



































DYNAMIC ECONOMETRIC MODELS


© 2016 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.2016.008  Vol. 16 (2016) 145−164 

Submitted November 8, 2016  ISSN (online) 2450-7067 

Accepted December 21, 2016 ISSN (print) 1234-3862 

Magdalena Osińska, Tadeusz Kufel,  

Marcin Błażejowski, Paweł Kufel
*
 

Modelling and Forecasting Business Cycle in CEE 

Countries using a Threshold Approach
 

A b s t r a c t. We propose to apply a time-series-based nonlinear mechanism in the threshold 

autoregression (TAR) form in order to examine business cycles in Central and Eastern Euro-

pean economies and compare them to the entire EU business cycle. The threshold variables, 

such as consumer price index, short and long interest rates, unemployment rate and an ex-

change rate vs. the U.S. Dollar, have been considered. The purpose of the paper is to model 

and to predict business cycles in Central and East European (CEE) economies (the EU Mem-

ber States) and compare them to business cycles of the entire EU28 area and Eurozone EU19. 

We found that the exogenous mechanism played an important role in diagnosing the phases of 

business cycles in CEE economies, which is in line with the entire EU economic area. The 

results of business cycle forecasting using bootstrap technique are quite promising, while 

bootstrap confidence intervals are used for diagnosis. 

K e y w o r d s: business cycle, central and eastern economies, threshold models, forecasting, 

bootstrap 

J E L Classification: C24, C53, E32. 

                                                 
* Correspondence to: Magdalena Osińska, Nicolaus Copernicus University, Faculty of 

Economic Sciences and Management, 11A Gagarina Street, 87-100 Toruń, Poland, e-mail: 

emo@umk.pl; Tadeusz Kufel , Nicolaus Copernicus University, Faculty of Economic Scienc-

es and Management, 11A Gagarina Street, 87-100 Toruń, Poland, e-mail: tadeusz.ku-

fel@umk.pl; Marcin Błażejowski, WSB University in Toruń, e-mail: marcin.blaze-

jowski@wsb.torun.pl; Paweł Kufel, WSB University in Toruń, e-mail: pawel.ku-

fel@wsb.torun.pl. 
 This work was financed from National Center of Science – Grant No 

2012/07/B/HS4/02927. 



Magdalena Osińska, Tadeusz Kufel, Marcin Błażejowski, Paweł Kufel 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

146 

Introduction  

 The purpose of the paper is to model and predict a business cycle in Cen-

tral and East European (CEE) economies (the EU Member States) and to 

compare it to the business cycle of the entire EU28 area and Eurozone 

EU19. Our analysis is based on the theory of economic convergence, intro-

duced by Barro, Sala-i-Martin (1992); however, newest empirical facts re-

sulting from the economic crisis of the recent years have been taken into 

consideration, too. For at least two last decades, it has been assumed that 

Central and Eastern European Economies have undergone the process of 

catching up with the most developed Western European Economies. Since 

2004 (as well as before), huge structural funds have been spent to speed up 

the entire process of economic unification of the EU area. Common currency 

– the Euro – has become one of the symbols of the unification. At present, 

19 of 28 economies use this currency, eliminating one of the internal risk 

factors but exposing themselves to the external ones. However, the economic 

crisis of 2007–2009 has broken the process of economic convergence and 

reveals many differences among the countries. It is worth noting that, after 

2004, Central and East European (CEE) countries usually experienced 

a sigma-type convergence and a conditional beta-type convergence (see 

Kluth, 2016). 

 In recent literature, two important issues can be found. The first is relat-

ed to the problem of economic convergence and divergence (decoupling). 

The hypothesis of decoupling between business cycles in the developed and 

emerging countries after 2009 has become the subject of a widespread aca-

demic debate. In their paper, Claassen, Kabundi, Loots (2013) stated that 

decoupling between advanced and emerging economies took place, but in 

recent years the process of re-coupling has started. Kawa (2013) demonstrat-

ed that regardless the fact that many CEE countries introduced the defense 

mechanisms against the shocks to their regulation systems in the 90s, they 

remain vulnerable to the external debt, budget deficit and foreign trade im-

balance. Stańczyk, Wyrobek (2013) have analyzed the issue of business 

cycle synchronization between the USA and emerging economies in 1995–

2009. The authors concluded that no evidence was found that emerging 

economies as a whole and in subgroups had their business cycles synchro-

nized. However, cycles in many emerging economies were more synchro-

nized with the US economy, particularly at the time of the global economic 

crisis. They also stated that unexpected and unusual phenomena like global 

crises, disrupted the relationships among the economies observed in a “nor-

mal” state of development. 



