Microsoft Word - 00_tresc.docx DYNAMIC ECONOMETRIC MODELS Vol. 9 – Nicolaus Copernicus University – Toruń – 2009 Milda Maria Burzała Poznań University of Economics The Synchronization of Regional Business Cycles with Nationwide Cycles A b s t r a c t. This paper attempts to assess the level of synchronization between the business cycles of Poland’s regions and those of the country as a whole. The measure of economic activity was an index of total industrial output sold, recorded monthly from January 1999 to December 2008, adjusted for seasonal and random fluctuations. The analysis of dominant business cycles was performed using spectral analysis. To assess the synchronization of cycles, characteristics of cospectral analysis were used: coefficient of coherence, amplitude intensification and phase difference. In the conclusion, an attempt is made to construct a synthetic indicator as a means of ranking the regions by degree of business cycle synchronization. K e y w o r d s: spectral analysis, cospectral analysis, business cycle, synthetic indicator. 1. Introduction Comparison of the level of economic activity in Poland’s regions (also called provinces or voivodeships) with that of the nation as a whole provides a source of information for both the regional authorities and central government. From a macroeconomic point of view, the observation of changes in a region may be an important factor for evaluating the effectiveness of anti- cyclic policy and monitoring the channels by which fluctuations spread. The concept of synchronization of fluctuations is understood to relate to analysis of particular components of the business cycle in terms of similarity of shape, amplitude of fluctuations and relative time lags. To perform such an analysis, a measure of economic activity must be adopted. In the empirical investigation, the measure used was the monthly recorded indices of total sold industrial output from January 1999 to December 2008 (PR_IRt = =100 ⋅ PR_IRt / PR_IRt-12), adjusted to eliminate seasonal and random fluctuations (Statistica 8 program, Census 2 method). Hence the concept of economic activity is associated with changes resulting from the joint effect Milda Maria Burzała 62 of growth factors and business cycle fluctuations. Frequency domain analysis was carried out, including both spectral and cospectral analysis. Spectral analysis, in relation to the Polish economy, has been primarily used in macroeconomic research1, because its use depends on a sufficient length of time series2. The fact that the present regional division of Poland has only been in existence since 1999 was a significant barrier in applying the spectral analysis. 2. Tools of Spectral and Cospectral Analysis Spectral and cospectral analysis refer to stationary stochastic processes and to the frequency domain. Transition from the time domain to the frequency domain is accomplished by means of Fourier transformation. In the study, the stationarity assumption of the stochastic process was verified using the Dickey– Fuller (ADF) test. Spectral analysis leads to the determination of a power spectrum, namely a spectrum of the considered time series: ],,[for )( 2 1 cos)( 2 1 )( ππω τ π ωττ π ω τ ωτ τ −∈ == ∑∑ ∞ −∞= − ∞ −∞= KeKf i (1) where K(τ) is the autocovariance function, τ = t–s is the distance between the two analysed points in time, and ω = 2π/N is the frequency of harmonic components. The power spectrum constitutes a distribution of variance of the analysed time series