Wavelet multidimensional scaling analysis of European economic sentiment indicators. (English) Zbl 07473945
Summary: We propose the use of wavelet coefficients, which are generated from nondecimated discreet wavelet transforms, to form a correlation-based dissimilarity measure in metric multidimensional scaling. This measure enables the construction of configurations depicting the associations between objects across different timescales. The proposed method is used to examine the similarities between the economic sentiment indicators of the EU member states that are published monthly by the European Commission. The results suggest that economic sentiment differs considerably among the member states in the short term. In contrast, several similarities emerge when considering the associations over longer time horizons. These similarities tend to be related to the countries that are geographically close or that exhibited similar economic behaviour prior to the introduction of the euro. Furthermore, the results of a detailed simulation study suggest that the proposed dissimilarity measure is particularly well suited for identifying long-term associations between nonstationary time series.
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
Keywords:
nondecimated discreet wavelet transform; multidimensional scaling analysis; wavelet covariance; correlation distance; economic sentiment indicatorsReferences:
| [1] | Aboufadel, E.; Schlicker, S., Discovering wavelets (1999), New York: John Wiley & Sons, New York · Zbl 0940.42017 |
| [2] | Aguiar-Conraria, L.; Soares, MJ, Business cycle synchronization and the euro: A wavelet analysis, Journal of Macroeconomics, 33, 477-489 (2011) |
| [3] | Aguiar-Conraria, L.; Soares, MJ, The continuous wavelet transform: Moving beyond uni- and bivariate analysis, Journal of Economic Surveys, 28, 2, 344-375 (2014) |
| [4] | Aguiar-Conraria, L.; Martins, MMF; Soares, MJ, Convergence of the economic sentiment cycles in the Eurozone: A time-frequency analysis, Journal of Common Market Studies, 51, 377-398 (2013) |
| [5] | Ambrosi, K.; Hansohm, J., Ein dynamischer Ansatz zur RepraÈ sentation von Objekten, In: Operations research proceedings 1986 (1987), Berlin: Springer-Verlag, Berlin |
| [6] | Ausloos, M.; Lambiotte, R., Clusters or networks of economies? A macroeconomy study through gross domestic product, Physica A, 382, 16-21 (2007) |
| [7] | Basalto, N.; Bellotti, R.; De Carlo, F.; Facchi, P.; Pantaleo, E.; Pascazio, S., Hausdorff clustering of financial time series, Physica A, 379, 635-644 (2007) |
| [8] | Basalto, N.; Bellotti, R.; De Carlo, F.; Facchi, P.; Pascazio, S., Clustering stock market companies via chaotic map synchronization, Physica A, 345, 196-206 (2008) |
| [9] | Beetsma, R.; Uhlig, H., An analysis of the stability and growth pact, Economic Journal, 109, 546-571 (1999) |
| [10] | Bloomfield, P., Fourier analysis of time series: An introduction (2000), New York: John Wiley and Sons, New York · Zbl 0994.62093 |
| [11] | Camacho, M.; Perez-Quiros, G.; Saiz, L., Are European business cycles close enough to be just one?, Journal of Economic Dynamics and Control, 30, 1678-1706 (2006) · Zbl 1162.91522 |
| [12] | Cardinali, A.; Nason, GP, Practical powerful wavelet packet tests for second-order stationarity, Applied and Computational Harmonic Analysis, 44, 558-583 (2018) · Zbl 1387.62099 |
| [13] | Christiano, L.; Fitzgerald, TJ, The band pass filter, International Economic Review, 44, 435-465 (2003) |
| [14] | Cox, TF, Multidimensional scaling used in multivariate statistical process control, Journal of Applied Statistics, 28, 365-378 (2001) · Zbl 0992.62109 |
| [15] | Cox, TF, An introduction to multivariate statistical analysis (2005), London: Hodder Arnold, London · Zbl 1096.62052 |
| [16] | Cox, MAA, Analysis of stock market indices through multidimensional scaling, Journal of Statistical Computation and Simulation, 83, 2015-2029 (2013) · Zbl 1453.62704 |