Modelling and Forecasting Business Cycle in CEE Countries… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

147 

 The second issue – more recent and yet more open to questions – is fo-

cused on the problem of the so-called “middle-income trap”. Our choice of 

the Central and Eastern Economies has been motivated by the fact that they 

are threatened by what has become known as the middle-income trap. This 

means that compared to the richest economies, their per-capita income stays 

low and there is little chance to overcome this difficulty. Spence (2011) re-

fers to the middle-income countries as to those in the 5,000–10,000 USD 

range of per capita income. He indicates that in developing countries “the 

industries that drove the growth in the early period start to become globally 

uncompetitive due to rising wages”. Among the CEE countries, only Bulgar-

ia and Romania entered this range in 2015. The countries analyzed in-depth 

in the paper have their GDP per capita above 10,000 USD, but some of 

them, particularly Poland, Hungary and Slovakia, are not very far from this 

limit. The concept of middle-income trap is still a subject of the economic 

debate. Recently, it has been widely discussed in Im, Rossenblatt (2015). If 

the middle-income trap is what the developing European economies are try-

ing to avoid, they should speed up the catching up process by undertaking 

intensive reforms. That is why the business cycle forecasts must be taken 

into account.  

 Our research is a part of a bigger project and it has been preceded by 

earlier reports. Osińska, Kufel, Błażejowski, Kufel (2016a) have examined 

the business cycles synchronization within the EU economies in comparison 

to the U.S. and Japan, using spectral analysis methodology. Both the quarter-

ly and monthly data has been analyzed, supporting the same results. They 

found that most European countries, including the CEE countries, had their 

economic cycles synchronized with the entire EU. Only Hungary represent-

ed the opposite case. As for the U.S.A. and Japanese business cycles, the two 

were more synchronized together compared with the EU. In the paper by 

Osińska, Kufel, Błażejowski, Kufel (2015), a business cycle clock method-

ology for the same economies has been applied. In the paper by Osińska, 

Kufel, Błażejowski, Kufel (2016b) the threshold autoregression models 

(TAR) has been applied to reveal the most likely threshold mechanisms, 

which underlie the business cycles in the EU economies. The concept that 

debt/GDP ratio could be the indicator of the changes between the business 

cycle phases, has been rejected.  

 In the reported research, the quarterly data of 1995–2014 were analyzed. 

The gross domestic product (GDP) growth rate was traditionally used as the 

business cycle measure. The following research questions have been formed: 

which threshold variable(s) help to reveal a threshold mechanism within the 

business cycles observed in Central and Eastern European economies; what 



Magdalena Osińska, Tadeusz Kufel, Marcin Błażejowski, Paweł Kufel 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

148 

is the scope of differences between the regimes, what is the forecasting abil-

ity of the estimated TAR models and what similarities/differences between 

the observed countries can be indicated. The methodology assumes using 

a stationary TAR model as the basis for applying bootstrap technique. The 

threshold variable prediction was a key factor in the entire procedure. Boot-

strap confidence intervals have been used for ex ante forecast evaluation. 

The novelty of the paper lies in defining a simulation-based procedure for 

forecasting TAR models and its application to the business cycle in CEE 

countries.  

 The paper is organized as follows: in Section two, the data has been ana-

lyzed from both perspectives: the economic convergence process and busi-

ness cycle analysis; in Section three, the research methodology has been 

described. In Section four, the empirical results have been presented. In Sec-

tion five the conclusion is summarised.   

1. Characteristics of the Data 

One of the most popular perspectives of classification of economies is based 

on the criterion of initial wealth measured by the GDP per inhabitant. The 

initial wealth is crucial for understanding the individual process of economic 

development and the final stage proves the convergence of a given economy 

along its long-run path. As it has been already mentioned, the process of 

catching up may be slowed down while the country experiences the middle-

income trap. The new EU Member States that belong to the Central and 

Eastern European group are Bulgaria, The Czech Republic, Estonia, Croatia, 

Hungary, Lithuania, Latvia, Poland, Romania, the Slovak Republic and Slo-

venia. In the beginning of the analyzed period i.e., in 1995, all these coun-

tries had their GDP per inhabitant below 10,000 USD, while in 2015 only 

Bulgaria and Romania had the GDP per capita remaining below this limit. In 

the same year, Slovenia’s GDP, with its 20,713.1 USD (in current prices), 

surpassed Portugal and Greece, where both countries were included in the 

group EU15. This means that some of the newest EU Member States that 

acceded the EU in 2004, managed to make a successful progress in the pro-

cess of economic convergence, measured by the dispersion from the average 

level. This process was broken by the recession of 2007–2009, when each 

country was faced with its own economic decisions being more or less in 

line with the EU economic policy (Osińska and Kluth, 2011). Countries like 

Poland and Hungary, with their GDP p.c. equal to 12,494.5 USD and 

12,259.1 USD, respectively, may be concerned about the middle-income trap 

unless the structure of the productive sectors of the economies will change. 



