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Seasonal Unit Root Test for LS

Method: Traditional HEGY

Null Hypothesis: Unit root at specified frequency Periodicity (Seasons): 4

Non-Seasonal Deterministics: None Seasonal Deterministics: None

Lag Selection: 0 (Automatic: AIC, maxlags=12) Sample Size: 48


	Significance Level
Test Stat.	1% 5%	10%
Frequency 0 -2.969746 n=40	-2.53 -1.88	-1.59
n=60	-2.57 -1.92	-1.60
n=48*	-2.55 -1.90	-1.59
Frequency 2PI/4 and 6PI/4 13.00475 n=40	30.65 7.98	3.66
n=60	30.93 7.99	3.73
n=48*	30.76 7.98	3.69
Frequency PI -5.427517 n=40	-2.53 -1.88	-1.59
n=60	-2.57 -1.92	-1.60
n=48*	-2.55 -1.90	-1.59
All seasonal frequencies 154.8884 n=40	21.15 5.75	2.91
n=60	21.27 5.75	2.98
n=48*	21.20 5.75	2.94
All frequencies 122.1865 n=40	16.59 4.88	2.83
n=60	16.65 4.87	2.92
n=48*	16.61 4.88	2.86

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*Note: Obtained using linear interpolation.

Seasonal Unit Root Test for NS

Method: Traditional HEGY

Null Hypothesis: Unit root at specified frequency Periodicity (Seasons): 4

Non-Seasonal Deterministics: None Seasonal Deterministics: None

Lag Selection: 5 (Automatic: AIC, maxlags=12) Sample Size: 43


	Significance Level
Test Stat.	1% 5%	10%
Frequency 0 -0.450300 n=40	-2.53 -1.88	-1.59
n=60	-2.57 -1.92	-1.60
n=43*	-2.54 -1.89	-1.59
Frequency 2PI/4 and 6PI/4 5.526042 n=40	30.65 7.98	3.66
n=60	30.93 7.99	3.73
n=43*	30.69 7.98	3.67
Frequency PI -3.392458 n=40	-2.53 -1.88	-1.59
n=60	-2.57 -1.92	-1.60
n=43*	-2.54 -1.89	-1.59
All seasonal frequencies 7.109448 n=40	21.15 5.75	2.91
n=60	21.27 5.75	2.98
n=43*	21.17 5.75	2.92
All frequencies 5.489919 n=40	16.59 4.88	2.83
n=60	16.65 4.87	2.92
n=43*	16.60 4.88	2.84

*Note: Obtained using linear interpolation.

Seasonal Unit Root Test for TG

Method: Traditional HEGY

Null Hypothesis: Unit root at specified frequency Periodicity (Seasons): 4

Non-Seasonal Deterministics: None Seasonal Deterministics: None

Lag Selection: 0 (Automatic: AIC, maxlags=12) Sample Size: 48


	Significance Level
Test Stat.	1% 5%	10%
Frequency 0 -1.733403 n=40	-2.53 -1.88	-1.59
n=60	-2.57 -1.92	-1.60
n=48*	-2.55 -1.90	-1.59
Frequency 2PI/4 and 6PI/4 14.91793 n=40	30.65 7.98	3.66
n=60	30.93 7.99	3.73
n=48*	30.76 7.98	3.69
Frequency PI -4.624888 n=40	-2.53 -1.88	-1.59
n=60	-2.57 -1.92	-1.60
n=48*	-2.55 -1.90	-1.59
All seasonal frequencies 93.01049 n=40	21.15 5.75	2.91
n=60	21.27 5.75	2.98
n=48*	21.20 5.75	2.94
All frequencies 102.7873 n=40	16.59 4.88	2.83
n=60	16.65 4.87	2.92
n=48*	16.61 4.88	2.86

*Note: Obtained using linear interpolation.

Seasonal Unit Root Test for TM

Method: Traditional HEGY

Null Hypothesis: Unit root at specified frequency Periodicity (Seasons): 4

Non-Seasonal Deterministics: None Seasonal Deterministics: None

Lag Selection: 11 (Automatic: AIC, maxlags=12) Sample Size: 37


	Significance Level
Test Stat.	1% 5%	10%
Frequency 0 -1.308644 n=20	-2.45 -1.85	-1.55
n=40	-2.53 -1.88	-1.59
n=37*	-2.52 -1.88	-1.58
Frequency 2PI/4 and 6PI/4 6.833039 n=20	24.78 7.20	3.38
n=40	30.65 7.98	3.66
n=37*	29.77 7.86	3.61
Frequency PI -1.020198 n=20	-2.45 -1.85	-1.55
n=40	-2.53 -1.88	-1.59
n=37*	-2.52 -1.88	-1.58
All seasonal frequencies 5.496060 n=20	17.41 5.23	2.74
n=40	21.15 5.75	2.91
n=37*	20.59 5.68	2.89
All frequencies 5.331548 n=20	13.77 4.56	2.73
n=40	16.59 4.88	2.83
n=37*	16.17 4.83	2.81

*Note: Obtained using linear interpolation.

