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© 2013 Nicolaus Copernicus University. All rights reserved.  
http://www.dem.umk.pl/dem 

D Y N A M I C  E C O N O M E T R I C  M O D E L S  
DOI: http://dx.doi.org/10.12775/DEM.2013.010  Vol. 13 (2013) 175−194 

Submitted November 8, 2013 ISSN 
Accepted December 30, 2013 1234-3862 

Andrzej Geise, Mariola Piłatowska*  

Synchronization of Crude Oil Prices Cycle  
and Business Cycle for the Central Eastern  

European Economies∗∗  

A b s t r a c t. The main purpose of the paper is to study the degree to which the Brent crude 
oil price cycle is correlated and synchronized with business cycle in a set of chosen Central 
Eastern European (CEE) economies. To indentify the oil price cycle and business cycles for 
chosen individual countries the Markov-switching autoregressive model (MS-AR) is used. 
The identification of the smoothed probabilities of being in regime 1 and regime 2 enables the 
calculation of correlation coefficients between those probabilities and the concordance index 
to evaluate the synchronization of oil price cycle and business cycles for the CEE economies.  

K e y w o r d s: Markov switching model, crude oil prices, business cycle, price cycle.  

J E L Classification: C22, C32, E23, Q40. 

Introduction 
 The energy prices have the significant impact on the economic and civi-
lization development. Rising energy prices observed in recent years acceler-
ated the realization of well-balanced energy consumption programs and the 
reduction of global energy intensity. Energy prices can be affected not only 
by economic factors but to high extent also by unpredictable and non-

                                                 
* Correspondence to: Andrzej Geise, Department of Econometrics and Statistics, 13A 

Gagarina Street, 87-100 Toruń, Poland, e-mail: a.geise@doktorant.umk.pl, Mariola 
Piłatowska, Department of Econometrics and Statistics, 13A Gagarina Street, 87-100 Toruń, 
Poland, e-mail: mariola.pilatowska@umk.pl.  

∗∗ This work was financed from grant no 1482-E.  



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS vol.13 (2013) 175–194 

176 

economic events, such as wars, political situation in regions of fossil fuels 
mining or devastating weather. Specifically, the ecology and the interna-
tional environmental protection should be taken into account when having in 
mind the future development of fossil fuel market. Special significance in 
the energy consumption structure has the crude oil which is treated as a ma-
jor determinant of world economic activity. The economic and social signifi-
cance of crude oil did not diminish along with the development of alternative 
energy source, like wind, water and sun energy. Irrespective of the potentials 
of renewable energy the impact of crude oil on the economy is still strong. 
Therefore, it is expected that the relation between economic growth and 
crude oil prices volatility exists.  
 The main purpose of the paper is to study the degree to which the crude 
oil price cycle is correlated and synchronized with business cycle in Czech 
Republic, Hungary, Poland and Slovenia. First, the Markov-switching auto-
regressive model (MS-AR) is used to identify oil price cycle and the busi-
ness cycle for chosen individual countries. Next, the correlation coefficients 
between smoothed probabilities of a recession for business cycle in given 
countries and crude oil price cycle are calculated in order to evaluate the 
extent to which turning points in the two series occur near each other. Final-
ly, the concordance index is computed to reflect the degree to which two 
series are in the same state or in other words are synchronized. The concept 
of a research study is presented in Scheme 1.  
Scheme 1. The concept of studying the synchronization of oil price cycle and busi-

ness cycle  

 

In the analysis the monthly data of Brent crude oil prices from January 1995 
to April 2013 (220 observations) and industry production index for a set of 
Central Eastern European (CEE) economies from January 1995 to April 

Analysis of oil 
price cycle 

Analysis of busi-
ness cycle for 
chosen CEE 

countries 

Analysis of prob-
abilities of being 

in regime 1 

Application of Markov-switching autoregressive 
models to identify the dating of cycles and calcu-

late probabilities of recession  
 
  

Application of correlation coeffi-
cient and concordance index to 

evaluate the degree of cycle 
synchronization   



Synchronization of Crude Oil Price Cycle and Business Cycle... 

DYNAMIC ECONOMETRIC MODELS vol. 13 (2013) 175–194 

177

2013 were used1. The data were taken from the U.S. Energy Information 
Administration database (www.eia.gov) and the OECD database 
(www.stats.oecd.org). 
 The analysis of relations between crude oil prices and economic activity 
is an important issue. The volatility of crude oil prices has become one of the 
most important indicator of economic growth due to the significant share of 
crude oil in the energy consumption structure. Moreover, the government 
policy is driven by the crude oil market as the tax revenues (e.g. oil excise, 
oil VAT, oil fee) from oil sector are significant. Table 1 is as an example of  
the significance of oil sector to the Polish budget.  

