EVIEWS tutorial: Cointegration.and error correction Professor Roy Batchelor City University Business School, London & ESCP, Paris EVIEWS Tutorial 1 © Roy Batchelor 2000 — EV
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EVIEWS tutorial:
Cointegration.and error correction
Professor Roy Batchelor
City University Business School, London
& ESCP, Paris
EVIEWS Tutorial 1 © Roy Batchelor 2000
—
EVIEWS
O On the City University system, EVIEWS 3.1 is in
Start/ Programs/ Departmental Software/CUBS
Oo Analysing stationarity in a single variable using VIEW
f1 Analysing cointegration among a group of variables
O Estimating an ECM model
O Estimating a VAR-ECM model
EVIEWS Tutorial 2 © Roy Batchelor 2000
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=I EViews
File Edit Objects View Procs Quick Options Window Help
—— View| Procs|Objects| Save|Label+/-| Show|Fetch| Store| Delete| Genr| Sample|
Range: 1975:01 2000:12 Filter: * Default Eq: None
Sample: 1975:01 2000:12
[Œœ] c
conf
= S View| Procs| Objects | Print | Name| Freeze| Edit+/-| Smpl+z- | InsDel| Transpose| Title | Sample
WM earn
4 #500 obs obs FT500 EARN DIV RPI
Wi growth 1999:08 | 1999:08 14709.42 495.4300 326.5500 166.2C
(i inf 1999:09 | 1999:09 14178.95 505.1300 327.5300 166.5C
YA pe 1999:10 | 1999-10 14572.28 501.9700 327.6800 166.7C
A prod 1999:11 | 1999:11 15725.2B 520.3600 333.3800 167.3C
oe 1999:12 | 1999:12 16694.16 515.4100 330.5400 166.6C
R3 i 2000:01 | 2000-01 15612.37 518.5100 329.4200 167 5C
FAtb3 2000:02 | 2000:02 15826.98 491.8300 313.3700 168.4C
2000:03 | 2000:03 16355.85 521.3900 310.7600 170.1C 2000:04 | 2000-04 15784.34 528.4300 310.9500 170.70 2000:05 | 2000:05 15658.66 564.4800 311.6100 171.1C 2000:06 | 2000-06 15769.05 544.1400 303.0700 170.5C _2000:07 | 2000:07 15907 72 531.5000 305.4300 170.5C 2000:08 | 2000:08 16525.57 556.6000 309.0300 171.70 2000:09 | 2000:09 NA NA NA NA 2nnn-1n 2nnn:-1n NA NA NA NA
EVIEWS Tutorial 3 © Roy Batchelor 2000
Data transformation
O Generate a series for the natural log of the FT500 index (1ft500)
O Test for stationarity in
— the level of this series
— the first difference of this series (dlft500)
© Results show that Ift500 is an I(1) variable
EVIEWS Tutorial 4 © Roy Batchelor 2000
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| Generate In(FT500)
“1 /(
‘Fie Edt Dbe+z View Brocs Duck Oplere Window Help
qenr !Ñ5S-0=lsgifA5-01
genr learn = logflearn
qenr ldtư=lon(dw} 8m 5ø#6es PP [ SÍU VVoikldo: ÊE5(MÙMM
3ên! lpred=lsa(prod] 3/ew| Pas|[bvs| Fie | Manal Fieeze) Sangte|Goni| Sheet] Stats |icert| Lina] Ber |
10
mo
mais
“4
1w Tủ
1 ¬ 8+4 nf v“
TT z5 30
ụ
a
85 9ũ 85
Augmented Dickey-Fuller (ADF) Test
@@ Series: LFT500 Workfile: FT500M
View| Procs| Object s| Print [Name| Freeze| Sample| Genr| Sheet| Stats| Ident | Line | Bar |
10
Unit Root Test 'XỊ
~Ïi xI|
g Test Type: Include in test equation:
+ Augmented DickeyFullet | 4 Intercept
7 > Phillips-Perron > Trend and intercept
Test for unit root in: None Level
6 54st difference Lagged differences:
> 2nd difference fq
5
+ | X
EVIEWS Tutorial 6 © Roy Batchelor 2000
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| ADF results: level
ee ee ee |