Modelling and Forecasting Business Cycle in CEE Countries… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

149 

Slovakia with the GDP p.c. of 15,962.6 USD, seems to be more resistant and 

similar to the Czech Republic and Estonia, where the GDP p.c. exceeds 

17,000 USD. 

The study uses quarterly data from 1995–2014, taken from the OECD data-

base study. In several cases, some data were not complete, therefore, we 

decided to limit our investigation to the countries where databases were as 

broad as possible. Thus, the following countries have been examined: the 

Czech Republic, Estonia, Hungary, Poland, Slovakia and Slovenia. The 

mechanism of the creation of economic cycle in these countries has been the 

subject of comparison with both the entire EU28 and the entire Eurozone 

EA19.  

 The figure 1 shows the business cycle dynamics for three selected coun-

tries and the EU28. 

EU28 Hungary 

  
Poland Slovenia 

  

Figure 1. Business cycles in selected CEE countries and in the EU28 

 The original GDP series (seasonally adjusted) has been transformed for 

extracting a business cycle by taking logs and filtering by the Hodrick-

Prescott filter with the smoothing parameter equal to 1,600 (Hodrick, Pres-

cott, 1997). In Figure 1, the differences among selected countries, consider-

ing the amplitude and phase of the cycle, can be noticed. 

 In the threshold autoregression (TAR) models, the assumption of thresh-

old variable is of key importance. In our study, we assumed that the set of 



Magdalena Osińska, Tadeusz Kufel, Marcin Błażejowski, Paweł Kufel 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

150 

exogenous thresholds consists of the following: the consumer price index, 

short interest rate, long interest rate, unemployment rate and exchange rate. 

The choice of variables has been determined by data availability and their 

relation to business cycle analysis. It can be mentioned that when compared 

to the reference variable, namely the GDP growth rate, the CPI and long 

interest rate are considered as exhibiting the same changes over time, while 

the short interest rate and exchange rate are leading indicators for the cycle. 

The reaction of the unemployment rate usually lags behind. These assump-

tions are empirically verified; however, they may differ among the countries 

(Zarnowitz, 1999). 

 All these series were checked for stationarity using the ADF/KPSS ap-

proach and finally they were taken at both levels (I(1)) and (I(0)). 

2. The Model and Forecasting Procedure 

The threshold autoregression models have been applied to the U.S. business 

cycle modeling by Tong (Tong, 1990). Recently, their particular assessment 

of economic growth has been determined in the publications such as by  and 

Niebuhr, 2005 who shed the light on the regional perspective of growth in 

Germany and al., 2013, who introduced a dynamic panel threshold model to 

estimate inflation thresholds for a long-term economic growth, to mention 

only a few. In our research, TAR models have been used as well because 

that allows considering different threshold variables as playing a possible 

rule in regime changes.  

When the lagged endogenous variable is a threshold variable, the model is 

known as a self-exciting threshold autoregression (SETAR). This difference 

allows identifying exogenous or endogenous mechanism of changes between 

the regimes that correspond to business cycle phases. This interpretation 

coincides with the endogenous and exogenous growth idea in economics.

 Let tY  denotes k-dimensional random vector. The model of the follow-

ing form: 

tttt J
t

J
t

J
t

J
t CHYAYBY   1 , (1) 

where tJ
 
is a random variable taking values of finite set of natural numbers  

 p,...,3,2,1 , tJ
B , tJ

A , tJ
H  are kk – dimensional matrices of the coeffi-

cients, t  is the k – dimensional white noise, tJ
C  is a constant vector is 

called a canonical form of the threshold model. It defines a wide class of the 

models depending on the choice of  tJ .  



Modelling and Forecasting Business Cycle in CEE Countries… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

151 

 When tJ  is the function of an exogenous variable, say, 
t

X  
),,1},{( miXX itt 
 

then we obtain a TAR model. The 

TAR(              ) model is defined in the following way: 

t
j

k

i

it
j

i
j

t hYY
j

  




1

0  (2) 

conditionally on pjRX jdt ,...,1,  . The dtX   
is called a threshold varia-

ble. The more convenient form of presenting (2) is as follows: 

 




























1110

21
22

1
2
1

2
0

1
11

1
1
1

1
0

...

...

...