Table 1. Tax revenues from oil sector in Poland in 2012  

Tax categories  Tax category revenue as percentage 
of total oil tax revenue (PLN 52bn) 

Oil tax as percentage of  
total tax category2 

Oil excise 51.93% 41.00% 
Oil VAT 40.38% 15.85% 
Oil fee 7.69% 1.39% 

Source: elaborated on the base of POPiHN, Przemysł i handel naftowy – raport roczny 2012 
(Industry and Oil trade − annual report 2012), Warszawa, 2013. 

Tax revenues from oil sector are an important part of state income in Poland 
(in 2012 tax revenue reached ca. PLN 52 billion. The structure of taxes com-
ing from oil sector was dominated by an oil excise and oil VAT which con-
stituted respectively: 41% of total excise and 16% of total VAT. This con-
firms that the oil sector is of importance to the budget of Poland. Conse-
quently, the relation between crude oil prices volatility and business cycle is 
expected. Therefore, the analysis directed to evaluate the degree to which the 
crude oil price cycle is correlated and synchronized with business cycle is 
needed.  

1. The Relationship between Crude Oil Prices and Economic 
Activity − the Literature Review 

 The economic theory suggests that assets prices should be determined by 
their expected, discounted cash flows. Then, every factor influencing the 
discounted cash flows should have a significant impact on assets prices 
(Fisher, 1930). Expanding this rule to the crude oil prices we have that every 

                                                 
1 The Brent crude oil constitutes the global benchmark of crude oil coming from North 

Eastern Europe and reflects changes in crude oil prices in the European region.  
2 E.g. oil excise as percentage of total excise, oil VAT  as percentage of total VAT, etc. 



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS vol.13 (2013) 175–194 

178 

rise in crude oil prices entails the increase of production costs which causes 
the profits and capital value to drop. Hence, every rise of oil prices brings on 
the decrease of stock prices. This effect should have occurred both for crude 
oil exporters and importers. However, many economists discuss whether the 
influence of oil price dynamics on the stock price dynamics results from an 
indirect effect which is escalated by the impact of macroeconomic indica-
tors. According to Bjornland (2008) and Jimenez-Rodriguez, Sanchez (2005) 
the rise of oil prices has a positive effect on domestic income in oil exporting 
countries. Also, the increase in expenditure and investment is expected 
which as a result will cause the increase of productivity and reduction of 
unemployment. By contrast, in oil importing countries every rise in oil prices 
will bring on the opposite effect, in the form of decrease in income (Bacon, 
2005; Hooker, 2002). Rising oil prices lead to an increase in production 
costs in oil-importing countries because the crude oil is the important input 
in the production process (Arouri, Nguyen, 2010; Backus, Crucini, 2000; 
Kim, Loungani, 1992). 
 The increase in costs is transferred to consumers by increasing consumer 
prices, and this leads to the reduction of demand and consumer expenditure. 
The decrease in demand may result in an decrease in production, and hence 
in an increase in unemployment. Consequently, the reaction of stock market 
will be negative.  However, it should be remembered that the influence of oil 
shocks on stock market depends on the type of shock (demand or supply 
shock). In the case of demand shock the stock market is supposed to react 
positively, and in the case of supply shock − negatively (Hamilton, 1988, 
2006; Abel, Bernanke, 2001; Brown, Yucel, 1999, 2002). Summing up, ris-
ing oil prices may lead to positive economic effects (like an increase in do-
mestic income) in oil exporting countries, and negative ones (like a decrease 
in domestic income) in oil importing countries.   
 Studying relationship between the oil price volatility and economic ac-
tivity many economists have suggested that the indirect transmission mecha-
nism may have a fundamental impact in indentifying which oil price shocks 
are important from a macroeconomic point of view. For example, Loungani 
(1986) and Davis, Haltiwanger (2001) investigated the relationship between 
oil prices and employment market; Bernanke (1983) and Dixit, Pindyck 
(1994) analyzed connections of oil prices and uncertainty of investment; 
Hamilton (1988) and Lee, Ni (2002) studied the ability of oil price volatility 
to smooth the consumption in durable goods sector; Pierce, Enzler (1974) 
and Bruno, Sachs (1982) analyzed the impact of oil price volatility on infla-
tion. It should be emphasized that these studies did not decide clearly neither 
about the impact of crude oil price on economic growth, nor the impact of 



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DYNAMIC ECONOMETRIC MODELS vol. 13 (2013) 175–194 

179

economic growth on oil price levels. Therefore, it is important to investigate 
how the oil shocks are transmitted into economic activity.  

