Long-run relationships between selected central European indexes.
Published online: 26 April 2011 [c] International Atlantic Economic Society 2011
Abstract In the paper we discuss the results of the long-run relationships (cointegration) between the Warsaw Stock Exchange and the other three stock exchanges situated in Central Europe: the Vienna Stock Exchange, the Prague Stock Exchange, and the Budapest Stock Exchange. Cointegration analysis is applied to check if the markets are integrated. Highly integrated markets are not isolated from international shocks.
Keywords Central European Stock Exchanges.Long-run relationships Cointegration
Capital markets in Central and Eastern Europe (CEE) are becoming increasingly popular with international investors - made evident by their capitalization increases year by year. In the paper we discuss the results of the long-run relationships between the four stock exchanges situated in Central Europe: the Warsaw Stock Exchange (WSE), the Vienna Stock Exchange (VSE), the Prague Stock Exchange (PSE), and the Budapest Stock Exchange (BSE).1 Their capitalizations in 2009 are presented in Table 1.
Table 1 Market capitalization of European stock exchanges at the end of 2009 Stock Exchange Value at year % of total end (EUROm) capitalization of all markets associated in FESE Warsaw Stock 105,157.15 1.29% Exchange Vienna Stock 79,511.02 0.98% Exchange Prague Stock 31,265.36 0.38% Exchange Budapest Stock 20,887.90 0.26% Exchange Total 8,145,941.61 100.00% capitalization of European stock exchange associated in FESE Own calculation based on FESE data
The WSE is likely to be the leading equity market2 in Central and Eastern Europe and compete with the VSE. The VSE and WSE market capitalization, the changes of the capitalization, and the participation of both stock exchanges (in %) in total turnover of European capital markets (associated in FESE) are presented in Table 2. From 2000 to 2001 the WSE had a slightly bigger capitalization than the VSE. From 2002 to 2007, the VSE was characterized by a larger turnover than the VSE, but in the years 2008 and 2009 turnover was bigger for the WSE. In 2008 capitalization was decreasing in the global equity market, so this could be explained by the fact that during the crisis, the Polish capital market was better perceived than the Austrian capital market.
From the investors' point of view, it is very important to define the relationship between capital markets. A close relationship denotes that financial markets are integrated, and it has important implications. Highly integrated markets are not isolated from international shocks. Consequently, effective portfolio risk diversification between integrated markets cannot be achieved (see e.g., Hassan & Naka, 1996; Crowder & Wohar, 1998; Phylaktis & Ravazzolo, 2005; Syriopoulos, 2007).3 The level of integration could be examined by means of cointegration analysis.
In the paper, we discuss the results of investigation of the long-run relationships (cointegration) between selected Central European capital markets by applying the Johansen method. The analysis concerns the following pairs of stock exchanges: WSE--VSE, WSE--PSE, WSE--BSE. There are analyzed relationships between WSE and other stock exchanges because of the leading position of the Polish capital market to the others mentioned. This investigation can be explained if analyzed stock exchanges are isolated from one another. The research is based on data concerning observations of the indexes quoted at mentioned European Stocks Exchange between January 2000 and March 2009. The investigation also concerns the sub-periods as follows: the bear market (when the indexes were falling), stagnation, and the bull market (when the indexes were rising).
Table 2 WSE and VSE capitalization in years 2000-2009 Warsaw Stock Exchange Vienna Stock Exchange Year (A) (B) (C) (A) (B) (C) 2000 33,760.81 -- 0.34% 31,884.00 -- 0.32% 2001 28,845.79 -14.56% 0.34% 28,307.00 -11.22% 0.34% 2002 27,055.35 -6.21% 0.46% 32,235.00 13.88% 0.54% 2003 29,349.76 8.48% 0.43% 44,811.00 39.01% 0.65% 2004 51,888.26 76.79% 0.68% 64,577.00 44.11% 0.85% 2005 79,353.46 52.93% 0.83% 107,036.00 65.75% 1.11% 2006 112,825.56 42.18% 0.99% 151,013.00 41.09% 1.32% 2007 144,323.31 27.92% 1.23% 161,730.70 7.10% 1.38% 2008 65,177.59 -54.84% 1.05% 54,752.40 -66.15% 0.89% 2009 105,157.15 61.34% 1.29% 79,511.02 45.22% 0.98% Own calculation based on FESE data. Column (A)--Value at year end (EUROm), Column (B)--capitalization changes year to year, Column (C)--percentage of capitalization markets associated in FESE
The concept of cointegrated variable was defined by Granger (1981). (4) We can say that two considered variables [x.sub.t] and [y.sub.t] are cointegrated CI(d, b) if both are integrated in the same order d: [x.sub.t][Tilde]I(d) and [y.sub.t][Tilde]I(d) and there is a linear combination of variables ([[alpha].sub.1] [x.sub.t] +[[alpha].sub.2] [y.sub.t] that is integrated of order d-b, where d [greater than or equal to] b [Greater than] 0). Usually financial time series (like quotation of shares or indices) are integrated of order one. So, if the [x.sub.t][Tilde]I(1), [y.sub.t][Tilde]I(1), the relationship between them should be I(0), and then [x.sub.t], [y.sub.t] are CI(1,1).