22

11

pdtt
p

kt
p

kt
pp

dttktkt

dttktkt

t

rXforhYY

rXrforhYY

rXforhYY

Y

pp







 (3) 

In a SETAR model the threshold variable is lagged endogenous variable 

namely,
 tY . It is useful to present the two regimes model with  the I(x) func-

tion of the form: 

 













01

00

dt

dt

xwhen

xwhen
xI  (4) 

and the corresponding TAR(2, k1, k2) model 

 
 

    tdtktkt

ktktt

XIYY

YYY













22110

11110

...

...
. (5) 

If all k10 ,...,β,ββ
 
parameters are zeros then (5) becomes the linear auto-

regressive model. When the autoregressive model is considered, its 

stationarity becomes the crucial point. For the linear autoregressive model, 

the conditions of stationarity are well known and easy to satisfy (see: 

Greene, 1993). In the case of SETAR or TAR, the problem is much more 

complicated. Even stationary models within the regimes do not guarantee the 

stationarity of the whole system. Giordano, Niglio and Vitale (2012) ana-

lyzed this problem, basing it on the papers by Petruccelli and Woolford 

(1984) and Chan et al. (1985). 

In the case of two regime SETAR model (3) when k is greater than 1, the 

following stationarity conditions must be satisfied (An, Huang, 1996; 

Lin, 1999):  



Magdalena Osińska, Tadeusz Kufel, Marcin Błażejowski, Paweł Kufel 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

152 













k

i

j
ij

k

i

j
ij

a

a

1

)(

1

)(

.1||max

1||max

 

 Estimation of TAR/SETAR models can be done by conditional ordinary 

least squares or maximum likelihood methods. However, the forecasting is 

more complex. First of all, it is important to determine the predicted values 

of the threshold variable in the forecasting possibility. For this reason, we 

started our procedure for the TAR models first because they underlay the 

exogenous threshold mechanism.  

 Our proposal consists of the application of a simulation methodology for 

forecasting both: the threshold variable 
dt

X


 as well as the endogenous var-

iable tY , which is the which is the business cycle (as presented in Figure 1). 

The idea of forecasting TAR models has been developed by Brown and 

Mariano (1984). Forecasting procedure proposed and applied in this paper 

has been presented in Gretl environment (Threshold_Models package). It is 

based on the already-estimated TAR model and it is implemented in one of 

the two common simulation approaches, i.e., the bootstrap simulation tech-

nique (see Dvison et al., 1986) or Monte Carlo method (see Rubinstein and 

Kroese, 2011). A simulation-based forecasting procedure applies to both 

endogenous and threshold variables, but the starting point is to simulate the 

possible paths of the threshold variable. The whole procedure is carried out 

in the following steps: 

1. Estimation of the predictive model for the threshold variable. The 

SARIMA(p,d,q)(P,D,Q) approach with the specification selection based 

on the Schwarz information criterion (BIC) is applied. 

2. Generating a noise for the simulation procedure: 

 when in the bootstrap approach, residuals from estimated SARIMA 

model are used (empirical distribution), 

 when in the Monte Carlo approach, random numbers are drawn from 

one of the theoretical distributions, i.e., normal or t-Student with 

a mean of zero and a standard deviation equal to the value from the 

estimated SARIMA model. 

3. Addition of Phase Noise to the values of threshold variable, re-

estimation of the SARIMA model and prediction of the threshold varia-

ble for h periods ahead. 



Modelling and Forecasting Business Cycle in CEE Countries… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

153 

4. Determination of regimes in which the endogenous variable will be in 

the future (on the basis of the threshold variable forecasts generated in 

the previous stage). 

5. Usage of the already-estimated TAR model to generate forecasts of the 

endogenous variable. 

6. Stages 2–5 are repeated N times. 

3. The Empirical Results 

 The following quarterly data from 1995–2014 are included and have 

been analyzed (short names are given in brackets): the GDP growth rate 

(GDP), unemployment rate (UEMP), interest rates (long IR and short IR), 

CPI and first differences of CPI, exchange rates in USD (EXR) and its first 

differences. It was assumed that the GDP growth rate was the endogenous 

variable and the remaining lagged variables were supposed to be thresholds 

for regime changes. The regimes correspond to the phases of economic cy-

cle. To eliminate non-stationarity, the original GDP series were de-trended 

using HP filter where λ=1600.  