Phụ lục A-2a - Xác định độ trễ của VAR

VAR Lag Order Selection Criteria Endogenous variables: NS TM LS TG GDP

Exogenous variables: C @EXPAND(@QUARTER,@DROPLAST) Date: 08/31/21 Time: 13:57

Sample: 2005Q1 2017Q4

Included observations: 48

Lag

LogL	LR	FPE	AIC	SC	HQ
0	-733.4833	NA	29730678	31.39514	32.17481	31.68978
1	-559.8075	282.2232	61906.24	25.20031	26.95456*	25.86325
2	-525.3009	48.88435	44445.66	24.80421	27.53304	25.83544
3	-503.4319	26.42507	58333.26	24.93466	28.63808	26.33419
4	-428.5312	74.90074*	9500.895*	22.85547*	27.53347	24.62329*

* indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error

AIC: Akaike information criterion SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

Phụ lục A-2b1 – Kiểm định độ vững của VAR với mức trễ 4

Roots of Characteristic Polynomial Endogenous variables: NS TM LS TG GDP

Exogenous variables: C

@EXPAND(@QUARTER,@DROPLA ST)

Lag specification: 1 4

Date: 08/31/21 Time: 14:01

Root

Modulus
-0.005939 - 1.025484i	1.025501
-0.005939 + 1.025484i	1.025501
1.022976	1.022976
-1.009673	1.009673
0.839927 + 0.274626i	0.883683
0.839927 - 0.274626i	0.883683
0.483632 + 0.633557i	0.797054
0.483632 - 0.633557i	0.797054
0.734106	0.734106
-0.500026 - 0.534201i	0.731708
-0.500026 + 0.534201i	0.731708

0.556575 + 0.347909i

0.656366
0.556575 - 0.347909i	0.656366
-0.304961 - 0.553731i	0.632155
-0.304961 + 0.553731i	0.632155
0.208541 + 0.462776i	0.507593
0.208541 - 0.462776i	0.507593
-0.266155 + 0.151564i	0.306284
-0.266155 - 0.151564i	0.306284
0.106206	0.106206

Warning: At least one root outside the unit circle. VAR does not satisfy the stability condition.

Phụ lục A-2b2 – Kiểm định độ vững của VAR với mức trễ 3

Roots of Characteristic Polynomial Endogenous variables: NS TM LS TG GDP

Exogenous variables: C

@EXPAND(@QUARTER,@DROPLA ST)

Lag specification: 1 3

Date: 08/31/21 Time: 14:04


Root	Modulus
0.998454	0.998454
0.738556 - 0.369776i	0.825954
0.738556 + 0.369776i	0.825954
0.048989 - 0.793479i	0.794990
0.048989 + 0.793479i	0.794990
0.350752 - 0.633071i	0.723744
0.350752 + 0.633071i	0.723744
0.639825	0.639825
0.479548 - 0.419686i	0.637262
0.479548 + 0.419686i	0.637262
-0.597146	0.597146
-0.210694 - 0.511680i	0.553361
-0.210694 + 0.511680i	0.553361
-0.464501 - 0.193854i	0.503330
-0.464501 + 0.193854i	0.503330
No root lies outside the unit circle.
VAR satisfies the stability condition.

Phụ lục A-2c – Kết quả ước lượng mô hình tổng thể VAR (với trễ 3)

Vector Autoregression Estimates Date: 08/31/21 Time: 14:04 Sample (adjusted): 2005Q4 2017Q4