and makes it possible to identify the harmonic structure of the series and determine the contribution of individual components of the series to the variance of the process. Joint spectral analysis enables testing the relations between particular frequencies of two time series. The basic magnitude in this case is the cross- spectrum, which is a distribution of the joint covariance of the two processes Kyx(τ): ].,[for )( 2 1 cos)( 2 1 )( ππω τ π ωττ π ω τ ωτ τ −∈ == ∑∑ ∞ −∞= − ∞ −∞= yx i yxyx KeKf (2) 1 Cf. for example P. Skrzypczyński (2006, 2008), S. Dudek, D. Pachucki, K. Walczyk (2008); include review of research with regard to synchronization of fluctuations, L. Talaga, Z. Zieliński (1986). 2 In the literature it is stated that the minimum length of a time series should be such as to in- clude approximately 100 observations. The Synchronization of Regional Business Cycles with Nationwide Cycles 63 Using De Moivre’s lemma, the cross-spectrum can be written in complex form: ),()( sin)( 2 1 cos)( 2 1 )( ωω ωττ π ωττ π ω τ τ yxyx yxyxyx iqc KiKf −= =−= ∑ ∑ ∞ −∞= ∞ −∞= (3) where cyx(ω) is the co-spectrum (the real part of the cross-spectrum); qyx(ω) is the quadrature spectrum (the negative imaginary part of the cross-spectrum). In cospectral analysis three characteristics are introduced which form a basis for comparison of the course of two processes. In the study, the variable X was associated with a series of nationwide output indexes, while the variable Y was associated with the corresponding series for a region. a) Gain of the variable X with respect to Y is interpreted as the modulus of the coefficient β in the regression of variable Y with respect to X for a given frequency ω (Gyx(ω) >1 means that the amplitude of process yt for fre- quency ω is associated with a lower amplitude of process xt): ].;[ 0)(, )( ])()([ )( 5,022 ππω ω ω ωω ω −∈ ≥ + = for G f qc G yx x yxyx yx (4) b) The phase difference identifies leads or lags of variable X with respect to Y (a positive value represents a lag, a negative value represents a lead) for frequency ω: ].;[ )( )( )( ππω ω ω ωφ −∈⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = for c q arctg yx yx yx (5) c) Coherence is a measure of the fit (R2) in the regression of Y with respect to X for frequency ω: ].;[1)(0, )()( )()( 2 22 2 ππωω ωω ωω −∈≤≤ ⋅ + = forK ff qc K yx yx yxyx yx (6) In the empirical analyses we consider only such leads or lags at a given frequency which is associated with a high value of the coefficient of coherence (for strongly correlated frequency components). 3. Study Results in Frequency Domain Theoretically, when adjusted for seasonal and random fluctuations, the annual indices of industrial output represent changes resulting not only from the business cycle, but also the underlying trend. The ADF test applied to the Milda Maria Burzała 64 annual indices of output adjusted for seasonal and random fluctuations, in the case of the series for each of the analysed regions, indicated a significant negativity of the parameter δ in the model (7): .