The most popular methods of testing for cointegration are the Engle-Granger two-step procedure (Engle & Granger, 1987), Cointegrating Regression Durbin-Watson (CIDW, see e.g., Charemza & Deadman, 1997) Test and the Johansen Tests (Johansen, 1988; Johansen & Juselius, 1990). In the presented research the Johansen procedure is applied.
In order to test for cointegration using the Johansen method, we estimate the parameter of vector error correction model (VECM):
[DELTA][Z.sub.t] = [[k - 1].summation over (i = 1)][[GAMMA].sub.i][DELTA][Z.sub.[t - i]] + [PI][Z.sub.[t - k]] + [e.sub.t] 1
that is a transformation of the vector autoregression model (VAR):
[Z.sub.t] = [k.summation over (i = 1)][A.sub.i][Z.sub.[t - i]] + [V.sub.t] (2)
[Z.sub.t] Is a vector of considered n notlagged variables, [Z.sub.t] = [[[Z.sub.1t] [Z.sub.2t] ... [Z.sub.nt]].sup.'],
[delta][Z.sub.t] Is a vector of considered n variables--first differences of [Z.sub.t], [delta][Z.sub.t]= [[[delta][Z.sub.1t][delta][Z.sub.2t][delta][Z.sub.nt]].sup.'],
[Z.sub.t-i], [delta][Z.sub.t-i], [delta][Z.sub.t-k] Explanatory variables, lagged observation of variables [Z.sub.t] and [delta][Z.sub.t],
[A.sub.i] Parameters of model (2),
[[GAMMA].sub.i], [PI] Parameters of model (1), [[GAMMA].sub.i]= -I + [A.sub.1] + ... + [A.sub.i], [PI] = (-I + [A.sub.I] + ... + [A.sub.i])
I Identity matrix, and [[epsilon].sub.t], [V.sub.t]] Error terms of models (1) and (2).
The Johansen procedure uses two test statistics: [[lambda].sub.trace] (trace test) and [[lambda].sub.max] (maximum eigenvalue test). The test statistics in both tests are based on the eigenvalues of the [PI] matrix (see formula 1). The tests help to define the rank r of [PI] matrix. The defined rank r is the number of cointegrating vectors.
Cointegration occurs in between, when 0 [Less than] r [Less than] n In such a situation, VECM is recommended. If r = 0, the processes are not cointegrated. The VAR model can be used only for the analysis of the differences between variables. If r = n, the VAR model can be estimated using both differences and levels of the variables.
The hypotheses in the Johansen tests are as follows:
[H.sub.0]: there are r cointegrating vectors,
[H.sub.1]: there are r + 1 cointegrating vectors.
The test statistics are defined by formulas (3) and (4):
[[lambda].sub.trace](r) = - T[n.summation over (i = r + 1)]ln[gamma](1 - [[lambda].sub.i]) (3)
[[lambda].sub.max[gamma]](r,r + 1) = - Tln[gamma](1 - [[lambda].sub.[r + 1]]) (4)
where: [[lambda].sub.1], ..., [[lambda].sub.2] are eigenvalues of [PI] matrix that are settled in a descending order.
Both statistics: [[lambda].sub.trace] and [[lambda].sub.max] are [X.sup.2](n-r) distributed. The Johansen maximum eigenvalue test is considered to be superior to the trace test (see Kennedy, 2003, p. 355).
When we construct the VECM model from the VAR model, the deterministic variables can influence the results. Therefore, five cases are considered:
(1) No intercept and no trend in the model,
(2) The model contains the intercept that is represented in the cointegrating vector (restricted intercept),
(3) The model contains the intercept that is not represented in the cointegrating vector (unrestricted intercept),
(4) The model contains the linear trend that is represented in the cointegrating vector (restricted trend),
(5) The model contains the linear trend that is not represented in the cointegrating vector (unrestricted trend).