Included observations: 49 after adjustments

Standard errors in ( ) &

t-statistics in [ ]
	NS	TM	LS	TG	GDP
NS(-1)	-0.433080	0.048604	0.050800	0.046286	9.539932
	(0.19446)	(0.04921)	(0.11737)	(0.13474)	(3.52052)
	[-2.22705]	[ 0.98779]	[ 0.43281]	[ 0.34352]	[ 2.70981]
NS(-2)	-0.068276	-0.036474	0.086540	-0.093193	4.030488
	(0.19776)	(0.05004)	(0.11936)	(0.13702)	(3.58013)
	[-0.34525]	[-0.72891]	[ 0.72504]	[-0.68013]	[ 1.12579]
NS(-3)	0.013765	0.010332	0.104037	-0.062563	2.195009
	(0.19230)	(0.04866)	(0.11607)	(0.13324)	(3.48134)
	[ 0.07158]	[ 0.21235]	[ 0.89637]	[-0.46955]	[ 0.63051]
TM(-1)	-1.205157	0.699355	0.660682	0.053657	14.35595
	(0.68823)	(0.17414)	(0.41539)	(0.47686)	(12.4595)
	[-1.75110]	[ 4.01597]	[ 1.59050]	[ 0.11252]	[ 1.15220]
TM(-2)	-0.165859	-0.161559	0.000211	-0.376472	6.023171
	(0.81202)	(0.20547)	(0.49011)	(0.56263)	(14.7006)
	[-0.20425]	[-0.78630]	[ 0.00043]	[-0.66913]	[ 0.40972]
TM(-3)	-0.504020	-0.210158	0.753422	0.141696	16.95376
	(0.77205)	(0.19535)	(0.46598)	(0.53494)	(13.9770)
	[-0.65283]	[-1.07579]	[ 1.61684]	[ 0.26488]	[ 1.21298]
LS(-1)	3.53E-05	-0.007515	1.145907	-0.331224	-11.24692
	(0.30288)	(0.07664)	(0.18281)	(0.20986)	(5.48325)
	[ 0.00012]	[-0.09805]	[ 6.26839]	[-1.57832]	[-2.05114]
LS(-2)	-0.691108	0.160055	-0.608328	0.344352	11.11110
	(0.45852)	(0.11602)	(0.27675)	(0.31770)	(8.30092)
	[-1.50726]	[ 1.37955]	[-2.19814]	[ 1.08390]	[ 1.33854]
LS(-3)	0.577992	-0.129760	0.237150	-0.187151	1.462594
	(0.32384)	(0.08194)	(0.19546)	(0.22438)	(5.86264)
	[ 1.78483]	[-1.58359]	[ 1.21332]	[-0.83408]	[ 0.24948]
TG(-1)	-0.440495	0.142325	0.103990	1.273989	2.212760
	(0.30894)	(0.07817)	(0.18647)	(0.21406)	(5.59296)
	[-1.42583]	[ 1.82069]	[ 0.55769]	[ 5.95162]	[ 0.39563]
TG(-2)	0.049023	-0.068989	0.096733	-0.443043	-1.187871
	(0.50164)	(0.12693)	(0.30277)	(0.34758)	(9.08157)

[ 0.09773]	[-0.54352]	[ 0.31949]	[-1.27466]	[-0.13080]
TG(-3)	0.079436	-0.086794	0.071805	0.032307	9.665360
	(0.33145)	(0.08387)	(0.20005)	(0.22965)	(6.00046)
	[ 0.23966]	[-1.03490]	[ 0.35893]	[ 0.14068]	[ 1.61077]
GDP(-1)	-0.015480	0.003191	-0.008774	0.012193	0.240262
	(0.01325)	(0.00335)	(0.00800)	(0.00918)	(0.23984)
	[-1.16850]	[ 0.95186]	[-1.09729]	[ 1.32831]	[ 1.00176]
GDP(-2)	0.011627	-0.000490	-0.007572	-0.003057	-0.067319
	(0.01148)	(0.00290)	(0.00693)	(0.00795)	(0.20777)
	[ 1.01312]	[-0.16860]	[-1.09317]	[-0.38448]	[-0.32401]
GDP(-3)	0.023532	0.001376	-0.007156	0.002960	-0.050112
	(0.01029)	(0.00260)	(0.00621)	(0.00713)	(0.18622)
	[ 2.28773]	[ 0.52865]	[-1.15256]	[ 0.41526]	[-0.26910]
C	23.34852	-1.190441	-15.67225	8.662233	-455.5278
	(10.8899)	(2.75547)	(6.57275)	(7.54535)	(197.147)
	[ 2.14406]	[-0.43203]	[-2.38443]	[ 1.14802]	[-2.31060]
@QUARTER=1	-1.806359	-0.872963	2.385525	-1.285540	-294.3785
	(2.22915)	(0.56404)	(1.34544)	(1.54453)	(40.3560)
	[-0.81034]	[-1.54769]	[ 1.77305]	[-0.83232]	[-7.29455]
@QUARTER=2	-7.628665	0.182270	0.756040	0.336772	-87.46177
	(3.07067)	(0.77698)	(1.85335)	(2.12760)	(55.5907)
	[-2.48436]	[ 0.23459]	[ 0.40793]	[ 0.15829]	[-1.57332]
@QUARTER=3	-6.497779	-0.090615	0.744281	-1.550075	-113.9739
	(3.65381)	(0.92453)	(2.20532)	(2.53165)	(66.1478)
	[-1.77836]	[-0.09801]	[ 0.33749]	[-0.61228]	[-1.72302]
R-squared	0.649615	0.735421	0.899116	0.987895	0.961559
Adj. R-squared	0.439385	0.576673	0.838585	0.980631	0.938494
Sum sq. Resids	176.1498	11.27794	64.17000	84.56627	57732.45
S.E. equation	2.423151	0.613132	1.462532	1.678951	43.86816
F-statistic	3.090012	4.632642	14.85393	136.0130	41.68932
Log likelihood	-100.8761	-33.53818	-76.13602	-82.89801	-242.7860
Akaike AIC	4.892902	2.144415	3.883103	4.159102	10.68514
Schwarz SC	5.626465	2.877978	4.616666	4.892665	11.41870
Mean dependent	-1.708539	-0.609990	0.053195	107.4782	570.0210
S.D. dependent	3.236294	0.942359	3.640272	12.06392	176.8844
Determinant resid covariance (dof adj.)		10110.04
Determinant resid covariance		869.7186
Log likelihood		-513.4601
Akaike information criterion		24.83511
Schwarz criterion		28.50292
Number of coefficients		95

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