ADF Test Statistic “1.437515 1% Cơlical'⁄alue7 -3.4537
5% Critical Vale -38712
i Critcal Value -2.5719
"MacKirenn critical values tor rjaction of hypolieee of & unk root
Augmented Cickay-Fuler Test Equation De asder( Vadetlx DẠ TRO The hypothesis that 1
Date: 1042740) Tiree 19:17 Ift500 has a unit root
reluded obsenations: 304 ater adjusting endpoints cannot be re] ected
ariahle Coefsemn Štd Erer 3 1+-Stateste Prob
LFTS00¢-1) A0 001227 -1497515 01516
DỊLFTEDO-1]) Dœ®<4:re 0056513 0564425 0.3355
DỊLFTEDO-2I) -nh1se==^ 0 055887 -2E2212 am4
DỊLF TEDO-3I|) -D CES! 22 0054354 -! 1EEU24 0.2383
Cc OD42113 0.018105 2 2 0.0207
R-squated DHSEtWỀ hicz: defcrr$vt vài 0.014228
Adjisted R-squared DOQEES? SD dependent var 0.050041
5E rugtosaice: DDASZD khao (no crlerion -3 lh=43
Bum squared resid 7277 ScIw+r cillefi0n 3.101505
Log tkelihood 4857217 F-statistic 3074577
DurhinV/sison stat 2018652 ProbiF-statistic) 0.01679
EVIEWS Tutorial 7 © Roy Batchelor 2000
ADF test results: first difference
Fll=
| Samctel Gere] Sheet! Sate! ieee! Line! Car
ry FulleNnit Root Test on DALFTSOO) -
5 971815 1% `€rtical ⁄4ue* -34^#
1 Mi Value -25719
*Mackinnon crtcal values for rejection of hypothesis XM unit root
Deperdiant Vatiabie: CXUFTSOO 2) The hypothesis that
Sampbisdjustect: 1975.06 200008
eluded observations: 203 after adjusting endpants 1ft500 has a unit root
Vevlable Cosficiers Std Enor 1-Statiatic Prob can be rejected :
DỊLFTS%9-1II 1182675 (1111 -1971816 (0ŒU
DỊLFTSX-1)Z) ñ2313⁄4 006411 2.390390 (001441
DILFTS-2)Z) A0013 00/699 !1023%6 02070
DILFTSOOES) 2% D0822 0022129 015836 06756 So Lft500 is TOL)
c ñ0IE679 000242: 50222 lo oe v7
R-squared 0450503 Mean dependent var 6 6EE-05
Aulpested R-aquared 0483555 SD doepersent var aœẨE4
S.E of regression 0089555 Aksike nfo crtenon 3 155066
Sum squared read 0731811) Schwarz crienon 302203
Log tkethood 482 93% F-statistic 7172277
DurbrrsVateon stat 1.969213 ProtF-statistic) oom
EVIEWS Tutorial 8 © Roy Batchelor 2000
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| Cointegration: two variables
0 The variables 1ft500 (log of stock index) and Idiv (log of
dividends per share) are both I(1)
O We can test whether they are cointegrated
— that is, whether a linear function of these is I(O)
— An example of a linear function is
1ft500, =a, + a,ldiv, + u,
when u, = [Ift500, - ap - a,ldiv] might be I(0)
© The expression in brackets [] is called the cointegrating vector, which has normalised coefficients [ 1, -ap , -a, |
EVIEWS Tutorial 9 © Roy Batchelor 2000
Form new group
ae Wt2flx- T500 M - Íc \eviswe+ TAexarmds [lnxAft5DÔm wó1) PE(«) 5
View | Piocs| Ob ts) Save Labete-| Show) Ferd Shore] Dette | Gers] Sanpke}
Range: 1976.01 2000: 12 Fitter: ” Default Eq eeÐ!1
Samole: 197501 2000: 12
(c rm ro
dv
ddr
— deam
C] sJ8<(11/ PretiNone
Ai arpi ini 197591) 5.077952
A tha Me 497312 | = 23137 2.551668
aco return 538883 | 2644755
5311979 | 285576
5401374 | 2635083
549055 | 268528 5.630421 | 2.700016
5654780 | 2.712706 5BM74% | 2723924 5SEĐ146 | 1712418
#883183 | 174840 _
by] zl
EVIEWS Tutorial 10 © Roy Batchelor 2000
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| Common trends?