2. Univariate Markov Switching Model  
 In recent years many theoretical and empirical business cycle studies 
have analyzed the co-movements of macroeconomic time series and the 
regime-switching nature of macroeconomic activity. As the statistical meas-
urement of macroeconomic fluctuations the Markov-switching autoregres-
sive time series model has become increasingly popular since Hamilton's 
(1989) application of this technique to measure the US business cycle. In the 
Markov-switching models the recessions and expansions are modeled as 
switching regimes of the stochastic process generating the growth rate of 
economic activity indicator, e.g. GDP (Artis et al., 2004). The general form 
of switching model for growth rate of gross output tyΔ  can be written 
(Krolzig, Toro, 2005): 

,)(...)(
111 tsqtqstst qttt

yyy εμαμαμ +−Δ++−Δ=−Δ
−− −−   (1)  

where ( )2,0~ σε Nt  is an independent and identically distributed series with 
zero mean and finite variance, { }Mst ,...,1∈  − regime variable. The regimes 
are associated with different conditional distributions of the growth rate of 
real output, where the mean 

tsμ  depends on the value of a discrete state 

variable .ts  For instance, in two-regime model the mean may be negative in 
the first regime (recession), ,01 <μ  and positive in the second regime (ex-
pansion), .02 >μ  The variance of the disturbance term tε  is assumed to be 
the same in both regimes (Artis et al., 2004).   
The general idea behind the class of regime-switching models is that the 
parameters of equation (1) depend upon a stochastic, non-observable regime 
variable { }.,...,1 Mst ∈  The stochastic process generating the unobservable 
regimes is an ergodic Markov chain defined by the transition probabilities 
(Artis et al., 2004; Kośko, 2006; Stawicki, 2004):  

( ),|Pr 1 isjsp ttij === +   1
1

=∑
=

M

j
ijp   { }.,...,1, Mji ∈∀  (2) 

To highlight the stylized fact of growth output, i.e. greater volatility in reces-
sions than expansions, the approach with time-dependence in the variances 
of the growth output depending on the regime can be used. 



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS vol.13 (2013) 175–194 

180 

 In this paper the Markov two regime-switching autoregressive model 
with regime-dependent intercepts, variances and autoregressive parameters 
will be applied.  

3. Brent Crude Oil Price Cycle in 1995−2013 Period  
 The data correspond to monthly Brent crude oil prices from January 
1995 to April 2013 (220 observations in US dollars per barrel) and were 
drawn from the U.S. Energy Information Administration database. Based on 
these data the two-regime Markov switching model was estimated where 
regime 1 stands for the drops in crude oil prices and regime 2 stands for the 
rises in crude oil prices. 
 We consider a two-regime switching Markov model where the logs of 
crude oil prices are modeled in first differences:  

),,0(~|, 2

1
, ttt sttt

q

j
jtsjst iidscc σξξγμ +Δ+=Δ ∑

=
−   (3) 

where tcΔ  stands for the log first differences of Brent crude oil prices3, 
2

, ,,
ttt ssjs σγμ − denote regime-dependent intercept, autoregressive parame-

ters and variance of disturbance term tξ  respectively. The unobserved varia-
ble 1=ts  in the first regime (drop in oil prices) and 2=ts  in the second 
regime (rise in oil prices). 
 The Markov-switching autoregressive models allowing the switches 
between regimes in different parameters according to a hidden Markov chain 
were chosen based on the Akaike Information Criterion (AIC) and log-
likelihood function (LL). We considered four types of Markov switching 
models introducing switches in the intercept (MSI), in intercept and variance 
(MSIH), in intercept and autoregressive parameters (MSIA) and in intercept, 
variance and autoregressive parameters (MSIHA). The value of AIC and 
LogLik for different MS-AR models4 are given in Table 2.   

                                                 
3 To test the non-stationarity of the logs of Brent crude oil prices the ADF test was used. 

The ADF statistic for log-levels amounts 0.85 (p=0.89) − without intercept, and −3.6 (p=0.03) 
− with intercept and trend, and for log-first differences: −6.76 (p=0.00) − without intercept, 
and −6.92 (p=0.00) − with intercept and trend. This indicates that the log-levels of crude oil 
prices are non-stationary and become stationary when they are first differenced. Therefore the 
log-differences of crude oil prices are used in further analysis.   

4 In this paper we focus on the maximum likelihood estimation of parameters. All the cal-
culations in the paper were carried out in OxMetrics6.  



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181

Table 2. The Akaike Information Criterion (AIC) and log-likelihood function (LL) 
for the univariate Markov switching model for the crude oil prices, January 
1995 to April 2013  

Markov switching model AIC LL 
MSI(2)-AR(1) –674.27 343.13 

MSIH(2)-AR(1) –672.48 343.24 
MSIA(2)-AR(1) –687.23 350.61 

MSIHA(2)-AR(1) –678.62 347.31 
MSI(2)-AR(2) –715.86 364.86 

MSIH(2)-AR(2) –722.10 369.05 
MSIA(2)-AR(2) –716.98 368.49 

MSIHA(2)-AR(2) –719.35 368.57 

Table 3. Univariate MSIH(2)-AR(2) model for Brent crude oil prices  
Parameters Parameters estimates p-value 

Regime-dependent intercepts 

μ1 
–0.0063 
(0.0149) 

0.102 

μ2 
0.0156 

(0.0069) 
0.004 

Autoregressive parameters 
γ1 

0.8678 
(0.0629) 

0.000 

γ2 –0.4611 
(0.0627) 

0.000 

Regime-dependent variances   
σ21 

0.0645 
(0.0083) 

0.000 

σ22 
0.0359 

(0.0033) 
0.000 

LL 369.05  
AIC –722.1  

LR test 15.63 0.0036 
Jarque-Bera test 0.8013 0.6699 

RCM 37.99  Transition probabilities across regimes 
 p1i p2i 

Regime 1 0.9321 0.0292 
Regime 2 0.0679 0.9708 

Note: in parentheses the standard errors of estimates are given.  