___ 1 1 ∑ = −− +Δ+=Δ k k tititt IRPRIRPRIRPR εδδ (7) The ADF test statistics rejects the null hypothesis of unit root at the α = 0.001 significance level assuming first order autoregression (k=1). The stationarity of the time series means that any stochastic trend occurring in the annual indices of output can be regarded as a realization of low-frequency fluctuations. For example, figure 1 shows indices of total industrial output sold for Poland. Test for stationarity was carried out based on the model: ._95.0_032.0_ 11 POL t POL t POL t IRPRIRPRIRPR −− Δ+−=Δ For parameter δ = -0,032 the statistic ADF is equal to -6.128. Sty-1999 Paź-1999 Lip-2000 Kwi-2001 Sty-2002 Paź-2002 Lip-2003 Kwi-2004 Sty-2005 Paź-2005 Lip-2006 Kwi-2007 Sty-2008 Paź-2008 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Figure 1. Indices of total industrial output sold for Poland from January 1999 to De- cember 2008 Analysis of the dominant cycles was carried out based on the power spec- trum. For a clear majority of regions it is possible to indicate one cycle which to a significant degree explains the fluctuations in the output indices (shown in bold type in Table 1). The 40-month cycle turned out to be such a dominant cycle. In the case of the nationwide cycle it explains more than 52% of the variability of output indices. The effect of the remaining cycles is quite different. For the Wielkopolskie region we can notice an equivalent effect from three cycles (120, 60 and 40 months). Generally it is possible to identify groups of regions where economic activity is ruled by long cycles (120, 60 months), medium cycles (40, 30 months) and short cycles (24, 20 months). The regions with dominating long cycles are as follows: Lubuskie (59.8%), Wielkopolskie (59.05%) and Mazowieckie (58.27%). Medium cycles dominate in Podkarpackie (70.86%), Zachodniopomorskie (70.24%), Świętokrzyskie (63.41%) and Warmińsko- Mazurskie (62.97). The Synchronization of Regional Business Cycles with Nationwide Cycles 65 Table 1. Dominant cycles: percentage of explained variability of the time series Length of time Series Regions Frequency (duration in months) 0.008 (120) 0.017 (60) 0.025 (40) 0.033 (30) 0.042 (24) 0,050 (20) 120 POLAND 9.46 6.19 52.10 0.92 15.61 4.42 120 Dolnośląskie 3.46 8.94 42.43 6.97 5.17 4.51 120 Kujawsko-Pomorskie 3.99 13.75 40.01 4.70 16.71 8.90 120 Lubelskie 0.33 6.94 40.48 14.52 11.04 1.35 120 Lubuskie 15.33 44.46 6.73 16.65 0.44 0.20 120 Łódzkie 41.14 5.33 20.46 5.79 7.51 1.50 120 Małopolskie 6.96 3.14 33.43 13.37 3.19 2.82 118 Mazowieckie* 17.88 40.39 18.58 0.28 7.54 7.69 60 Opolskie*** xxx 29.66 xxx 37.53 xxx 2.26 120 Podkarpackie 6.21 9.77 59.26 11.61 3.53 5.87 120 Podlaskie 13.50 7.94 30.51 8.49 3.35 3.92 120 Pomorskie 7.11 12.90 10.20 20.38 14.58 25.72 114 Śląskie** 0.97 12.96 28.62 6.23 16.56 3.04 120 Świętokrzyskie 5.17 6.90 62.12 1.28 4.67 0.61 120 Warmińsko-Mazurskie 15.81 2.89 59.74 3.23 14.57 0.11 120 Wielkopolskie 28.03 31.01 30.41 0.21 3.19 6.73 120 Zachodniopomorskie 10.02 7.32 67.58 2.66 1.47 1.77 Note: With a number of observations less than 120, the length of the analysed cycles changes: * 118, 59, 39.3, 29.5, 23.6, 19.7; ** 114, 57, 38, 28.5, 22.8, 19; ***60, 30, 20 months. Short cycles dominate mainly in Pomorskie (40.30%). In the mentioned above regions, the variability of the series of output indices is explained to a much higher degree than for Poland as a whole, where long cycles explain hardly 15.65%, medium cycles 53.02% and short cycles 20.02%. Taking dominant cycles as a criterion, the greatest similarity to nationwide activity was displayed by those regions where medium-length cycles dominate. Therefore the greatest synchronization is observed in the Warmińsko-Mazurskie and Świętokrzyskie regions. Cospectral analysis was performed for all cycles lasting from 20 to 120 months3. The cospectral analysis characteristics are presented in Tables 2, 3 and 4. The measure of correlation in