 All the original data were seasonally adjusted, transformed into logs and 

tested for stationarity using ADF-GLS and KPSS tests. The number of re-

gimes was restricted to maximum three for the following reasons: the rela-

tively short time series and reasonable interpretation of the business cycle in 

case of prosperity, recession and the intermediary states of increasing and 

decreasing of the GDP. The number of regimes has been chosen based on 

the quartiles of the threshold variable. In practice, the following model has 

been considered:  























2
3

1
3
1

3
0

21
2

1
2
1

2
0

1
1

1
1
1

1
0

33

22

11

rXforGDPGDP

rXrforGDPGDP

rXforGDPGDP

GDP

dttktkt

dttktkt

dttktkt

t













 

where a set of threshold variables 
dt

X


 is the same as it was described at the 

beginning of this section. As many threshold models were to be estimated 

we decided to use  Bayesian Information Criterion (BIC) for the model se-

lection. The results of model selection are presented in Tables 1, 2 and 3.   
  



Magdalena Osińska, Tadeusz Kufel, Marcin Błażejowski, Paweł Kufel 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

154 

Table 1: Values of Schwartz criterion and threshold values for Czech Republic, 

Estonia and Hungary 

 Czech Rep. Estonia Hungary 

 BIC threshold BIC threshold BIC threshold 

EXR –522,202 20,314    –558,056 176,364 
d_EXR –520,460 –0,042    –540,131 –0,032 

CPI –522,902 1,757 –307,094 3,057 –544,147 6,906 
d_CPI –527,509 –0,018 –292,824 –0,02 0,020 –542,474 –0,01 0,010 
longIR –372,092 3,502    –395,920 7,469 

d_longIR –374,295 –0,001    –392,023 –0,001 
shortIR –522,206 3,843 –364,478 3,968    

d_shortIR –519,079 –0,001 –344,437 –0,004    
UNEMP –416,655 7,283 –265,276 7,474 –409,457 7,382 

d_UNEMP –408,035 –0,245 –270,077 –0,89 0,383 –398,233 0,040 
SETAR –522,752 –0,005 –371,486 –0,002 –525,239 –0,001 
sd_EXR –469,528 26,594    –456,666 174,182 

sd_d_EXR –471,243 –0,012    –450,686 0,015 
sd_CPI –469,097 1,757 7,689 –272,050 3,057 –453,485 6,906 

sd_d_CPI –472,006 –0,018 –250,539 –0,020 –450,934 –0,012 
sd_longIR –355,049 4,193    –351,032 6,807 

sd_d_longIR –346,873 –0,003    –341,508 –0,001 
sd_shortIR –475,691 2,090 9,762 –314,583 3,955 6,359    

sd_d_shortIR –477,825 –0,004 –301,225 –0,001    
sd_UNEMP –392,193 6,709 –225,906 10,154 –359,549 7,400 

sd_d_UNEMP –382,344 –0,245 –224,844 –0,140 –350,690 0,040 
sd_SETAR –464,230 –0,023 –309,123 –0,016 –438,251 –0,001 

Note:  BIC – value of Schwarz criterion, treshold – value of threshold (if one value is given means model 
with 2 regimes, if 2 values id given means model with 3 regimes), the best value of BIC for each country 

has been bolded, d_ – means first differences, sd_ – means seasonal differences. 

Empirical analysis of business cycles in CEE countries has revealed the most 

likely threshold variables in the countries in terms of interest. These are: the 

CPI in the case of Slovenia and ΔCPI in the case of the Czech Republic, 

a short interest rate in the case of Estonia and the exchange rate against the 

USD for the other four cases, i.e., Hungary, Poland, the EU28 and the EU19. 

In the case of Slovak Republic, the difference in the exchange rate has been 

indicated. It shows the importance of the exchange rate channel in the risk 

exposure of such economic bodies as the European Union and its Member 

States. The two other countries were more sensitive to the consumer price 

changes and the last one, namely, Estonia, to the monetary policy changes. 

Obviously, the statistical identification of the thresholds may be limited by 

the availability of data, but the most likely differences for the mechanism 

change within similar economic system area is interesting. The level of eco-

nomic development of particular EU countries remains still diversified and 

determines the expected results. For these reasons, we assumed the same set 



Modelling and Forecasting Business Cycle in CEE Countries… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

155 

of threshold variables that were the subject of testing for the GDP growth 

rate. Tables 4 and 5 present the estimated TAR models for selected thresh-

olds. 