| [17] | Croux, C.; Forni, M.; Reichlin, L., A measure of comovement for economic variables: Theory and empirics, Review of Economics and Statistics, 83, 232-241 (2001) |
| [18] | D’Urso, P.; Maharaj, EA, Wavelets-based clustering of multivariate time series, Fuzzy Sets and Systems, 193, 33-61 (2012) · Zbl 1237.62079 |
| [19] | Dose, C.; Cincotti, S., Clustering of financial time series with application to index and enhanced-index tracking portfolio, Physica A, 355, 145-151 (2005) |
| [20] | EC-DGEFA, The joint harmonised EU Programme of business and consumer surveys: User guide (2017), Brussel: Directorate-General for Economic and Financial Affairs, European Commission, Brussel |
| [21] | Everitt, B.; Hothorn, T., An introduction to applied multivariate analysis with R (2011), New York: Springer, New York · Zbl 1306.62010 |
| [22] | Fong, DKH; DeSarbo, WS; Park, J.; Scott, CJ, A Bayesian vector multidimensional scaling procedure for the analysis of ordered preference data, Journal of the American Statistical Association, 105, 482-492 (2010) · Zbl 1394.91325 |
| [23] | Frankel, JA; Rose, AK, The endogeneity of the optimum currency area criteria, Economic Journal, 108, 1009-1025 (1998) |
| [24] | Fryzlewicz, P.; Delouille, V.; Nason, GP, GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisz transform, Journal of the Royal Statistical Society C, 56, 99-116 (2007) · Zbl 1490.62507 |
| [25] | Gallegati, M.; Gallegati, M.; Ramsey, JB; Semmler, W., The US wage Phillips curve across frequencies and over time, Oxford Bulletin of Economics and Statistics, 73, 489-508 (2011) |
| [26] | Gallegati, M.; Gallegati, M.; Ramsey, JB; Semmler, W.; Gallegati, M.; Semmler, W., Does productivity affect unemployment? A time-frequency analysis for the US, Wavelet applications in economics and finance (2014), Switzerland: Springer, Switzerland · Zbl 1298.91029 |
| [27] | Gardner, W. A. (1992). A unifying view of coherence in signal processing. Signal Processing, 29, 113-140. · Zbl 0775.94036 |
| [28] | Gencay, R.; Selcuk, F.; Whitcher, B., An introduction to wavelets and other filtering methods in finance and economics (2002), New York: Academic Press, New York · Zbl 1068.42029 |
| [29] | Gower, JC, Adding a point to vector diagrams in multivariate analysis, Biometrika, 55, 582-585 (1968) · Zbl 0167.17802 |
| [30] | Gower, JC; Ngouenet, RF, Nonlinearity effects in multidimensional scaling, Journal of Multivariate Analysis, 94, 344-365 (2005) · Zbl 1122.62061 |
| [31] | Greene, WH, Econometric analysis (2018), New York: Pearson, New York |
| [32] | Hartigan, JA; Wong, MA, Algorithm AS 136: A K-means clustering algorithm, Applied Statistics, 28, 100-108 (1979) · Zbl 0447.62062 |
| [33] | Hitchcock, DB; Casella, G.; Booth, JG, Improved estimation of dissimilarities by presmoothing functional data, Journal of the American Statistical Association, 101, 211-222 (2006) · Zbl 1118.62336 |
| [34] | Hubert, L.; Arabie, P., Comparing partitions, Journal of Classification, 2, 193-218 (1985) · Zbl 0587.62128 |
| [35] | In, F.; Kim, S., An introduction to wavelet theory in finance: A wavelet multiscale approach (2013), Singapore: World Scientific Publishing, Singapore · Zbl 1276.91003 |
| [36] | Jansen, WJ; Nuis, NJ, The stock market and consumer confidence: European evidence, Economics Letters, 79, 89-98 (2003) |
| [37] | Kim, S.; In, F., Portfolio allocation and the investment horizon: A multiscaling approach, Quantitative Finance, 10, 443-453 (2010) |
| [38] | Knight, M.; Nason, GP; Nunes, M., A wavelet approach to long-memory estimation, Statistics and Computing, 27, 1453-1471 (2016) · Zbl 1384.62289 |
| [39] | Lemmens, A.; Croux, C.; Dekimpe, MG, Consumer confidence in Europe: United in diversity, International Journal of Research in Marketing, 24, 2, 113-127 (2007) |
| [40] | Lin, L.; Fong, DKH, Bayesian multidimensional scaling procedure with variable selection, Computational Statistics and Data Analysis, 129, 1-13 (2019) · Zbl 1469.62105 |