particular fluctuation bands is the coefficient of coherence. The highest values of K2 (which averages 0.933 across the regions) is observed for the dominant 40-month cycle and the long-term activity 3 For three regions, some data could not be obtained. In those cases the cycles analysed are accordingly shorter. These regions are asterisked in the tables, and the duration of the components is given at the foot of the table. The shortest series, for the Opolskie region, allowed only 3 cycles to be analysed. Milda Maria Burzała 66 represented by the 120-month cycle (average 0.830 across the regions). The most weakly correlated are the 30-month cycles (average K2 across the regions: 0.451). The results obtained confirm certain intuitive suppositions that the differentiation in economic activity may refer to shorter cycles. In the long term a higher coherence can be expected between regional and nationwide economic activity. Analysing the various fluctuation bands, certain groups of regions can be identified where K2 ≥ 0.95 (shown in bold type in Table 2). For short, 24- and 20-month cycles there are far fewer such regions than for long cycles (120 and 60 months), which confirms the intuitive assumptions referred to above. Taking as a criterion the average value of K2 for all frequencies, it is possible to identify the regions with high average coefficients of coherence (Mazowieckie and Wielkopolskie, with averages of 0.913 and 0.894 respectively) and with relatively low average coefficients of coherence (Lubuskie and Lubelskie, with averages of 0.448 and 0.491 respectively). The averages given are a measure of the mean correlation between the cycles distinguished for a given region and the nationwide cycles. Table 2. Values of coefficient of coherence Length of time Series Regions Frequency (duration in months) 0.008 (120) 0.017 (60) 0.025 (40) 0.033 (30) 0.042 (24) 0,050 (20) 120 Dolnośląskie 0.817 0.809 0.970 0.071 0.862 0.891 120 Kujawsko-Pomorskie 0.579 0.511 0.964 0.639 0.966 0.921 120 Lubelskie 0.219 0.691 0.948 0.038 0.822 0.227 120 Lubuskie 0.733 0.616 0.671 0.253 0.267 0.145 120 Łódzkie 0.982 0.361 0.940 0.461 0.938 0.667 120 Małopolskie 0.975 0.938 0.963 0.203 0.749 0.930 118 Mazowieckie* 0.960 0.737 0.897 0.972 0.977 0.934 60 Opolskie*** Xxx 0.967 Xxx 0.912 xxx 0.662 120 Podkarpackie 0.980 0.970 0.974 0.027 0.660 0.577 120 Podlaskie 0.955 0.856 0.984 0.553 0.827 0.692 120 Pomorskie 0.827 0.718 0.851 0.191 0.665 0.583 114 Śląskie** 0.644 0.870 0.964 0.360 0.917 0.887 120 Świętokrzyskie 0.923 0.909 0.993 0.526 0.912 0.100 120 Warmińsko-Mazurskie 0.964 0.060 0.975 0.746 0.967 0.437 120 Wielkopolskie 0.991 0.827 0.963 0.740 0.930 0.912 120 Zachodniopomorskie 0.993 0.986 0.995 0.531 0.707 0.573 Note: With a number of observations less than 120, the length of the analysed cycles changes: * 118, 59, 39.3, 29.5, 23.6, 19.7; ** 114, 57, 38, 28.5, 22.8, 19; ***60, 30, 20 months. Gain coefficients make it possible to compare the amplitudes of cycles ob- served in a region with the amplitude of nationwide cycles within particular bands of fluctuations. Analysing the values given in Table 3, it is noticed that The Synchronization of Regional Business Cycles with Nationwide Cycles 67 the average coefficients of intensification for 120- and 60-month cycles (1.141 and 1.296 respectively) indicate that on average, the amplitude of long-term fluctuations within regions is higher than the amplitude of nationwide fluctua- tions. Table 3. Gain coefficients Length of