mã Group: UNTITLED ‘Workfile: FT500M
View| Procs| Objec' ts| Print | Name| Freeze| Sample | Sheet| Stats| Spec|
10
8-
ii
{
2 + + + + + + I + + I + + + + + +
75 80 85 90 95 oo
EVIEWS Tutorial 11 © Roy Batchelor 2000
Engle-Granger: first stage regression
View| Procs| Object s| Print | Name| Freeze| Estimate | Forecast| Stats| Resids|
Dependent Variable: LFT500
Method: Least Squares
Date: 11/02/00 Time: 11:01
Sample: 1975:01 1995:12
Included observations: 252
Variable Coefficient Std Error t-Statistic = Prob
S.E of regression 0.140042 ikeinfo criterion -1.085842 ahout this
Durbin-V¥atson stat 0.167088 Prob(F-statistic) 0.000000
EVIEWS Tutorial 12 © Roy Batchelor 2000
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| Save first-stage residuals (u, = RES)
@ Equotion UNTITLED Worklie: FTSOOM
Mew — SprotwEstnate =
Forecast
Vein Residual Sent
_ Make Regeez cee Group
Nodal
te 7a ee; Make Residuals
Voriable Residual type:
——————— * [idiai [ : RES
Modified: 197501 2000 12 f makers
ee are Modified 1975.0) 2000 12 / makeresid
SE da | \i>dfsd: 197E:01 196: 12 // makers
S.E of regression Name for residual series: Mearce = —
Sum squared resid ———————— 3z
Durtin-Watsori stat | -004DGI4 ˆ
| -D11B110 |
| -ữIBE83 `
H O.D40675
#7/5IM | (0(69495 WIS | 01217
S58 | 0.002806
_*/5:M - nEB7 -
*975Ml\ | (0(£C25
EVIEWS Tutorial 13 © Roy Batchelor 2000
Engle-Granger:stage two (ECM) regression
View| Procs| Object s| Print | Name| Freeze| Estimate| Forecast| Stats| Resids|
Dependent Variable: DLFT500
Method: Least Squares
Date: 11/02/00 Time: 11:06
Sample(adjusted): 1975:03 1995:12
Included observations: 250 after adjusting endpoints
Variable Coefficient Std Error t-Statistic Prob
c 0.010568 O.005777 1.629286 0.0686
DLFTS500(-1) 0.059286 0.062509 0.948434 0.3438
DLDI⁄ 0.148933 0.257720 0.577887 0.5639
DLDIV(-1) 0.125376 255328 0.491037 0.6238
RES(-1) -0.073868 ~ nasa 2 262700 0.0035
R-squared 0.035776 Mean dependent var 0.014948
S.E of regression 0.053443 Akaike info criterion -3.000588 disequilibrium
Log likelihood 380.0748 F-statistic 2.272610 corrected” each Durbin-¥V¥atson stat 1.929673 Proh(F-statistic} 0.062054 month
EVIEWS Tutorial 14 © Roy Batchelor 2000
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General model: stage one (I(1) variables)
ms Equation: UNTITLED Workfile- FTS00H
VIÉ4 P9: LÍÙ gel: i rvs] Fiesas) © inate)
Dependart x/anabla: LF [S02
Method Least Squares
Dae: 110200 Time: 11:09
Semple 1975:01 1995-12
Included obsemwabons: 22
Vanable Coeficient Sid Enor t-Statistic Prob
c 44396314 1006762 440899 00000
LDIV ññ245% 0 070706 11 66295 0.0090
LEARN 0400457 0085511 6112045 0000
LPROO -0.633347 210528 -2Ø64443 0.0045
LAPI 00418739 OF1065460 0.397051 O6917
CONF 0005704 00483 113371 0000
TES -1857279 0271673 -BB3B4B5 00000
R-squared 0.993328 Mean dependent var 7 395240
Adusted R-squared 0985164 SD dependent var 1.197501
S.E of regression 0.092376 Akaike info cnterion -1.999520
Surn squared resid 2080654 Schwarz cnterion -1.900430
Log likelihood 246.2135 = F-statietic 6079.104
Durbin- Watson stat 0451859 ProbiF-statistic) 0.000000
EVIEWS Tutorial 15 © Roy Batchelor 2000
General model: stage two
Si Equation UNTITLED Wortlie FISOUM
fren) Proce | tees) Pret] Mer
Dapercent Yanable: OLFTSOO
Methiod: Leset Squares
Date 1140200 Time 11:13
Satrg:k{8đjusted|: 137503 1995:12
Included observations: 250 after adjusting endpoints
Varebk Coefficient Std Error = t-Stotistic Prob
C 34 D025ŒW 1.669178 D1133
OLFTSO0¢-15 0.07595 O05) 12431 02135
DLO 0.296624 026242) 1.726143 O2612
OLEARK 0.088621 012735 0.690090 04904
DLPROD 0.209909 O224758 1.25950) 01984
ñLEPI 0.044355 D4541 009793 092322
OCONF 0.001335 OOO 2768113 00161
OTBS 25427 O4051 £2209 0o00000
RES(-1) 0.18205 O097466 -40⁄223 00001
R- squared 0.195254 Mes dependant var 0.012948