 Using the AIC and the LL function the Markov switching model with 
regime-dependent intercept and variance (MSIH(2)-AR(2)) was found to be 
the best. The detailed estimation results for the period January 1995 to April 
2013 are displayed in Table 3. 



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS vol.13 (2013) 175–194 

182 

 The transition matrix allows us to observe the asymmetry of oil price 
cycle in terms of the duration of drops (regime 1) and rises (regime 2) in oil 
prices. Drops have the duration of approximately 15 months and rises have 
an average duration of two times the regime 1 (34 months). Both states are 
characterized by high probability of remaining in regime ( ,93.011 =p  

)97.022 =p  − see Table 3 and 4. In the regime 1 the oil prices tend to de-
crease )0( 1 <μ  while in regime 2 they tend to increase );0( 2 >μ  the volatili-
ty of oil prices is higher in the regime 1 (drops in oil prices) than in regime 2 
(rises in oil prices) )( 2

2
2
1 σσ >  − see Table 3. The RCM (Regime Classifica-

tion Measure5) statistic indicates that the MSIH(2)-AR(2) model is able to 
confidently distinguish which regimes are occurring at each point in time 
(RCM < 50).  
 In the studied period the first serious oil prices fall was observed in 
1997−1999 period (Table 4 and Figure 1) which may be connected with 
financial (currency) crisis in South Eastern Asia and then in Russia. The 
situation in Russia has made the market react by falling oil prices because 
Russia is the greatest crude oil producer (with average daily production 
about 10 millions of barrels; see International Energy Agency, 2013). The 
next two oil prices falls in 2001 and 2008−2009 period may be influenced by 
the economic crises in the U.S. (the third largest oil producing and the larg-
est oil consuming country in the world).  
 The decrease in oil prices in 2001 corresponds to the recession in the 
U.S. that occurred in March 2000 when the NASDAQ crashed following the 
collapse of the Dot-com bubble (Figure 1). Consequently, the decline of 
stock prices occurred in many countries (Galbraith, Hale, 2004). The second 
decline in oil prices, i.e. in 2008−2009 period, is connected with the sub-
prime mortgage crisis that broke out in the latter half of 2007. This financial 
crisis spread to the oil market (and other commodity markets) which is driv-
en by global changes in supply and demand along with a number of other 
geopolitical factors.  
                                                 
 5 The RCM statistic was proposed by Ang, Bekaert (2002). For two regimes it takes the 

form: ),1(1400
1∑=

−=
T

t tt pp
T

RCM  where tp  is a smoothed probability of being in a cer-

tain regime at time t. The constant serves to normalize the statistic to be between 0 and 100. 
The RCM is a summary point statistic which describes the quality of regime classifications. 
An ideal model is that classifying regimes sharply and having smoothed probabilities which 
are either close to zero or one. If the RCM is close to zero, the regime classification is perfect 
whereas a value of 100 means that no information about regimes is revealed. The cut-off 
value of RCM statistic is 50 which is often used as a benchmark (Chan, et al., 2011).  



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Table 4. Dating of crude oil price cycle  
Regime 1 Regime 2  

 1995(04)–1997(10) 
1997(11)–2001(11) 2001(12) –2006(07) 
2006(08)–2006(12) 2007(01)–2008(06) 
2008(07)–2009(02) 2009(03)–2013(04) 

62 months (28.57%) out of 217 are in regime 1 
Average duration d(i) 14.73 months 

155 months (71.43%) out of 217 are in regime 
2 Average duration d(i) 34.24 months 

 

 

Figure 1.  Smoothed probabilities of being in regime 1 and regime 2 for the univari-
ate Markov switching model for the crude oil prices, January 1995  
to April 2013  

 The oil price decline in 2006 is difficult to explain. In the second half of 
2006 the oil price decline indeed occurred but it was rather small, however 
the MS-AR model captured it as a recession. Hence, this behavior of oil 
prices may be rather combined with general economic situation of oil ex-
porters and importers and uncertainty on financial markets (although there 
were some inflammatory events in 2006, like the attack on Shell pipeline in 
Nigeria, worries over Iranian nuclear plans or Israel's War against Hez-
bollah).  



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS vol.13 (2013) 175–194 

184 

 In the next section the business cycle of chosen Central Eastern Europe-
an economies (Poland, Czech Republic, Hungary, Slovenia) is identified. 

