june 26th – 29th 2007 tartu, estonia ana Čuvak and dr. Žilvinas kalinauskas, vilnius gediminas...

June 26th – 29th 2007 Tartu, Estonia

Ana Čuvak and dr. Žilvinas Kalinauskas, Vilnius Gediminas Technical University, Lithuania

Application of Multiple Application of Multiple Regression Models for Lithuanian Regression Models for Lithuanian

inflationinflation


Ana Čuvak and dr. Žilvinas Kalinauskas, Vilnius Gediminas Technical University, Lithuania 2

.

Inflation is one of the crucial modern macroeconomic problems. As a statistical concept, inflation is based on measuring net changes in prices using harmonized consumer price index (HCPI). HCPI is the main indicator of inflation. The Department of Statistics to the Government of the Republic of Lithuania declare 12, 38 and 93 common groups of goods and services of HCPI. In this task we use 12 common groups.V(1) – Food products and non-alcoholic beverages;V(2) – Alcoholic drinks and tobacco products;V(3) – Clothing and footwear;V(4) – Housing, water, electricity, gas and other fuels;V(5) – Furnishings, household equipment and routine maintenance;V(6) – Health care;V(7) – Transport;V(8) – Communications;V(9) – Recreation and culture;V(10) – Education; V(11) – Hotels, cafes and restaurants;V(12) – Miscellaneous goods and services.



The Multivariate time series model was proposed for Lithuanian inflation modelling.

Thus we define a VECM model given as:

where:

.T,.......,2,1t

,eqintco nn

The model

)()()()(12

1 1,

1

iiciViV tjti

m

jjin

k

nnt

12,1i ,



The Dataset(1)

84

88

92

96

100

104

108

112

96 97 98 99 00 01 02 03 04 05 06

V1

72

76

80

84

88

92

96

100

104

108

96 97 98 99 00 01 02 03 04 05 06

V2

92

96

100

104

108

112

116

120

96 97 98 99 00 01 02 03 04 05 06

V3

40

50

60

70

80

90

100

110

120

96 97 98 99 00 01 02 03 04 05 06

V4



The Dataset(2)

96

100

104

108

112

116

120

96 97 98 99 00 01 02 03 04 05 06

V5

70

80

90

100

110

96 97 98 99 00 01 02 03 04 05 06

V6

50

60

70

80

90

100

110

96 97 98 99 00 01 02 03 04 05 06

V7

20

40

60

80

100

120

140

96 97 98 99 00 01 02 03 04 05 06

V8



The Dataset(3)

92

96

100

104

108

112

96 97 98 99 00 01 02 03 04 05 06

V9

76

80

84

88

92

96

100

104

108

96 97 98 99 00 01 02 03 04 05 06

V12

72

76

80

84

88

92

96

100

104

108

96 97 98 99 00 01 02 03 04 05 06

V11

60

70

80

90

100

110

96 97 98 99 00 01 02 03 04 05 06

V10



Augmented Dickey-Fuller and Phillips-Perron test statistics

V(1) V(2) V(3) V(4) V(5) V(6) V(7) V(8) V(9) V(10) V(11) V(12) Augmented Dickey-Fuller test statistic

- 7.091

-8.000

-2.909

-8.885

-1.738

-2.942

-9.092

-11.022

-8.731

-8.853

-4.584

-10.042

1% level

-2.585

5% level

-1.944

Test critical values:

10% level

-1.615

Phillips-Perron test statistic

-6.993

-8.021

-5.522

-9.371

-7.395

-5.291

-9.037

-11.021

-8.717

-9.463

-8.274

-10.017

1% level

-2.585

5% level

-1.944

Test critical values:

10% level

-1.615



First we undertake a VAR lag Order selection process. We adopt the AIC criteria and use 8 lags.

The VAR model

VAR Lag Order Selection Criteria Endogenous variables: V1 V10 V11 V12 V2 V3 V4 V5 V6 V7 V8 V9 Exogenous variables: C Sample: 1996M01 2006M12 Included observations: 124

Lag LogL LR FPE AIC SC HQ 0 -3556.924 NA 1.62e+10 57.56330 57.83623 57.67417

1 -1697.327 3329.280 0.015719 29.89236 33.44046* 31.33368* 2 -1530.321 266.6696 0.011493 29.52131 36.34457 32.29308 3 -1386.344 202.0327 0.013458 29.52168 39.62011 33.62390 4 -1232.865 185.6602 0.015923 29.36879 42.74238 34.80146 5 -1064.509 171.0714 0.019094 28.97595 45.62471 35.73907 6 -867.1526 162.3415 0.021245 28.11536 48.03929 36.20893 7 -583.0586 178.7043* 0.011053 25.85578 49.05487 35.27980 8 -213.9339 160.7478 0.004626* 22.22474* 48.69900 32.97921 * 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



The VECM model(1)