time Series Regions Frequency (duration in months) 0.008 (120) 0.017 (60) 0.025 (40) 0.033 (30) 0.042 (24) 0.050 (20) 120 Dolnośląskie 0.859 1.408 1.318 0.509 0.841 1.301 120 Kujawsko-Pomorskie 0.711 1.165 1.139 1.262 1.354 1.739 120 Lubelskie 0.180 1.029 1.126 0.432 1.026 0.387 120 Lubuskie 1.558 2.115 0.509 1.095 0.228 0.226 120 Łódzkie 1.822 0.519 0.555 0.687 0.619 0.463 120 Małopolskie 0.951 0.830 0.902 0.818 0.518 0.816 118 Mazowieckie* 1.273 1.646 0.602 0.565 0.674 1.070 60 Opolskie*** xxx 1.486 xxx 1.733 xxx 0.496 120 Podkarpackie 0.974 1.344 1.246 0.314 0.529 0.925 120 Podlaskie 0.792 0.639 0.524 0.672 0.322 0.524 120 Pomorskie 1.147 1.339 0.635 1.144 1.213 2.304 114 Śląskie** 0.473 1.609 1.312 1.073 1.701 1.282 120 Świętokrzyskie 1.163 1.600 1.737 1.184 0.836 0.240 120 Warmińsko-Mazurskie 1.457 0.256 1.234 1.215 1.106 0.399 120 Wielkopolskie 1.985 1.856 0.883 0.662 0.531 1.202 120 Zachodniopomorskie 1.773 1.888 1.959 1.426 0.489 0.771 Note: With a number of observations less than 120, the length of the analysed cycles changes: * 118, 59, 39.3, 29.5, 23.6, 19.7; ** 114, 57, 38, 28.5, 22.8, 19; 60, 30, 20 months. In turn, the short cycles (24 and 20 months, with average values 0.799 and 0.884 respectively) are characterized by a higher amplitude of nationwide fluctuations. Closest to unity are the average gain coefficients for medium-term fluctuations (40 and 30 months, average values 1.045 and 0.924 respectively), which indicate the greatest degree of synchronization with nationwide fluctuations. For each band of fluctuations it is also possible to indicate the region displaying the greatest synchronization with the nationwide cycle: − Podkarpackie and Małopolskie for the 120-month cycle; − Lubelskie for the 60-month cycle; − Małopolskie for the 40-month cycle; − Śląskie for the 30-month cycle; − Lubelskie for the 24-month cycle; − Mazowieckie for the 20-month cycle. Milda Maria Burzała 68 Table 4. Phase difference in radians (in months) Length of time series Regions Frequency (duration in months) 0.008 (120) 0.017 (60) 0.025 (40) 0.033 (30) 0.042 (24) 0,050 (20) 120 Dolnośląskie -0.563 (-10.8) 0.485 (4.6) 0.017 (0.1) 0.527 (2.5) 0.652 (2.5) 1.058 (3.4) 120 Kujawsko-Pomorskie -1.490 (-28.5) 1.099 (10.5) 0.048 (0.3) 0.045 (0.2) 1.043 (4.0) 0.654 (2.1) 120 Lubelskie -0.760 (-14.5) 1.099 (10.5) 0.421 (2.7) -0.502 (-2.4) 0.123 (0.5) 2.339 (7.4) 120 Lubuskie -1.215 (-23.2) 0.497 (4.7) 0.722 (4.6) 0.278 (1.3) 1.299 (5.0) 1.762 (5.6) 120 Łódzkie -1.766 (-33.7) -1.147 (-11.0) 0.556 (3.5) 1.194 (5.7) 1.428 (5.5) 0.323 (1.0) 120 Małopolskie -0.212 (-4.0) 0.338 (3.2) 0.170 (1.1) -0.706 (-3.4) -0.132 (-0.5) -0.026 (-0.1) 118 Mazowieckie* -0.635 (-11.9) -0.682 (-6.4) -0.081 (-0.5) -0.097 (-0.5) -0.087 (-0.3) -0.424 (-1.3) 60 Opolskie*** xxx 0.145 (1.4) xxx -0.420 (-2.0) xxx -0.221 (-0.7) 120 Podkarpackie -0.444 (-8.5) -0.087 (-0.8) 0.072 (0.5) 1.038 (5.0) 2.261 (8.6) -0.972 (-3.1) 120 Podlaskie -0.624 (-11.9) 0.419 (4.0) 0.743 (4.7) 0.677 (3.2) 1.563 (6.0) 2.140 (6.8) 120 Pomorskie -0.615 (-11.7) 0.797 (7.6) 0.531 (3.4) 0.740 (3.5) -1.431 (-5.5) 1.626 (5.2) 114 Śląskie** -0.002 (-0.04) 0.449 (4.1) 0.018 (0.1) 0.881 (4.0) -0.404 (-1.5) 0.143 (0.4) 120 Świętokrzyskie -0.268 (-5.1) 0.520 (5.0) 0.280 (1.8) 0.526 (2.5) 0.693 (2.6) -1.892 (-6.0) 120 Warmińsko-Mazurskie -2.058 (-39.3) -1.711 (-16.3) -0.266 (-1.7) -0.068 (-0.3) 1.070 (4.1) 1.186 (3.8) 120 Wielkopolskie 0.438 (8.4) 0.139 (1.3) -0.163 (- 1.0) -0.129 (- 0,6) -0.676 (- 2.6) -0.594 (- 1.9) 120 