4. Identification of Business Cycle in Central Eastern European 
(CEE) Economies in 1995−2013 Period 

 The data consists of seasonally adjusted6 monthly industry production 
index for a set of CEE economies from January 1995 to April 2013. These 
monthly series were taken from the OECD database. Our analysis is restrict-
ed to a subset of four CEE countries: Czech Republic, Hungary, Poland, 
Slovenia7. Log-transformed data along with seasonally adjusted data are 
displayed in Figure 2. It is seen that the economies experienced the trend 
break in 2008 referring to the raging financial crisis (subprime mortgage 
crisis). Specifically, the serious decline in the industry production index is 
apparent in the case of Czech Republic, Hungary and  Slovenia. In the case 
of Poland the impact of financial crisis on the industry production index was 
not so evident.  

Table 5. The ADF test results for industry production index (IPI) in a set of CEE 
countries  

Time series Lag 
ADF test for IPI   ADF test for ΔIPI  

without inter-
cept 

with intercept 
and trend 

without inter-
cept 

with intercept 
and trend 

Czech Republic 5 1.3983 
(0.96) 

–2.7621 
(0.2116) 

–4.4468 
(0.0000) 

–4.7682 
(0.0005) 

Hungary 5 2.3805 
(0.9962) 

–0.8783 
(0.9569) 

–4.5967 
(0.0000) 

–9.7907 
(0.0000) 

Poland 5 3.9040 
(0.9999) 

–2.7320 
(0.2235) 

–32319 
(0.0012) 

–8.7368 
(0.0000) 

Slovenia 5 1.0068 
(0.9178) 

–1.9891 
(0.6067) 

–6.3661 
(0.0000) 

–6.4719 
(0.0000) 

Note: in parentheses the p-values are given.  

 To test the non-stationarity of series the ADF test was applied. Table 5 
reports the results of the ADF unit root test for the logs of industry produc-
tion index (IPI) for levels and the first differences. For all IPI series in levels 
the null hypothesis of a unit root cannot be rejected ).05.0value( =>− αp  
The ADF results for first differences, ΔIPI, allow to reject the null hypothe-

                                                 
6 For seasonal adjustment the TRAMO/SEATS procedure was used.  
7 The intention of a research was to include all CEE economies. However, the final choice 

of countries was determined by the availability of data, i.e. sufficient length of time series.  



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DYNAMIC ECONOMETRIC MODELS vol. 13 (2013) 175–194 

185

sis ΔIPI~I(1) ).05.0value( =<− αp The results of the ADF test indicate that 
all industry production indexes under consideration are non-stationary in 
their levels and become stationary when they are first differenced. Hence, in 
further analysis the first differences of IPI for given CEE economies were 
used. 

 

Figure 2.  Industry production index in the CEE countries  

 To identify the business cycle of different CEE countries we applied the 
Markov switching model. The two-regime Markov switching model for in-
dustry production index modeled in first differences takes the form:  

),,0(~|,
1

, ttt sttt

q

j
jtsjst iidsyy σεεφμ +Δ+=Δ ∑

=
−  (4) 

where tyΔ  stands for first differences of the natural log of industry produc-
tion index for a given country (economy), 2

,, ,
t t ts j s sμ ϕ σ  − denote regime-

dependent intercept, autoregressive parameters and variance of disturbance 
term tε  respectively. The unobserved variable 1=ts  in the first regime (re-
cession) and 2=ts  in the second regime (expansion). 



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186 

 Like in the case of the MS-AR models for crude oil price, four type of 
Markov switching models were considered, i.e. MSI, MSIH, MSIA, 
MSIHA. The value of AIC and LL for different MS-AR models are reported 
in Table 6. 

Table 6.  The Akaike Information Criterion (AIC) and log-likelihood function (LL) 
for the univariate Markov switching model for industry production index 

Markov swi-
tching model 

Czech Republic Poland Hungary Slovenia 
LL AIC LL AIC LL AIC LL AIC 

MSI(2)–AR(1) 774.99 –1537.9 849.35 –1686.7 798.03 –1584.1 1055.4 –2098.9 
MSIH(2)–AR(1) 778.55 –1543.1 850.91 –1687.8 801.15 –1588.2 1056.0 –2088.0 
MSIA(2)–AR(1) 780.04 –1546.1 852.42 –1690.9 802.51 –1591.0 1055.6 –2097.2 

MSIHA(2)–
AR(1) 

784.92 1553.85 852.53 –1689.1 808.31 –1602.6 1061.1 –2106.2 
MSI(2)–AR(2) 804.30 –1594.6 876.61 –1739.2 807.19 –1600.4 1078.2 –2142.3 

MSIH(2)–AR(2) 811.06 –1606.1 879.28 –1742.6 822.95 –1629.9 1088.6 –2161.2 
MSIA(2)–AR(2) 814.48 –1611.6 893.47 –1768.9 828.67 –1639.3 1086.0 –2153.9 

MSIHA(2)–
AR(2) 