In order to differentiate cases (2) from (3) or (4) from (5) we can use the LR test, where the hypotheses are as follows:
[H.sub.0]: [PI] matrix is restricted (in cointegrating vectors a trend/intercept appears),
[H.sub.1]: [PI] matrix is unrestricted (in cointegrating vectors a trend/intercept does not appear).
The test statistic is calculated using formula (5):
LR = -T[n.summation over (i=r + 1)][ln[gamma](1-[[lambda].sub.i.sup.*])-ln[gamma](1-[[lambda].sub.i])] (5)
where [[lambda].sub.1], ..., [[lambda].sub.n] are eigenvalues of unrestricted [PI] matrix (settled in a descending order) and [[[lambda].sub.1].sup.*], ..., [[[lambda].sub.n].sup.*] are eigenvalues of restricted [PI] matrix (settled in a descending order).
Statistics LR is [x.sup.2](n-r) distributed. In the test we assume that values In (1--[[[lambda].sub.i].sup.*]) and In (1 -[[lambda].sub.i]), should be equal if the restriction can be rejected.
The research is based on the observations of the quotations of five indexes: ATX, BUX, PX50, WIG, and WIG20 between January 03, 2000, and March 27, 2009. We consider daily, weekly (the last quotation in the week), and monthly (the last quotation in the month) data. In the investigation monthly data in the sub-periods were not considered because of short samples. The data were transformed into natural logarithms:
The analysis was provided for the following pairs of indexes: WIG--BUX (performance indexes), WIG20--PX50 and WIG20--ATX (price indexes), and WIGWIG20 (Polish stock market indexes).
The periods and number of observations in each sample are presented in Table 3. The division into sub-periods are according to the Polish capital market (see also Fig. 1). One can notice that the period when the prices are increasing is divided into two subsamples. First, we can observe a different tendency (the slope in time regression is different). Second, this period is divided in order to obtain a comparable number of observations in the subsamples.
In the first step the order of the variables' integration is examined. (5) For the identification order of integrated variables, two kinds of unit root tests are used: the Augmented Dickey-Fuller (ADF) test and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test (see Dickey & Fuller, 1979 and 1981; Kwiatkowski et al., 1992; Maddala & Kim, 1998). The results are presented in Table 4. (6)
Table 3 The considered periods, number of observations, and notation of samples Frequency of data daily weekly monthly sample period A B A B A B Whole 03.01.2000-27.03.2009 PD0 2377 PW0 482 PM0 110 Bear Market1 03.01.2000-08.10.2001 PD1 455 PW1 92 - - Stagnation 09.10.2001-03.07.2003 PD2 445 PW2 90 - - Bull Market1 04.07.2003-27.10.2005 PD3 600 PW3 121 - - Bull Market2 28.10.2005-06.07.2007 PD4 434 PW4 89 - - Bear Market2 09.07.2007-27.03.2009 PD5 443 PW5 90 - - Own calculation. A--notation of sample, B number of observations
One can distinguish two types of these variations: stochastic or deterministic. The type of the trend that is recognized allows us to choose the proper method of transforming the nonstationary process into a stationary one. The process with the stochastic trend that contains the unit root is called difference stationary (DS). Thus, differencing is the method of obtaining the stationary process. The process with the deterministic trend is called trend stationary (TS), and applying the trend model as a filter is a method of detrending the process. The problems of choosing the detrending method and its consequence have been discussed in literature (see: Enders, 1995; Maddala & Kim, 1998).
DS--I(1) denotes that an analyzed process is nonstationary at levels but stationary at first differences (difference stationary process). TS denotes that a process is trend stationary. I(0) denotes that a process is stationary (integrated of order zero). For the whole period (samples PDO, PWO, and PMO) all time series are DS. For daily data (subsamples PD1, PD2, PD3, PD4, PD5) all the analyzed processes are DS, except one (index BUX in PD1 subsample is TS). For weekly data, in sub-periods PW4 and PW5, they are also DS. For PW 1 and PW3 subsamples, the test indicated that processes are mostly TS (except BUX for PW3 that is DS). The quotation of indexes BUX, ATX, and WIG20 and WIG for PW2 are stationary--I(0). With reference to the definition of cointegration, the analyzed processes should be[Tilde]I(d), where d [Greater than] 0; therefore, in further analysis, PW I, PW2, and PW3 subsamples are excluded (where the time series were stationary or stationary with a deterministic trend). Considering the results obtained for the PD1, PD2, and PD3 sub-periods, it is necessary to mention that the frequency of realization (quotation) influences the financial time series properties.