Sample (adjusted): 1996M09 2006M12 Included observations: 124 after adjustments Trend assumption: Quadratic deterministic trend Series: V1 V10 V11 V12 V2 V3 V4 V5 V6 V7 V8 V9 Lags interval (in first differences): 1 to 7

Unrestricted Cointegration Rank Test (Trace) Hypothesized Trace 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * 0.882942 1295.722 358.7184 0.0001

At most 1 * 0.835106 1029.732 306.8944 0.0001 At most 2 * 0.776055 806.2277 259.0294 0.0000 At most 3 * 0.698297 620.6795 215.1232 0.0000 At most 4 * 0.645790 472.0890 175.1715 0.0000 At most 5 * 0.530824 343.3936 139.2753 0.0000 At most 6 * 0.469218 249.5531 107.3466 0.0000 At most 7 * 0.381454 171.0110 79.34145 0.0000 At most 8 * 0.326337 111.4434 55.24578 0.0000 At most 9 * 0.260994 62.46019 35.01090 0.0000 At most 10 * 0.182294 24.95653 18.39771 0.0052 At most 11 9.42E-06 0.001168 3.841466 0.9720

Trace test indicates 11 cointegrating eqn(s) at the 0.05 level

A natural progression from a VAR representation is the VECM model,especially when the level series are non-stationary. We initially test forthe rank of the cointegration using the methodology by Johansen (1988).



The VECM model(2)The normalized cointegration coefficients only load on the V(9).Thus we have:

)9(V*3672.2)1(V*0000.1 )9(V*7348.3)10(V*0000.1 )9(V*2920.0)11(V*0000.1 )9(V*2912.0)12(V*0000.1

)9(V*6488.0)3(V*0000.1 )9(V*7484.3)4(V*0000.1

)9(V*8660.0)5(V*0000.1 )9(V*4236.5)6(V*0000.1 )9(V*7363.3)2(V*0000.1 )9(V*5844.4)7(V*0000.1

)9(V*4401.7)8(V*0000.1



The VECM model(3)

)i(Vt

2R

AIC

SC

SSR

)1(Vt 0.89 2.0556 4.2618 11.86

)2(Vt 0.84 3.2442 5.4503 38.94

)3(Vt 0.97 1.8840 4.0901 9.93

)4(Vt 0.83 2.7698 4.9760 24.23

)5(Vt 0.95 -0.8552 1.3510 0.65

)6(Vt 0.88 1.1085 3.3147 4.6

)7(Vt 0.81 3.5993 5.8055 55.55

)8(Vt 0.86 4.7979 7.0041 184.16

)9(Vt 0.93 1.1352 3.3413 4.72

)10(Vt 0.81 2.5729 4.7791 19.90

)11(Vt 0.91 0.4482 2.6544 2.37

)12(Vt 0.80 2.1905 4.3967 13.5

84

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96 97 98 99 00 01 02 03 04 05 06

V1 V1 (Baseline)


Ana Čuvak and dr. Žilvinas Kalinauskas, Vilnius Gediminas Technical University, Lithuania

The VECM model(4)

-1.0

-0.5

0.0

0.5

1.0

96 97 98 99 00 01 02 03 04 05 06

RESID01

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

96 97 98 99 00 01 02 03 04 05 06

RESID02

-.4

-.3

-.2

-.1

.0

.1

.2

.3

.4

96 97 98 99 00 01 02 03 04 05 06

RESID03

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

96 97 98 99 00 01 02 03 04 05 06

RESID04

-3

-2

-1

0

1

2

96 97 98 99 00 01 02 03 04 05 06

RESID05

-1.2

-0.8

-0.4

0.0

0.4

0.8

96 97 98 99 00 01 02 03 04 05 06

RESID06

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

96 97 98 99 00 01 02 03 04 05 06

RESID07

-.2

-.1

.0

.1

.2

96 97 98 99 00 01 02 03 04 05 06

RESID08

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

96 97 98 99 00 01 02 03 04 05 06

RESID09

-2

-1

0

1

2

96 97 98 99 00 01 02 03 04 05 06

RESID10

-4

-3

-2

-1

0

1

2

3

96 97 98 99 00 01 02 03 04 05 06

RESID11

-.6

-.4

-.2

.0

.2

.4

.6

96 97 98 99 00 01 02 03 04 05 06

RESID12



ConclusionConclusion

• Vector error correction (VECM (7,11)) model of Lithuanian inflation processes is investigated and proposed for the inflation modelling.

• The VECM (7,11) model describes short-term relationships taking into account long-run development among all 12 common HCPI groups.

• According to the Macroeconomics theory, inflation is caused not only by price changes of common HCPI groups, but by other economic indicators (such us oil prices index, GDP, interest rates, etc.) too. To get better modelling results and to predict better forecasts it is useful to include other economic indicators into the model, in the future.

june 26th – 29th 2007 tartu, estonia ana Čuvak and dr. Žilvinas kalinauskas, vilnius gediminas...

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