Table 2: Values of Schwartz criterion and threshold values for Poland, Slovak Re-

public, Estonia and Slovenia 

 Poland Slovak Rep. Slovenia 

 BIC threshold BIC threshold BIC threshold 

EXR –498,012 2,772 –449,867 0,759 –502,767 0,763 0,803 
d_EXR –493,983 0,006 –457,259 –0,009 –509,749 –0,03 –0,01 

CPI –491,671 4,224 –447,620 2,882 –519,869 5,641 
d_CPI –492,383 –0,035 –451,712 –0,01 0,014 –500,665 –0,018 
longIR –357,629 5,750 –306,867 4,640 –291,729 4,647 

d_longIR –357,032 –0,004 –273,577 –0,001 –294,096 –0,001 
shortIR –492,587 4,590 20,660   –312,699 3,697 4,728 

d_shortIR –500,652 –0,013   –294,841 0,000 
UNEMP –491,760 13,031 –444,902 12,354 –378,125 6,025 

d_UNEMP –490,523 –0,410 –439,242 –0,392 –382,968 –0,256 
SETAR –480,468 0,002 –450,458 –0,004 –475,356 –0,003 
sd_EXR –423,530 3,175 3,824 –400,520 0,762 –422,020 0,800 

sd_d_EXR –426,900 –0,023 –389,912 –0,032 –416,761 –0,007 
sd_CPI –421,851 2,084 13,050 –388,697 3,009 5,655 –416,292 6,562 

sd_d_CPI –428,644 –0,036 –389,507 –0,030 –425,120 –0,008 
sd_longIR –309,168 5,232 –255,755 4,640 –264,005 4,647 

sd_d_longIR –307,192 –0,004 –253,535 –0,001 0,002 –259,146 –0,004 
sd_shortIR –436,382 6,883 21,770    –265,775 3,697 

sd_d_shortIR –425,519 –0,012    –267,981 –0,003 
sd_UNEMP –423,913 10,022 –389,320 12,377 –333,151 6,025 

sd_d_UNEMP –422,224 –0,410 –388,072 –0,099 –325,931 –0,256 
sd_SETAR –412,556 –0,013 –381,351 –0,010 –397,089 0,004 

Note:  BIC – value of Schwarz criterion, treshold – value of threshold (if one value is given means model 

with 2 regimes, if 2 values id given means model with 3 regimes), the best value of BIC for each country 
has been bolded, d_ – means first differences, sd_ – means seasonal differences. 

Only in one case, i.e., the EU28, a three-regime model has been selected. In 

the other cases, two-regime models have been preferred for the data. Figure 

2 illustrates the “goodness-to-fit” calculator of the empirical TAR model. 

which is very good in all cases. 
  



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DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

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Table 3: Values of Schwartz criterion and threshold values for European Union and 

Euro Area 

Note:  BIC – value of Schwarz criterion, treshold – value of threshold (if one value is given means model 

with 2 regimes, if 2 values id given means model with 3 regimes), the best value of BIC for each country 
has been bolded, d_ – means first differences, sd_ – means seasonal differences. 

Table 4: Estimated threshold models with lowest BIC values for Czech Rep., Esto-

nia, Hungary and Poland 

 
Czech Rep.  
d_CPI (–4) 

Estonia 
shortIR (–3) 

Hungary 
EXR(–3) 

Poland  
EXR(–3) 

r1 const –0,006*** 0,002 –0,002 –0,003 
  r1 Yt–1 1,133*** 0,518*** 0,61*** 0,167 
  r1 Yt–2 –0,533*** 0,898***   
  r1 Yt–3  –0,016   
  r1 Yt–4  –0,539***   

r2 const 0,001 –0,005* 0,000 0,001 
  r2 Yt–1 1,313*** 0,951*** 1,312*** 0,841*** 
  r2 Yt–2 –0,413*** 0,294* –0,175  
  r2 Yt–3 0,091 –0,476*** –0,34***  
  r2 Yt–4 –0,025    
    r2 Yt–5 –0,177***    

Note:  *** – 1% significance level, ** – 5%  significance level, * – 10%  significance level, r1 means 
regime 1, r2 – regime 2, r3 – regime 3. 

 EU28 EA19 
 BIC threshold BIC threshold 

EXR –529,737 1,120 1,312 –573,899 1,250 
d_EXR –525,366 0,011 0,033 –560,899 0,009 

CPI –347,452 0,550 –392,309 1,200 2,250 
d_CPI –303,169 –0,016 0,014 –374,549 –0,001 
longIR –325,275 3,840 –572,221 4,445 

d_longIR –331,965 –0,002 –563,732 –0,001 
shortIR    –564,237 3,550 

d_shortIR    –573,089 –0,001 0,001 
UNEMP       

d_UNEMP       
SETAR –505,451 –0,001 0,008 –548,812 –0,004 0,008 
sd_EXR –445,998 1,122 1,312 –497,023 1,250 

sd_d_EXR –441,013 0,010 –491,274 0,009 
sd_CPI –292,039 0,550 –345,132 1,650 

sd_d_CPI –274,322 –0,016 –334,099 –0,001 
sd_longIR –295,131 4,200 –498,525 4,495 

sd_d_longIR –284,914 –0,002 –494,773 –0,001 
sd_shortIR   –500,722 3,450 

sd_d_shortIR   –494,463 –0,004 0,001 
sd_UNEMP      

sd_d_UNEMP      
sd_SETAR –429,992 –0,011 –472,383 –0,001 



Modelling and Forecasting Business Cycle in CEE Countries… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

157 

Table 5: Estimated threshold models with lowest BIC values for Slovak Rep., Slo-

venia, European Union and Euro Area. 