Cointegration analysis is conducted by means of the Johansen method. Usually tests [[lambda].sub.trace] and [[lambda].sub.max] yield the same results, but in some cases they are different. In such a situation, the [[lambda].sub.max] test indication is accepted. For each pair of indexes and each period five cases are considered: (1) the unrestricted trend, (2) the restricted trend, (3) the unrestricted intercept, (4) the restricted intercept, and (5) no trend and no intercept in the model. The result of investigation as a number of cointegrating vectors are presented in Tables 5, 6, 7, 8 and 9.
[FIGURE 1 OMITTED]
Table 4 Results of unit root tests: type of time series Sample INDEXES BUX WIG WIG20 ATX PX50 PM0 DS-I(1) DS-I(1) DS-I(1) DS-I(1) DS-I(1) PW1 DS-I(1) DS-I(1) DS-I(1) DS-I(1) DS-I(1) PW1 TS TS TS TS TS PW2 I(0) I(0) I(0) I(0) TS PW3 DS-I(1) TS TS TS TS PW4 DS-I(1) DS-I(1) DS-I(1) DS-I(1) DS-I(1) PW5 DS-I(1) DS-I(l) DS-I(1) DS-I(1) DS-I(1) PD0 DS-I(1) DS-I(1) DS-I(1) DS-I(1) DS-I(1) P01 TS DS-I(1) DS-I(1) DS-I(1) DS-I(1) PD2 DS-I(1) DS-I(1) DS-I(1) DS-I(1) DS-I(1) PD3 DS-I(1) DS-I(1) DS-I(1) DS-I(1) DS-I(1) PD4 DS-I(1) DS-I(1) DS-I(1) DS-I(1) DS-I(1) PD5 DS-I(1) DS-I(1) DS-I(1) DS-I(1) DS-I(1) Own calculation
The analyzed pair of indexes with daily and weekly observations in the whole period (PDO and PWO) are not cointegrated. Analyzing the monthly data, tests indicate that the pairs of indexes BUX--WIG, ATX--WIG20, and WIG--WIG20 have long-run relationships (except in the case of WIG--WIG20 when the intercept is included in the cointegrating vector). Based on the results obtained for WIG20 and PX50, one can claim that they are not cointegrated (in three cases we have no cointegrated vectors). We can interpret this situation as the Warsaw Stock Exchange having a stronger connection with the Vienna Stocks Exchange and Budapest Stock Exchange than with the Prague Stock Exchange.
Table 5 The number of cointegrating vectors for a pair of indexes BUX and WIG Sample (1) unrestricted (2) restricted (3) unrestricted trend trend intercept PM0 1 (a) 1 2 PD0 0 0 0 PD1 2 2 (a) 1 PD2 2 0 (a) 2 PD3 2 1 (a) 1 (a) PD4 2 1 (a) 0 (a) PD5 2 1 (a) 1 (a) PW0 0 0 0 PW4 2 1 (a) 0 (a) PW5 2 1 (a) 1 (a) Sample (4) restricted (5) no trend and intercept no intercept PM0 1 (a) 1 PD0 0 0 PD1 0 (a) 1 PD2 2 (a) 0 PD3 2 1 PD4 0 1 PD5 1 2 PW0 0 0 PW4 0 0 PW5 0 2 Own calculation. (a) indication of LR test Table 6 The number of cointegrating vectors for a pair of indexes WIG20 and ATX Sample (1) (2) (3) (4) (5) PM0 1 (a) 1 2 1 (a) 1 PD0 0 0 0 0 0 PD1 2 1 (a) 0 0 (a) 0 PD2 2 1 (a) 1 (a) 2 1 PD3 2 1 (a) 0 0 (a) 1 PD4 2 1 (a) 0 (a) 0 0 PD5 2 1 (a) 0 0 (a) 0 PW0 0 0 0 0 0 PW4 2 0 (a) 0 (a) 0 0 PW5 1 (a) 1 2 1 (a) 1 Own calculation. (a) indication of LR test
When the model is estimated in the unrestricted version, tests designate two cointegrating vectors. This means that the model can be estimated as VAR using the levels of the variables. When the model is estimated in a restricted version, tests usually designate one cointegrating vector. This means that the appropriate version of the model is VECM. Results of the LR test designates usually one cointegrating vector.
