Predicting the unemployment rate using autoregressive integrated moving average

Figures & data

Figure 1. Box-Jenkins methodology.

Table 1. Interpretation of MAPE value.

MAPE	Conclusion
$\le$10	Highly accurate
11–20	Good
21–50	Reasonable
>51	Inaccurate

Table 2. Descriptive statistics.

Statistics	Unemployment
Mean	6.475152
Median	6.170000
Maximum	11.24000
Minimum	2.550000
Std. Dev.	2.244085
Skewness	0.142788
Kurtosis	2.527790
Jarque-Bera	0.418738
Probability	0.811096
Sum	213.6800
Sum Sq. Dev.	161.1494
Observations	33*

Note. *The National Labor Force Survey was not conducted in 1995. Therefore, I employed predictions of missing values/imputation of open unemployment data.

Table 3. Stationarity test.

Variable	Degree of integration	Method	p-Value	Conclusion
Unemployment	I(0)	ADF	0.8125	Series is not stationary
Dlog(Unemployment)*	I(1)	ADF	0.0005	Series is stationary

Notes: ADF→Augmented Dickey-Fuller. *Dlog(unemployment) implies the logarithm of open unemployment at the first difference.

Table 4. ACF and PACF results.

Lag	AC	PAC	Q-Stat
1	0.060	0.060	0.1246
2	−0.130	−0.134	0.7376
3	0.073	0.092	0.9382
4	0.251	0.228	3.3838
5	−0.091	−0.111	3.7210
6	0.112	0.196	4.2489
7	0.130	0.052	4.9873
8	−0.019	−0.051	5.0029
9	−0.068	−0.002	5.2195
10	0.077	−0.023	5.5097
11	0.003	−0.030	5.5100
12	−0.105	−0.086	6.1069
13	−0.207	−0.248	8.5518
14	−0.002	−0.012	8.5520
15	−0.073	−0.111	8.8941
16	−0.049	0.007	9.0591

Table 5. Normality assumptions and white noise assumptions.

Models	Jarque-Berra	Prob	Conclusion	Conclusion
AR(1)	2.102806	0.349447	Normal distribution	Has white noise and is appropriate
AR(2)	2.215394	0.330319	Normal distribution	Has white noise and is appropriate
AR(4)	4.040821	0.132601	Normal distribution	Has white noise and is appropriate
ARMA(1,1)	1.969232	0.373583	Normal distribution	Has white noise and is appropriate
ARMA(1,2)	2.211022	0.331042	Normal distribution	Has white noise and is appropriate
ARMA(2,2)	0.501722	0.778130	Normal distribution	Has white noise and is appropriate

Note: Previous works (Ntim et al., 2011, 2015) consider the squared loss and assume the noise follows an i.i.d. (independently and identically distributed) random sequence.

Table 6. ARIMA models summary.

P	AR(1)				AR(2)				AR(4)				ARMA(1,1)				ARMA(1,2)				ARMA(2,2)
	$\beta$	σ	t	p	$\beta$	σ	t	p	$\beta$	σ	t	p	$\beta$	σ	t	p	$\beta$	σ	t	p	$\beta$	σ	t	p
a1	0.088	0.183	0.479	0.635	0.094	0.189	0.500	0.621	0.059	0.167	0.351	0.729	−0.303	1.360	−0.223	0.825	−0.005	2.871	−0.002	0.999	0.408	1.072	0.381	0.706
a2	–	–	–	–	−0.106	0.189	−0.557	0.582	−0.110	0.167	−0.659	0.516	–	–	–	–					0.262	0.812	0.323	0.749
a4	–	–	–	–	–	–	–	–	0.277	0.177	1.562	0.131	–	–	–	–	−0.095	0.204	−0.468	0.644	–	–	–	–
b1	–	–	–	–	–	–	–	–	–	–	–	–	0.414	1.296	0.320	0.752	0.106	2.862	0.037	0.971	1.031	−0.476	0.638	1.031
b2	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	−0.068	0.357	−0.192	0.849	0.936	−0.457	0.651	0.936
R^2	−0.017				−0.005				0.111				−0.011				−0.008				0.191
SSR	0.845				0.833				0.575				0.839				0.837				0.671
AIC	−0.701				−0.612				−0.834				−0.642				−0.581				−0.696
SBC	−0.654				−0.519				−0.692				−0.550				−0.442				−0.509

Notes: P is the parameters, β is the coefficient, σ is the standard error, t is the t-statistic, and p is the probability.

Figure 2. Fitting results of static method.

Figure 3. Fitting results for dynamic method.