| [41] | Machado, TJ; Duarte, FB; Duarte, GM, Analysis of financial data series using fractional Fourier transform and multidimensional scaling, Nonlinear Dynamics, 65, 235-245 (2011) |
| [42] | Machado, TJ; Duarte, FB; Duarte, GM, Analysis of stock market indices with multidimensional scaling and wavelets, Mathematical Problems in Engineering, 12, 819503 (2012) · Zbl 1264.91095 |
| [43] | Maharaj, EA; D’Urso, P., A coherence-based approach for the pattern recognition of time series, Physica A, 389, 3516-3537 (2010) |
| [44] | Maharaj, EA; D’Urso, P.; Galagedera, DUA, Wavelet-based fuzzy clustering of time series, Journal of Classification, 27, 231-275 (2010) · Zbl 1337.62307 |
| [45] | Man-Suk, O., A simple and efficient Bayesian procedure for selecting dimensionality in multidimensional scaling, Journal of Multivariate Analysis, 107, 200-209 (2012) · Zbl 1236.62013 |
| [46] | Man-Suk, O.; Raftery, AE, Bayesian multidimensional scaling and choice of dimension, Journal of the American Statistical Association, 96, 1031-1044 (2001) · Zbl 1072.62543 |
| [47] | Michis, AA, Time scale evaluation of economic forecasts, Economics Letters, 123, 279-281 (2014) |
| [48] | Michis, AA, Investing in gold: Individual asset risk in the long-run, Finance Research Letters, 11, 369-374 (2014) |
| [49] | Michis, AA, Multiscale analysis of the liquidity effect in the UK economy, Computational Economics, 45, 615-633 (2015) |
| [50] | Michis, AA, A wavelet smoothing method to improve conditional sales forecasting, Journal of the Operational Research Society, 66, 832-844 (2015) |
| [51] | Miskiewicz, J.; Ausloos, M., Correlation measure to detect time series distances, whence economy globalization, Physica A, 387, 6584-6594 (2008) |
| [52] | Myers, L. J., Erim, Z., & Lowery, M. M. (2004). Time and frequency domain methods for quantifying common modulation of motor unit firing patterns. Journal of NeuroEngineering and Rehabilitation, 1, 2. |
| [53] | Nason, GP, Wavelet methods in statistics with R (2008), New York: Springer, New York · Zbl 1165.62033 |
| [54] | Nason, GP, A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series, Journal of the Royal Statistical Society B, 75, 879-904 (2013) · Zbl 1411.62259 |
| [55] | Nason, GP; von Sachs, R.; Kroisandt, G., Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum, Journal of the Royal Statistical Society B, 62, 271-292 (2000) |
| [56] | Percival, DB; Walden, AT, Wavelet methods for time series analysis (2000), Cambridge: Cambridge University Press, Cambridge · Zbl 0963.62079 |
| [57] | Ramsey, JB; Gallegati, M.; Gallegati, M.; Semmler, W., Instrumental variables and wavelet decompositions, Economic Modelling, 27, 1498-1513 (2010) |
| [58] | Rose, A.; Engel, C., Currency unions and international integration, Journal of Money, Credit and Banking, 34, 1067-1089 (2002) |
| [59] | Rua, A.; Nunes, LC, International comovement of stock market returns: A wavelet analysis, Journal of Empirical Finance, 16, 632-639 (2009) |
| [60] | Spolaore, E., What is European integration really about? A political guide for economists, Journal of Economic Perspectives, 27, 125-144 (2013) |
| [61] | Steinley, D., Properties of the Hubert-Arabie adjusted Rand index, Psychological Methods, 9, 386-396 (2004) |
| [62] | Takayuki, M.; Takayasu, H.; Takayasu, M., Correlation networks among currencies, Physica A, 364, 336-342 (2006) |
| [63] | Taylor, SL; Eckley, IA; Nunes, MA, Multivariate locally stationary 2D wavelet processes with application to colour texture analysis, Statistics and Computing, 27, 1129-1143 (2017) · Zbl 1384.62297 |
| [64] | Witten, DM; Tibshirani, R., Supervised multidimensional scaling for visualization, classification, and bipartite ranking, Computational Statistics and Data Analysis, 55, 789-801 (2011) · Zbl 1246.62158 |
| [65] | Xie, Y.; Yu, J.; Ranneby, B., Forecasting using locally stationary wavelet processes, Journal of Statistical Computation and Simulation, 79, 1067-1082 (2009) · Zbl 1179.62135 |
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