The general conclusion is that, in a long period, markets seem not to be connected (there are no long-run relationships). However, when the period is divided into shorter sub-periods, the long-run relationships are often seen. Only a few cases are observed when the analyzed time series are not cointegrated. Such a situation is observed especially for the pair WIG20-PX50.
Table 7 The number of cointegrating vectors for a pair of indexes WIG20 and PX50 Sample (1) (2) (3) (4) (5) PM0 0 (a) 0 2 0 (a) 1 PD0 0 0 0 0 0 PD1 2 1 (a) 1 0 (a) 1 PD2 2 0 (a) 0 0 (a) 0 PD3 2 1 (a) 1 0 (a) 1 PD4 2 1 (a) 1 (a) 2 1 PD5 2 1 (a) 0 0 (a) 1 PW0 0 0 0 0 0 PW4 2 0 (a) 0 (a) 2 1 PW5 2 1 (a) 0 0 (a) 0 Own calculation. a indication of LR test Table 8 The number of cointegrating vectors for a pair of indexes WIG20 and WIG Sample (1) (2) (3) (4) (5) PM0 2 1 (a) 2 0 (a) 1 PD0 0 0 0 0 0 PD1 2 2 (a) 0 0 (a) 0 PD2 1 1 (a) 0 (a) 2 1 PD3 2 (a) 1 2 (a) 1 1 PD4 2 (a) 1 1 (a) 2 1 PD5 2 1 (a) 1 (a) 1 1 PW0 0 0 0 0 0 PW4 2 (a) 0 1 (a) 2 1 PW5 2 0 (a) 1 (a) 2 1 Own calculation. (a) indication of LR test
The long-run relationship can disturbed in a short time. There can be applied error terms (error correction mechanism-ECM) in order to analyze the speed of adjustment to the long-run relationship (see e.g., Enders 1995; Charemza & Deadman 1997; Maddala & Kim, 1998). The next step of the examination was the estimation of simple models with ECM. The results are presented in Table 6. They are parameters of the model that characterize the short-run adjustment. There are considered eight cases of an adjustment mechanism: index WIG with relation to indexes BUX or WIG20, which is denoted as WIG(BUX) or WIG(WIG20) in the Table 6; index WIG20: WIG20(ATX), WIG20(PX50), WIG20(WIG); index BUX: BUX(WIG); index ATX: ATX(WIG20); and index PX50: PX50(WIG20).
Table 9 ECM parameters (A)TX(WIG20) Sample W1G20((A)TX) Sample WIG20(PX) -0.0368 PM0 0.1086 (a) PM0 0.0773 (b) -0.0136 PD1 0.0036 PD1 -0.0279 (b) -0.0109 PD2 0.0187 (b) (c) PD2 -0.0170 (b) -0.0046 PD3 -0.0384 (a) PD3 -0.0408 (a) 0.0216 PD4 0.0442 (a) (c) PD4 0.0292 (a) -0.0263 PD5 -0.0216 (b) (a) PD5 -0.0282 (b) 0.1079 PW4 0.1992 (a) (c) PW4 0.1341 (a) 0.1253 PW5 0.1004 (b) (b) PW5 0.1154 (b) BUX(WIG) Sample WIG(BUX) Sample W1G(WIG20) -0.0685 PM0 0.0931 (b) (c) PM0 -0.0068 0.0406 PD1 -0.0370 (a) (a) PDI -0.2681 (a) -0.0342 PD2 0.0277 (b) (a) PD2 0.0018 0,0108 PD3 0.0311 (a) (b) PD3 -0.0070 (b) -0.0213 PD4 0.0030 (c) PD4 0.0028 0.0634 PD5 0.0294 (b) (a) PD5 -0.0260 (a) -0.1273 PW4 0.0233 (b) PW4 0.0066 -0.2168 PW5 0.1183 (b) (a) PW5 -0.1352 (a) ATX(WIG20) PX(WIG20) -0.0368 0.0240 -0.0136 0.0425 (a) -0.0109 -0.0073 -0.0046 0.0141 (a) 0.0216 0.0M3 -0.0263 0.0471 (a) 0.1079 0.0579 0.1253 0.1401 (a) BUX(WIG) WIG20(WIG) -0.0685 0.0121 0.0406 0.1732 (a) -0.0342 0.0015 0,0108 0.0080 (b) -0.0213 0.0017 0.0634 0.0355 (a) -0.1273 -0.0308 -0.2168 -0.1736 (a) Own calculation. (a) significant at the level 0.01, (b) significant at the level 0.05, (c) significant at the level 0.1
An insignificant parameter designates that an error correction mechanism is not active. All significant parameters presented in the Table 6 are negative. This assures restoration of the equilibrium.