Table 7. The predicted value for unemployment data.

Year	95 % Confidence Limit		Predicted
	Lower Predicted	Upper Predicted
2023	4.96	6.76	5.86
2024	4.96	7.92	6.44
2025	4.63	8.02	6.32
2026	4.25	7.90	6.08
2027	3.93	8.23	6.08
2028	3.72	8.81	6.26
2029	3.47	9.02	6.24
2030	3.22	9.09	6.15
2031	2.98	9.32	6.15
2032	2.78	9.65	6.21
2033	2.58	9.84	6.21
2034	2.38	9.98	6.18
2035	2.19	10.16	6.18
2036	2.02	10.38	6.20
2037	1.85	10.55	6.20
2038	1.68	10.69	6.19
2039	1.52	10.85	6.19
2040	1.37	11.02	6.19
2041	1.22	11.17	6.19
2042	1.07	11.31	6.19
2043	0.93	11.45	6.19
2044	0.79	11.59	6.19
2045	0.66	11.72	6.19
2046	0.53	11.85	6.19
2047	0.40	11.98	6.19
2048	0.27	12.11	6.19
2049	0.15	12.23	6.19
2050	0.03	12.35	6.19

Table 8. The sixteen economic policy packages.

Stages	Period	Policy packages
1st	September 9, 2015	Increase the competitiveness of national industries
2nd	September 29, 2015	Equalize licensing requirements and simplify the export procedure
3rd	October 7, 2015	Facilitate financial services, export funding, and eliminate business obstacles
4th	October 15, 2015	Social security and improvement of community welfare
5th	October 22, 2015	Improving the industrial climate and investment through tax incentives and deregulation of Syariah banking
6th	November 16, 2015	Stimulate economic activity in the outer regions and facilitate the availability of strategic commodity
7th	December 7, 2015	Stimulate business activities for the labor-intensive industry on a national scale through incentives for in-kind land certification processes for individual
8th	December 21, 2015	Settle land acquisition, intensifying local oil production and stimulating the domestic aircraft industry
9th	January 27, 2016	Speed up electricity, meat price stabilization and improve the logistics sector for rural-urban
10th	February 11, 2016	Revise the investment negative list and improve protection for Micro, Small and Medium Enterprises
11th	March 29, 2016	Stimulate the national economy through the facilitation of Micro, Small and Medium Enterprises and industry
12th	April 28, 2016	Improve Indonesia’s ranking in Ease of Doing Business (EoDB)
13th	August 24, 2016	Low-cost housing for the low-income community
14th	November 10, 2016	Roadmap for E-commerce
15th	June 15, 2017	Logistics Improvements
16th	November 16, 2018	Encourage policies for increased investment

Source: Indonesian Ministry of National Development Planning (2019).

Table 9. The impact of GDP on labor forces based on age groups (1990–2022).

Age groups	$\beta$	σ	t	p
15–19	1.938380	0.233910	8.286852	0.0000***
20–24	5.157669	0.654277	7.883002	0.0000***
25–29	5.659024	0.715943	7.904291	0.0000***
30–34	5.602805	0.716863	7.815724	0.0000***
35–39	5.641184	0.719941	7.835622	0.0000***
40–44	5.454412	0.718343	7.593050	0.0000***
45–49	5.137024	0.679685	7.557951	0.0000***
50–54	4.353323	0.579466	7.512645	0.0000***
55–59	3.403861	0.458736	7.420094	0.0000***
60+	4.919405	0.639556	7.691907	0.0000***

Notes: ***Significant at 1% of alpha level, β is the coefficient, σ is the standard deviation, t is the t-statistic, and p is the probability.

Table 10. The impact of COVID-19 periods on unemployment.

Variable	$\beta$	σ	t	p
Growth	−0.013235	0.044649	−0.296416	0.7692
Unemployment(-1)	1.007320	0.039691	25.37908	0.0000***
DUM2020	1.774381	1.002518	1.769924	0.0880*
DUM2021	−0.582743	0.980181	−0.594526	0.5571
DUM2022	−0.607249	0.977299	−0.621354	0.5396

Notes: *significant at 10% of alpha level. ***Significant at 1% of alpha level, β is the coefficient, σ is the standard deviation, t is the t-statistic, and p is the probability.

Ntim, C. G., Opong, K. K., Danbolt, J., & Dewotor, F. S. (2011). Testing the weak-form efficiency in African stock markets. Managerial Finance, 37(3), 195–218. https://doi.org/10.1108/03074351111113289

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Data availability statement

Data is available upon reasonable request.