815.77 –1611.6 886.97 –1753.9 824.23 –1628.5 1097.5 –2174.9 

 
 The AIC criterion and LL function found the MSIHA(2)-AR(2) model to 
be the best for Czech Republic and Slovenia, and the MSIA(2)-AR(2) model 
− for Poland and Hungary (Table 6). The detailed estimation results for these 
models for the period January 1995 to April 2013 are displayed in Table 7. 
 While the parameter estimation is successfully made by the Markov 
switching models, it is worthwhile to make a more formal assessment of the 
performance of these models. Therefore, the formal testing for nonlinearity 
in the context of Markov switching models is carried out. The results of the 
Likelihood Ratio (LR) test indicate that the significant evidence of nonlinear 
behavior in series under consideration has been found (see Table 7). There-
fore the Markov switching model are considered to be attractive in address-
ing the nonlinear nature of studied series (especially their asymmetric beha-
vior).   
 The state of low economic activity (regime 1) is highly persistent in case 
of Poland )93.0( 11 =p  and relatively persistent in case of Czech Republic 
and Hungary 73.0( 11 =p  and 0.70 respectively) − see Table 7, with excep-
tion of Slovenia for which the probability of remaining in regime 1 is equal 

5.011 =p  what along with 49.012 =p  may indicate a  poor  model  specifica- 
  



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Table 7. The univariate Markov switching model for industry production index for 
chosen CEE countries  

Parameters Czech Rep. Poland Hungary Slovenia 

  Type of Markov switching model 

 
MSIHA(2)–

AR(2) MSIA(2)–AR(2) MSIA(2)–AR(2) MSIHA(2)–
AR(2) 

Regime-dependent intercept     

μ1 
–0.0036 
(0.0012) 

–0.0014 
(0.0005) 

–0.0011 
(0.0011) 

–0.0017 
(0.001) 

μ2 
0.0037 
(0.001) 

0.0051 
(0.0006) 

0.0045 
(0.0009) 

0.0025 
(0.0005) 

Regime-dependent autoregressive parameters 

φ1–1 
1.2943 

(0.0827) 
0.7356 

(0.0974) 
1.0516 

(0.1199) 
1.0107 

(0.1772) 

φ1–2 
0.8437 

(0.0894) 
0.9876 

(0.0754) 
0.8048 

(0.0799) 
1.3040 

(0.0588) 

φ2–1 
–0.2759 
(0.0951) 

–0.4848 
(0.0829) 

–0.0706 
(0.0527) 

–0.8902 
(0.1948) 

φ2–2 
–0.6406 
(0.0698) 

–0.6155 
(0.0739) 

–0.6188 
(0.0928) 

–0,4957 
(0.0567) 

Regime-dependent variances     
σ21 

0.0056 
(0.0005) 

0.0034 
(0.0002) 

0.0049 
(0.0003) 

0.005 
(0.0015) 

σ22 
0.0042 

(0.0005) – – 0.0014 
(0.0001) 

LL 815.77 893.47 828.67 1097.5 
AIC –1611.6 –1768.9 –1639.3 –2174.9 

LR test 22.95 
(p=0.0008) 

33.72 
(p=0.000) 

31.28 
(p=0.000) 

34.47 
(p=0.000) 

Jarque–Bera test 5.549 
(p=0.0624) 

3.360 
(p=0.186) 

14.84 
(p=0.0006) 

3.516 
(p=0.172) 

RCM 62.28 10.16 58.37 6.66 
Transition probabilities     

p11 0.7309 0.9205 0.7026 0.5005 
p22 0.8094 0.9619 0.8648 0.9782 
p12 0.2691 0.0795 0.2974 0.4995 
p21 0.1906 0.0381 0.1352 0.0218 

Average duration of regime     
d(i)1 3.72 12.58 3.36 2.00 
d(i)2 5.25 26.25 7.40 45.87 

Note: in parentheses the standard errors of parameter estimates are given.  



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS vol.13 (2013) 175–194 

188 

tion8. What is interesting the RCM statistic (see Table 7, RCM=6.66 is sub-
stantially below 50) seems to indicate something opposite, i.e. that 
MSIHA(2)-AR(2) model for Slovenia performs well in distinguishing be-
tween two regimes. However, it should be noted that a low value of the 
RCM statistic does not necessarily imply that the switches are correctly pre-
dicted, but only that they are sharp, with a small frequency of periods of 
uncertainty on the nature of regimes (Guidolin, 2011). The regime 2 (expan-
sion) is highly persistent for all countries. In the recessionary periods the 
industry production index tends to decrease )0( 1 <μ  whereas in the expan-
sionary periods − tends to increase 2( 0)μ >  for all considered countries. The 
volatility of industry production index is higher in the regime 1 (recession) 
than in regime 2 (expansion) for Czech Republic and Slovenia ).( 2