 
Slovak Rep.  
d_EXR(–1) 

Slovenia  
CPI (–2) 

European Union  
EXR(–5) 

Euro Area 
 EXR(–2) 

r1 const 0,002 0,001 0,000 –0,001 
  r1 Yt–1 0,931*** 1,13*** 1,398*** 0,866*** 
  r1 Yt–2  0,181 –0,539***  
  r1 Yt–3  –0,178   
  r1 Yt–4  –0,195**    

r2 const –0,004 –0,001 0,001 0,000 
  r2 Yt–1 0,525*** 0,587*** 1,663*** 1,45*** 
  r2 Yt–2   –0,729*** –0,626*** 
  r2 Yt–3     
  r2 Yt–4     
    r2 Yt–5     

r2 const   –0,004***  
  r3 Yt–1   1,277***  
  r3 Yt–2   –0,883***  
  r3 Yt–3   0,548***  
  r3 Yt–4   –0,342***  

Note:  *** – 1% significance level, ** – 5%  significance level, * – 10%  significance level, r1 means 
regime 1, r2 – regime 2, r3 – regime 3. 

Czech Republic UE28 

  

Figure 2. Actual and fitted (based on TAR model) values of business cycle in Czech 

Republic and EU28 

Business cycle prediction was the next step of the analysis. According to the 

procedure described in Section 3, we used bootstrap technique for both fore-

casting the threshold variable and forecasting the business cycle using 1,000 

replications. The results of forecasting both the threshold variables indicated 

in Table 1 and the endogenous variable, are shown in Figure 3. Two cases 

have been omitted. The first is the case of the Slovak Republic, where the 

exchange rate difference serves as a threshold. The bootstrap forecasts for 

this variable are stable over a certain constant, thus the forecasts cannot be 



Magdalena Osińska, Tadeusz Kufel, Marcin Błażejowski, Paweł Kufel 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

158 

interpreted properly. The second case, the Eurozone (EU19), is pretty similar 

to the EU28. 

 

Czech Rep. – ΔCPI Czech Rep. – bootstrap forecast 

  
Estonia – short IR Estonia – bootstrap forecast 

  
Hungary – HUF/USD Hungary – bootstrap forecast 

  
Figure 3. Bootstrap forecasts of threshold variables and business cycle 

Note: Mean and median are shown. 90% and 95% confidence intervals are shadowed. A vertical line on 

figures placed on the LHS of the table separates the sample and forecasting period. All the figures have 

been prepared in Gretl package: Threshold_Models. 

 



Modelling and Forecasting Business Cycle in CEE Countries… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

159 

Poland – PLN/USD Poland – bootstrap forecast 

  
Slovenia – CPI Slovenia – bootstrap forecast 

  
EU28 – EUR/USD EU28 – bootstrap forecast 

  
Figure 3. Continued 

Note: Mean and median are shown. 90% and 95% confidence intervals are shadowed. A vertical line on 

figures placed on the LHS of the table separates the sample and forecasting period. All the figures have 
been prepared in Gretl package: Threshold_Models. 

It can easily be noted that the results of forecasting a business cycle using 

a threshold autoregression (TAR) model strongly depends on the results of 

forecasting the threshold variable. A proper selection of the regime is of 



Magdalena Osińska, Tadeusz Kufel, Marcin Błażejowski, Paweł Kufel 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

160 

particular importance. If the threshold tends to penetrate into one regime, the 

forecast seems to be more precise and the confidence intervals are narrower. 

In the opposite case, when the threshold is expected to penetrate two or more 

regimes, the difference between a mean and a median and the confidence 

interval limits are greater. In the abovementioned cases, the following con-

clusions can be made: 

1. For Estonia – a short interest rate, Hungary – HUF/USD and Slovenia – 

CPI the threshold variables penetrate only one regime in the forecasted 

period. 

2. For Poland, the exchange rate of PLN/USD penetrates one regime, apart 

from three values that fall into the second one. 

3. For the Czech Republic where ΔCPI and EU28 – EUR/USD the ratio of 

values that penetrate two regimes, is almost the same. 