Zachodniopomorskie 0.302 (5.8) -0.070 (-0.7) -0.170 (-1.1) -0.429 (-2.0) 0.379 (1.4) -2.003 (-6.4) Note: With a number of observations less than 120, the length of the analysed cycles changes: * 118, 59, 39.3, 29.5, 23.6, 19.7; ** 114, 57, 38, 28.5, 22.8, 19; 60, 30, 20 months. The phase differences presented in Table 4 enable analysis of the leads and lags of nationwide components of the business cycle relative to the corresponding components for a region. It should be noted that for most regions (apart from Wielkopolskie and Zachodniopomorskie), the 120-month cycle, connected with long-term activity, displays a lag with respect to nationwide activity. The longest lags are found in this fluctuation band (more than three years for the Warmińsko-Mazurskie region). For each component of the cycle it is possible to indicate the regions where economic activity runs in parallel with nationwide activity (without leading or lagging). However these results are different from those obtained using amplitude of fluctuations as a criterion. The greatest The Synchronization of Regional Business Cycles with Nationwide Cycles 69 number of regions, for which the phase difference in radians is smaller in absolute value than 0.1, can be indicated as having a dominant 40-month cycle. Such a phase difference is associated with lags (leads) in economic activity by up to one month. These are the regions Dolnośląskie, Kujawsko-Pomorskie, Mazowieckie, Podkarpackie and Śląskie. 4. Indicator of Synchronization of Fluctuations To summarise the study, an attempt was made to build a synthetic indicator as a basis for assigning ranks to each region depending on the degree of synchronization of fluctuations. For this purpose three characterictics of cospectral analysis were used, together with a cycle pattern perfectly synchronized with the national cycle. Such a cycle would be a cycle observed in a region having K2 = 1, G(ω) = 1 and φ(ω) = 0 (maximum correlation, no intensification of fluctuations and no phase difference). Table 5. Synthetic indicators and ranks for individual regions Regions Partial synthetic indicators Final syn- thetic indica- tor Ranks Frequency (duration in months) 0.008 (120) 0.017 (60) 0.025 (40) 0.033 (30) 0.042 (24) 0,050 (20) Dolnośląskie 0.179 0.239 0.094 0.519 0.181 0.265 0.175 2 Kujawsko-Pomorskie 0.431 0.367 0.055 0.197 0.251 0.309 0.191 4 Lubelskie 0.586 0.270 0.110 0.546 0.085 0.755 0.220 7 Lubuskie 0.407 0.487 0.341 0.320 0.633 0.742 0.429 15 Łódzkie 0.468 0.505 0.213 0.435 0.322 0.298 0.388 14 Małopolskie 0.051 0.113 0.062 0.420 0.228 0.075 0.148 1 Mazowieckie* 0.174 0.353 0.149 0.135 0.103 0.101 0.235 11 Opolskie*** xxx 0.156 xxx 0.277 Xxx 0.276 0.226 9 Podkarpackie 0.077 0.111 0.082 0.657 0.559 0.303 0.185 3 Podlaskie 0.158 0.201 0.233 0.334 0.455 0.532 0.255 12 Pomorskie 0.184 0.297 0.220 0.420 0.373 0.708 0.436 16 Śląskie** 0.257 0.264 0.095 0.364 0.265 0.131 0.196 6 Świętokrzyskie 0.106 0.259 0.231 0.284 0.171 0.772 0.227 10 Warmińsko-Mazurskie 0.422 0.756 0.106 0.152 0.191 0.515 0.192 5 Wielkopolskie 0.317 0.298 0.66 0.194 0.240 0.166 0.222 8 Zachodniopomorskie 0.243 0.242 0.271 0.331 0.285 0.490 0.272 13 Note: With a number of observations less than 120, the length of the analysed cycles changes: * 118, 59, 39.3, 29.5, 23.6, 19.7; ** 114, 57, 38, 28.5, 22.8, 19; 60, 30, 20 months. For each region in each band of fluctuations, the modulus of the distance from the pattern was analysed. These distances were normalized according to the simple