2
2
1 σσ >

The duration of recessions and expansions is asymmetric for all countries, 
e.g. the duration of expansions is about twice as long as the recession state 
(except Slovenia) − see Table 7.   
 Smoothed probabilities of being in a given regime are calculated (see 
Figure 3) and every observation is assigned to a given regime according to 
the highest smoothed probability. For the case of two regimes, the rule re-
duces to assigning the observation to the first regime if 5.0)|1Pr( >= Tt Ys  
and assigning it to the second regime if .5.0)|1Pr( <= Tt Ys Corresponding 
dating of business cycle in studied countries is given in Table 8.   
 According to the classical methodology of NBER (National Bureau of 
Economic Research) the U.S. economic recession occurred in 2001 (collapse 
of the Dot-com bubble, March 2001 to December 2001) and in 2007−2009 
period (subprime mortgage crisis, December 2007 to July 2009)9. The 
smoothed probabilities of being in a recession (Figure 3) obtained with the 
Markov switching models indicate that in case of Hungary and Poland the 
financial crisis affected these economies. The impact of the dot-com crisis 
has been demonstrated in the case of Hungary and Poland (see Figure 3 and 
Table 8). Generally, dating of business cycle obtained with the MS-AR 
models is partly consistent with the dating of world economic recession ob-
                                                 

8 In order to find a better specification with more plausible values of transition probabili-
ties we tried out different model specifications (see Table 6). Only for the MSIA(2)-AR(1) 
model the reasonable values of p11 and p12 were obtained, i.e. 0.74 and 0.26 respectively. 
However, simultaneously the RCM statistic took the higher value, RCM=36.06,  and what it 
is more important the switches between regimes occurred very often what indicates the diffi-
culties in distinguishing between two regimes. Therefore the results for Slovenia seem rather 
implausible and should be taken with caution.    

9 See: http://www.nber.org/-cycles/cyclesmain.html. 



Synchronization of Crude Oil Price Cycle and Business Cycle... 

DYNAMIC ECONOMETRIC MODELS vol. 13 (2013) 175–194 

189

tained with the NBER methodology, however there are other recessionary 
periods which are country specific, e.g. Poland.  

 

Figure 3.  Smoothed probabilities of being in a recession for industry production 
index in chosen CEE countries  

 Whereas for Poland the univariate MS-AR model seems to capture rela-
tively well the different recessionary periods, in the case of Czech Republic 
and Hungary the MS-AR model delivers the worst fit, with difficulties dis-
tinguishing clearly the recessionary periods (switches between regimes occur 
very often). Besides, the RCM statistic (higher than 50, see Table 7) in the 
case of Czech Republic and Hungary suggests rather that the chosen Mar-
kov-switching models are not able to distinguish between two regimes and 
as a result the existence of two regimes is doubtful (additionally, the model 
evaluation is weaken by the fact that the standarized residuals are not stand-
ard normally distributed − see Table 7). Only in the case of Poland the Mar-
kov-switching model can clearly differentiate one regime in each period 
considered (RCM statistic substantially below 50 and normal distribution of 
residuals − see Table 7).   
  



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS vol.13 (2013) 175–194 

190 

Table 8. Dating of business cycle (recessions) for considered Central Eastern Euro-
pean economies and crude oil price cycle (drops in oil prices), 1995−2013 

Oil price cycle 
(drops in oil prices) 

Business cycle (regime 1 − recession) 
Czech Rep. Poland Hungary Slovenia 

1997(11)–2001(11) 
2006(08)–2006(12) 
2008(07)–2009(02) 

1995(4)–1995(5) 
1995(9)–1995(11) 
1997(7)–1997(9) 

1997(12)–1998(10) 
1999(8)–1999(11) 
2000(3)–2000(6) 

2001(2)–2001(10) 
2003(2)–2003(2) 

2003(10)–2004(3) 
2004(7)–2004(10) 
2005(8)–2005(10) 
2006(5)–2006(12) 
2007(12)–2008(2) 
2008(5)–2008(11) 
2009(1)–2009(2) 
2010(5)–2010(5) 

2012(2)–2012(10) 

1998(5)–1999(1) 
2000(10)–

2002(4) 
2004(5)–2005(2) 
2008(2)–2009(1) 
2012(1)–2013(4) 

1995(9)–1995(10) 
1997(8)–1997(10) 
1999(7)–1999(9) 
2000(4)–2000(8) 
2001(5)–2001(6) 
2001(9)–2001(11) 
2008(3)–2008(12) 
2009(2)–2009(4) 
2011(3)–2011(6) 
2012(3)–2012(7) 
2012(9)–2012(10 

1996(9)–1996(9) 
1997(9)–1997(9) 
2008(11)–2009(2) 

 
 In order to evaluate the extent to which turning points in the two series 
occur near each other and to evaluate synchronization of cycles the correla-
tion of business cycle in given countries and crude oil price cycle and con-
cordance index respectively have been calculated10. For the comparison pur-
poses these calculations are carried out for all chosen countries, although 
only in the case of Poland they are sensible.   
 The correlation coefficients between probabilities of being in regime 1 
(recession and drops in oil prices for business cycle and crude oil price cycle 
respectively) are displayed in Figure 4.  
Generally, the correlations between probabilities of being in regime 1  (Fig-
ure 4) are weak what means that turning points of business cycle in the re-
cessionary periods does not occur close to turning points of crude oil price 
cycle. The highest correlation of business cycle and oil price cycle is ob-
served in the case of Poland (32%), and the lowest − in the case of Slovenia 
(10%). 

