [1]

It is either sent through formal and informal channels

INTRODUCTION Remittance is the money sent by migrant workers to their home countries. It is either sent through formal and informal channels. In some countries, remittance s make up a decent p ortion of their GDP (Mohapatra and Ratha, 2010). Remittances play a huge role in the economy of developing countries like the Philippines for it can help alleviate ...

work page 2010

[2] [2]

It starts with Model Identification then followed by Model Estimation and Diagnostic Checking

METHODS Montgomery, Jennings and Kulahci (2008), proposed the three iterative steps for Box -Jenkins forecasting method. It starts with Model Identification then followed by Model Estimation and Diagnostic Checking. An additional step called Model Evaluation is also suggested by several authors in order t o assess the validity of the model. Thus, putting ...

work page 2008

[3] [3]

There were 96 data points from the year 2009 to 2016

RESULTS Figure 1 shows the time series plot of monthly remittance from sea -based and land-based OFW. There were 96 data points from the year 2009 to 2016. The highest point recorded was the latest remittance which is in December 2016. The remittance in January 2009 was the lowest in the given data. An upward trend is obviously present when observing the ...

work page 2009

[4] [4]

From the first plot (Residual vs. Time), it is evident that there is no correlation among the residuals since the residuals International Journal of Statistics and Economics 41 are randomly positioned about the area of the plot. Also, there are no obvious patterns or systematic trends in the second plot (Residual vs. Fitted). The residual does not drift f...

work page 2017

[5] [5]

 Remittances of OFW in the Philippines exhibits trend and seasonal components

CONCLUSION AND RECOMMENDATION The following conclusions and recommendations are made as a result of the study.  Remittances of OFW in the Philippines exhibits trend and seasonal components. The peak occurs on the month of December of every year.  Furthermore, the forecast errors should be normally distributed so that it can be considered Gaussian white ...

work page

[6] [6]

REFERENCES Box, G. J. (2008). Time series analysis: forecasting and control. Hoboken: John Wiley & Sons, Inc. de Vera, B. O. (2018, October 08). Growth in OFW remittances in 2016 seen slowest in 10 years. Philippine Daily Inquirer. Dickey, D. F. (1979 ). Distribution of the estimators for autoregressive tiem series with a unit root. Journal of the America...

work page 2008