Error correction mechanism is significant for all cases in the period July 09, 2007, to March 27, 2009 (Bear Market2, subsamples PD5 and PW5). In this period the highest speed of adjustment has index BUX with relation to WIG. For weekly data we observe that 22% of the discrepancy in these two indexes from the previous week is eliminated in the present week, and the half-life is shorter than 3 periods (weeks). For daily observation, n 6% of disequilibrium has been eliminated during one period (half life is 11 periods in days). The adjustments with the lowest speed are recognized in WIG20 with relation to ATX (subsamples PW5 and PD5) and WIG with relation to WIG20 (PD5). For weekly observation, 10% of disequilibrium is eliminated during one period (half life is 7 periods--weeks), and daily data declines 3% of disequilibrium (half life is 26 periods--days). Additionally, we can observe that restoring the equilibrium is quicker in subsamples PW5 and PD5 than in the other subperiods. It is necessary to mention that investigated period (July 09, 2007 to March 27, 2009) captures the last crisis period. We can interpret that the long-run relationship between the investigated market during this period is stronger.
In the paper, the results of the examination of the long-run relationship between WSE Indexes (WIG, WIG20) and selected Central European stock exchanges indexes: ATX, BUX and PX50, using the Johansen method are presented. Data quoted daily, weekly, and monthly in the periods between January 03, 2000, and March 27, 2009, are analyzed. The preliminary unit root test indicates that the frequency of observation influences the financial time series properties and econometric test results. In the whole period, daily and weekly data are not cointegrated, whether for monthly observation cointegration appears. We can suppose that long-run relationships between the WSE and the Vienna, Prague, or Budapest Stock Exchanges exist, but they are sensitive. The division of the whole period into smaller sub-periods--the weekly or daily quotation of indexes became cointegrated. So we can observe the long-run relationship when the periods are shorter and characterized by market tendency. In shorter periods, the investigated capital markets are not isolated from shocks that can appear in those markets. Especially for the last investigated sub-period (July 09, 2007, to March 27, 2009) all time series characterize restoring the long-run equilibrium, and we can suppose that relationships between the Warsaw Stock Exchange and the other investigated market are stronger. Comparing the results obtained for the whole periods and sub-periods, we can suppose that different markets react to the changes of different tendency. Obtained results for pairs of indexes in sub-samples indicate also that the WSE and PSE are less integrated than the WSE and VSE or the WSE and BSE.
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(1) The VSE, PSE, BSE, and the Stock Exchange in Ljubjana operate as part of CEESEG.
(2) The leading position of WSE among other CEE stock exchanges is discuss in the papers: K. Kompa & E. Marcinkiewicz (2010). Causal Relationship between WIG20 and WIG20 Futures on the Warsaw Stock Exchange (presented in International Atlantic Economic Society Conference in Pague--Czech Republic, March 2010), M. Chrzanowska & D. Witkowska (2010). Comparison of Central and European Stock Markets: A Preliminary Investigation (presented in International Atlantic Economic Society Conference in Pague--Czech Republic, March 2010), M. Chrzanowska & K. Kompa (2010). Comparison of Regional Capital Markets in Europe. Application of Multidimensional Comparative Analysis (presented in Spatial Econometrics and Regional Economic Analysis Conference, Lodz--Poland, June 2010).
(3) Many papers concerning long-run relationships among stock exchanges were cited in the article Syriopoulos (2007).
(4) See also Engle & Granger (1987). More discuss about cointegration see Engle & Granger (1991).
(5) For the examination GRELT is used.
(6) Example of financial time series analysis using the unit root test is presented in, e.g., Matuszewska-Janica A. & Witkowska D. (2008). The Warsaw Stock Exchange Indexes Analysis: Trend or Difference Stationary in Medium and Small Samples, paper presented at the conference Forecasting Financial Markets and Economic Decision Making, Lodz, Poland.
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|Publication:||International Advances in Economic Research|
|Date:||May 1, 2011|
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