                                                 
 10 Harding, Pagan (2006) and Konopczak (2009) indicate that the correlation coefficient 
and concordance index are the most frequently used measures of the synchronization of cy-
cles identified by the Markov-switching model.  



Synchronization of Crude Oil Price Cycle and Business Cycle... 

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191

 

Figure 4. Correlation coefficients for probabilities of being in regime 1 for business 
cycle in given countries and crude oil price market in 1995–2013 period  

Table 9. Concordance index for oil price cycle and business cycle for given econo-
mies 

 
Crude oil price cycle vs. business cycle 

Czech Republic Poland Hungary Slovenia 
Concordance 

index 0.7143 0.6866 0.7051 0.7235 

 
 To evaluate synchronization of business cycle for different economies 
and oil price cycle the concordance index was applied. This index (for two 
series ,tx  ty  and a sample size of T ) takes the form (Harding, Pagan, 
2006):   

1 1

1 (1 )(1 ) ,
T T

xt yt xt yt
t t

I S S S S
T = =

⎡ ⎤
= + − −⎢ ⎥

⎣ ⎦
∑ ∑   (5) 

where xtS  and ytS denote binary variables that takes the value unity in case 
of recession regime and zero − in case of expansion regime at time .t  
 Values of concordance index measuring the synchronization of cycles (in 
terms of being in the same state) indicate a high degree of concordance of 
the business cycles and oil price cycle (Table 9). However, having in mind 
earlier remarks on the quality of regime classification, the above conclusion 
refers only to the case of Poland. This means that business cycle in Poland in 
1995−2013 period has the same state (recession or expansion) as the Brent 
oil price cycle (drops or rises in oil prices). Even in that case the caution 

 

0,2928
0,3174

0,2784

0,1012

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

Czech Republic Poland Hungary Slovenia



Andrzej Geise, Mariola Piłatowska 

DYNAMIC ECONOMETRIC MODELS vol.13 (2013) 175–194 

192 

should be taking when interpreting the results because a low value of corre-
lation coefficients corresponds to a high degree of concordance of business 
cycles and oil price cycle. This may suggest the overestimated degree of 
concordance.  

Conclusions 
 In this paper we used the approach innovated by Hamilton in his analysis 
of the US business cycle to identify the Brent crude oil price cycle and busi-
ness cycles in a set of CEE economies in 1995−2013 period. The obtained 
results support to a varying degree our modelling approach based upon 
Markov-switching. The MSIH(2)-AR(2) model produced the sharpest classi-
fication of regimes (drops or rises in oil prices) was obtained in the case of 
crude oil price cycle. While the MSIA(2)-AR(2) model produced the sharp-
est classification of regimes (recession on expansion) for Poland. In the case 
of Czech Republic and Hungary the MS-AR models were not able to distin-
guish between two regimes (switches between regimes occurred very often) 
and as a result the existence of two regimes is doubtful. The MS-AR models 
obtained for Slovenia indicated either a poor model specification or difficul-
ties in distinguishing between two regimes. Therefore the results for Slove-
nia should be taken with caution.  
 Our results indicated that the MS-AR models captured the different re-
gimes of Brent crude oil price cycle and business cycle for the case of Po-
land in a satisfactory way. The correlation of oil price cycle and business 
cycle in Poland turned out to be rather weak, however the synchronization of 
cycles occurred (a high degree of concordance) what indicates that there are 
co-movements in crude oil cycle and business cycles. Week correlation of 
oil price cycle and business cycle may come from the specificity of Poland, 
i.e. the size of crude oil imported by these countries from the North Sea re-
gion is small (in Poland the import of crude oil from Norway amounts to 
3.5% of total crude oil import; POPiHN, 2013). Poland but also the other 
CEE countries are still dependent on the crude oil imported from Russia 
which is cheaper but worse in quality (it contains a high amount of the impu-
rity sulfur and has high density).  

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Z a r y s  t r e ś c i. Głównym celem artykułu jest zbadanie, w jakim stopniu cenowe cykle 
ropy naftowej (Brent) są skorelowane i zsynchronizowane z cyklem koniunkturalnym dla 
wybranych gospodarek państw Europy Środkowo-Wschodniej (EŚW). W celu identyfikacji 
cyklu cenowego ropy naftowej i cyklu koniunkturalnego został zastosowany przełącznikowy 
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S ł o w a  k l u c z o w e: przełącznikowe modele Markowa, ceny ropy naftowej, cykle ko-
niunkturalne, cykle cenowe.  