Adjusted R-squared 0.168540 S.D depehdert vw 0.053287
S.E ofragression 0.049237 Akaike mo criterion 3 149994
Sum squared resid 0.584025 «= Schwarz citeron -30222
Log likelihood 20743 F-statistic 7 315B
ButtxfrW2z†tsor: s†al 1.59552) Prob|F-statishe) 0.000000
EVIEWS Tutorial 16 © Roy Batchelor 2000
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@ Equetion UNTITLED Woiklde: fT15DUM
View| Procs| Okjacts | Prt | Nerre| Fresze| Estate| Forscassi| State] Resids |
Dependent Variable DLF TSO
Wiethod: Least Squares
Date: 11/0200 Time: 11:14
Sampletadjusted): 197602 1995.12
Included obserrations: 251 after adjusting endpoints
Variable Cosficient Std Eror t-Statistic Prob
Cc OOS ñññ3412 4532523 0000
DCONF af024@ ñ0ñ05232 235391795 0ññi1£n
RES(-1) 0.128131 0.033335 3398063 00010
R-sqUared 0055255 ldaan dapandar4d vạr ñ.015741
Adjusted R-squared 0.045623 $.D dependent var 0.055328
S.E of regression 0.054045 Akaike info criterion -2.985023
Sum squared resid 0724444 Schwarz criterion 2.945856
Log likelihood 3777453 F-statistic 6.975430
Durbire Watson stat 1609954 ProbiF-statistic) 0.001129
EVIEWS Tutorial 17 © Roy Batchelor 2000
1-month ahead forecasts of Ift500 from first
genr res=IftS00-IftS00f
mi Equation: UNTITLED Workfile: FT500M =|R| xi |
View| Procs| Objects | Print | Name] Freeze Estimate | Forecast| Stats| Resids|
9.6
Forecast: LFTS00F Fetual: LFTS00
Include observations: 68 Root Mean Squared Eror 0.377337 Mean Absolute Error 0.287069 Mean Abs Percent Gror 3.019446 Theil Inequality Coefficient 0.020497 Bias Proportion 0.367632
‘Variance Proportion 0.174242 Covariance Proportion 0.468126
9.24 J
9.04
8.6
1995 1896 1997 1888 1888 2000
—LFT§0IF +2 $.E
EVIEWS Tutorial 18 © Roy Batchelor 2000
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| 1-month ahead forecasts of dlft500 from
the second stage ECM
@@ Equation: EQ02 Workfile: FT500M Jor]
View| Procs| Objects | Print | Name| Freeze| Estimate| Forecast| Stats| Resids|
0.20
Forecast: DLFTSOOF
mm he Sample: 1975:02 1995:12
owt? “at er) x4 PR hee Merve aay PEWS Include observations: 251
PN panto nll ipl Mean Abs Percent Error 160.3484
0.00 4 Theil Inequality Coefficient 0.725931
Bias Proportion 0.000074
-0.05 + Vhrianee Proportion 0.725911
s, eo (Sie By agate! Covariance Proportion 0.274015
0.10 FPS ~ es foc Arr! tua Benn ndeanaelly e
76 78 80 82 84 86 88 90 92 04
EVIEWS Tutorial 19 © Roy Batchelor 2000
1-month ahead changes in [ft500:
mi Group: UNTITLED Workfile: FT500M —ip[xi|
View| Procs| Objects | Print | Name| Freeze| Sample| Sheet| Stats| Spec|
0.05 -
0.00 -
-0.05 -
-0.10-
|—— DLFT500 —— DLFTSOOF |
EVIEWS Tutorial 20 © Roy Batchelor 2000
tỷ
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| Johansen method: make group of
associated I(1) variables (1ft500, ldiv)
Group Members Name] Freeze Edit+/-| Smpl+/-| InsDel| Transpose:
Dated Data Table 5.621089
Tests of Equality pe
Correlogram (1) 5.736282
Cross Correlation (2) 5.753017
EVIEWS Tutorial 21 © Roy Batchelor 2000
Set up Johansen procedure
Johansen Cointegration Test Ed
Cointegrating Equation (CE) and VAR specification: Information:
Test assumes no deterministic trend in data: es Sele is
> No intercept or trend in CE or test VAR eee aie
> Intercept (no trend) in CE - no intercept in VAR CE and data trend
Test allows for linear deterministic trend in data: oo apply to
@ Intercept (no trend) in CE and test VAR |
> Intercept and trend in CE - no trend in VAR mame Warning
Test allows for quadratic deterministic trend in data: Toes ales
> |ntercept and trend in CE - linear tend in VAR assuming no
exogenous series
Summary:
> Summarize all 5 sets of assumptions
Exogenous series in VAR: [ b—
{don't include C or trend)
‘beg intervals (pairs) in VAR: fi 1 w=|
⁄
EVIEWS Tutorial 22 © Roy Batchelor 2000