formula: modulus of observed distance divided by maximum distance. This approach meant that the range of variability could be normalized and the Milda Maria Burzała 70 distances made independent of the units used. The partial synthetic indicator in a given band is the arithmetic mean of the normalized distances. The final synthetic indicator for a given region, encapsulating information from all bands, was based on a weighted average, where the weights reflected the degree of variability explained by each component of the cycle. The values of the synthetic indicators and the ranks assigned to each region are presented in Table 5. The smaller the value of the synthetic indicator, the smaller the distance from the model. Hence a rank of 1 denotes the highest degree of synchronization. 5. Summary Summing up the results of the spectral and cospectral analysis, it is possible to identify one cycle which is dominant both for nationwide activity and for the majority of the regions. This is the 40-month cycle, which also displays the greatest synchronization when nationwide changes are compared with the changes observed in the regions. However, the classification of the regions varies depending on the criterion adopted for comparison. The indicator constructed in subsection 4 can take values from 0 to 1. The final values of the indicator appearing in the table lie within the interval [0.148, 0.436]. The relative narrowness of this interval and the values of the synthetic indicator (< 0.5) indicate a high level of synchronization between the business cycles recorded in the regions and those of the country as a whole. References Dudek, S., Pachucki, D., Walczyk, K. (2008), Synchronizacja cyklu koniunkturalnego polskiej gospodarki z krajami strefy euro w kontekście struktury tych gospodarek, http://www.nbpnews.pl/r/nbpnews/Pliki_PDF/NBP/Publikacje/analityczne/irg_sghP.pdf Skrzypczyński, P. (2006), Analiza synchronizacji cykli koniunkturalnych w strefie euro, Materiały i Studia NBP, vol. 210, National Bank of Poland Department of Macroeconomic and Structural Analysis, Warsaw. Skrzypczyński, P. (2008), Wahania aktywności gospodarczej w Polsce i strefie euro, Materiały i Studia NBP, vol. 227, National Bank of Poland Department of Macroeconomic and Structural Analysis, Warsaw. Talaga, L., Zieliński, Z. (1986), Analiza spektralna w modelowaniu ekonometrycznym, PWN, Warsaw. Zeliaś, A. (1988), Metody statystyki międzynarodowej, PWE, Warsaw. Synchronizacja cykli koniunkturalnych województw z cyklami ogólnokrajowymi Z a r y s t r e ś c i. W artykule podjęto próbę oceny stopnia synchronizacji cykli koniunkturalnych województw Polski z cyklami ogólnokrajowymi. Miernikiem aktywności gospodarczej były rejestrowane miesięcznie od stycznia 1999 do grudnia 2008 indeksy produkcji sprzedanej prze- mysłu ogółem oczyszczone z wahań sezonowych i przypadkowych. Analizę dominujących cykli koniunkturalnych przeprowadzono z wykorzystaniem analizy spektralnej. Do oceny synchroniza- cji cykli wykorzystano charakterystyki analizy kospektralnej: współczynnik koherencji, wzmoc- The Synchronization of Regional Business Cycles with Nationwide Cycles 71 nienie amplitudy oraz przesunięcie fazowe. W podsumowaniu artykułu podjęto próbę budowy miernika syntetycznego, który był podstawą przypisania rang poszczególnym województwom ze względu na stopień synchronizacji cyklu koniunkturalnego. S ł o w a k l u c z o w e: analiza spektralna, analiza kospektralna, cykl koniunkturalny, miernik syntetyczny.