Empirical results of forecasting quarterly GDP growth rates in selected 

economies on the basis of TAR models using a simulation approach, re-

vealed different possible paths. For such economies as the Czech Republic, 

Estonia, the European Union (UE28) (and the Eurozone EU19), the forecasts 

form the characteristic plume or ribbons. For Poland, the majority of realiza-

tions of simulation-based forecasts hit just one possible path and only in 

a few iterations different results were obtained. Finally, for Hungary and 

Slovenia, all 1,000 forecast values generated in the bootstrap procedure were 

identical. As concerns the forecasted tendency of business cycle in 5 cases, 

the phase of recovery has been indicated. Only in the case of Estonia a slow-

down has been shown. 

Conclusions 

 In 1995–2014, the CEE as well as all the EU economies experienced 

a business cycle. Its amplitude and phase were diversified among the coun-

tries but in general, they were similar. In 2007–2009, the economies were 

exposed to the global financial and economic recession. Thereafter, econom-

ic development divergence processes started. The recession revealed compli-

cated economic and social situations in many countries. At the time of their 

accession to the EU, CEE countries optimistically developed their econo-

mies. They lowered inflation, improved the economic efficiency and devel-

oped many economic institutions. Slovenia and Estonia became the leaders 

of institutional changes in Central European countries. At present, some of 

the CEE countries are facing a different problem, namely, how to avoid the 

middle-income trap and how to improve their competitiveness. 



Modelling and Forecasting Business Cycle in CEE Countries… 

DYNAMIC ECONOMETRIC MODELS 16 (2016) 145–164 

161 

 In this paper, we defined and applied a time series-based nonlinear 

mechanism in the threshold autoregression (TAR) form in order to examine 

a business cycle in Central and Eastern European economies compared to the 

entire EU business cycle. Threshold variables, such as consumer price index, 

short and long interest rates, unemployment rate, exchange rate vs. the U.S. 

Dollar have been considered. The purpose of the paper was to model and 

predict business cycles in Central and East European (CEE) economies (the 

EU Member States) and compare them to the business cycle of the entire 

EU28 area and Eurozone EU19. We found that the exogenous mechanism 

played an important role in diagnosing the phases of business cycle in CEE 

economies, which is in line with the entire EU economic area. The results of 

business cycles forecasting using bootstrap technique are quite promising, 

while bootstrap confidence intervals are used for diagnosis. 

 It is indicated that the results of forecasting a business cycle using 

a threshold autoregression (TAR) model strongly depends on the results of 

forecasting the threshold variable. Among the threshold variables, the fol-

lowing were confirmed by the data: the short interest rate (Estonia), 

HUF/USD (Hungary), CPI (Slovenia), PLN/USD (Poland), ΔCPI (Czech 

Republic) and EUR/USD (EU28 and EU19). The proper selection of the 

regime is of particular importance. If the threshold tends to penetrate into 

one regime, the forecast seems to be more precise and the confidence inter-

vals are narrower. In the opposite case, when the threshold is expected to 

enter two or more regimes, the difference between a mean and a median and 

the confidence interval limits are greater. In 5 cases, business cycle forecasts 

show a recovery phase. Only in the case of Estonia a slowdown has been 

predicted. 

 Although many analyses have been undertaken in the last few years on 

the monetary and fiscal policy instruments corresponding to different phases 

of the economic cycle, a proper diagnosis is still an open issue. The quality 

of institutions, state integrity, the position of the economy (core or peripher-

al), and the middle-income trap are some examples of states that might affect 

the economic growth pattern in different countries, including the EU Mem-

ber States. 

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Modelowanie i prognozowanie cyklu koniunkturalnego w krajach  
Europy Środkowej i Wschodniej za pomocą podejścia progowego 

Z a r y s  t r e ś c i :  Artykuł przedstawia badanie cykli koniunkturalnych gospodarek państw 

Europy Środkowej i Wschodniej w porównaniu do gospodarki Unii Europejskiej przy wyko-

rzystaniu nieliniowego podejścia – modeli progowych (TAR). Rozważanymi zmiennymi 

progowymi są: stopa inflacji, krótko i długoterminowa stopa procentowa, stopa bezrobocia 

oraz kurs walutowy do dolara. Celem artykułu jest modelowanie oraz prognozowanie cyklu 

koniunkturalnego w państwach Europy Środkowej i Wschodniej oraz porównanie ich do cykli 

dla całej Unii Europejskiej oraz strefy Euro. Prognozowanie cyklu koniunkturalnego za po-

mocą technik bootstrapowych daje obiecujące wyniki, szczególnie gdy wykorzystywane są 

bootstrapowe przedziały ufności.  

S ł o w a  k l u c z o w e: cykl koniunkturalny,  business cycle, central and eastern economies, 

threshold models, forecasting, bootstrap. 

 


