Gallegati, Marco Wavelet analysis of stock returns and aggregate economic activity. (English) Zbl 1452.62910 Comput. Stat. Data Anal. 52, No. 6, 3061-3074 (2008). Summary: The relationship between stock market returns and economic activity is investigated using signal decomposition techniques based on wavelet analysis. After the application of the maximum overlap discrete wavelet transform (MODWT) to the DJIA stock price index and the industrial production index for the US over the period 1961:1-2006:10 wavelet variance and cross-correlations analyses are used to investigate the scaling properties of the series and the lead/lag relationship between them at different time scales. The results show that stock market returns tend to lead the level of economic activity, but only at the highest scales (lowest frequencies) corresponding to periods of 16 months and longer, and that the leading period increases as the wavelet time scale increases. Cited in 10 Documents MSC: 62P20 Applications of statistics to economics 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62-08 Computational methods for problems pertaining to statistics Keywords:stock markets; industrial production; wavelet variance; wavelet cross-correlation Software:R; wmtsa PDFBibTeX XMLCite \textit{M. Gallegati}, Comput. Stat. Data Anal. 52, No. 6, 3061--3074 (2008; Zbl 1452.62910) Full Text: DOI References: [1] Abry, P., Gonçalvés, P., Flaundrin, P., 1995. Wavelet spectrum estimation, 1/f processes. Wavelet and Statistic. Lecture Notes in Statistics, vol. 103, 15-30.; Abry, P., Gonçalvés, P., Flaundrin, P., 1995. Wavelet spectrum estimation, 1/f processes. Wavelet and Statistic. Lecture Notes in Statistics, vol. 103, 15-30. [2] Abry, P.; Veitch, D., Wavelet analysis of long-range-dependent traffic, IEEE Trans. Inform. Theory, 44, 2-15 (1996) · Zbl 0905.94006 [3] Aminghafari, M.; Cheze, N.; Poggi, J.-M., Multivariate denoising using wavelets and principal component analysis, Comput. Statist. Data Anal., 50, 2381-2398 (2006) · Zbl 1445.62065 [4] Barro, R., The stock market and investment, Rev. Finance Stud., 3, 115-131 (1990) [5] Binswanger, M., Stock market booms and real economic activity: is this time different?, Internat. Rev. Econom. Finance, 9, 387-415 (2000) [6] Chen, N. F., International evidence on the stock market and aggregate economic activity, J. Finance, 46, 529-554 (1991) [7] Cheung, Y.; Lai, K., A search for long memory in international stock market returns, J. Internat. Money and Finance, 14, 597-615 (1995) [8] Cheung, Y. W.; Ng, L. K., International evidence on the stock market and aggregate economic activity, J. Empirical Finance, 5, 281-296 (1998) [9] Choi, J. J.; Hauser, S.; Kopecky, K., Does the stock market predict real activity? Time Series Evidence from the G-7 Countries, J. Banking Finance, 23, 1771-1792 (1999) [10] Coifman, R. R.; Donoho, D., Time-invariant wavelet de-noising, (Antoniadis, A.; Oppenheim, G., Wavelets and Statistics (1995), Springer-Verlag: Springer-Verlag New York), 125-150 · Zbl 0866.94008 [11] Crato, N., Some international evidence regarding the stochastic behavior of stock returns, Appl. Finance Econom., 4, 33-39 (1994) [12] Daubechies, I., Ten Lectures on Wavelets (1992), SIAM: SIAM Philadelphia · Zbl 0776.42018 [13] Diebold, F. X.; Rudebush, G. D., Long memory and persistence in aggregate output, J. Monetary Econom., 24, 189-209 (1989) [14] Duchesne, P., Testing for multivariate autoregressive conditional hetroskedasticity using wavelets, Comput. Statist. Data Anal., 50, 2142-2163 (2006) · Zbl 1157.62487 [15] Fama, E. F., Stock returns, real activity inflation, and money, Amer. Econom. Rev., 71, 545-565 (1981) [16] Fama, E. F., Stock returns, expected returns, and real activity, J. Finance, 45, 1089-1108 (1990) [17] Gabor, D., Theory of communication, J. Istr. Electr. Eng., 93, 429-457 (1946) [18] Gençay, R.; Selçuk, F.; Whitcher, B., Scaling properties of foreign exchange volatility, Physica A, 289, 249-266 (2001) · Zbl 0971.91511 [19] Gençay, R.; Selçuk, F.; Whitcher, B., An Introduction to Wavelets and Other Filtering Methods in Finance and Economics (2002), Academic Press: Academic Press San Diego · Zbl 1068.42029 [20] Geweke, J.; Porter-Hudak, S., The estimation and application of long memory time series models, J. Time Ser. Anal., 4, 221-238 (1983) · Zbl 0534.62062 [21] Gjerde, O.; Saettem, F., Causal relations among stock returns and macroeconomic variables in a small open economy, J. Internat. Finance Markets Instit. Money, 9, 61-87 (1999) [22] Granger, C. W.; Joyeux, R., An introduction to long-memory time series models and fractional differencing, J. Time Ser. Anal., 1, 15-29 (1980) · Zbl 0503.62079 [23] Greene, M. T.; Fielitz, B. D., Long-term dependence in common stock returns, J. Finance Econom., 5, 339-349 (1977) [24] Haubrich, J.G., Lo, A.W., 2001. The sources and nature of long-term memory in aggregate output. FRBC Econom. Rev. Q II, 15-30.; Haubrich, J.G., Lo, A.W., 2001. The sources and nature of long-term memory in aggregate output. FRBC Econom. Rev. Q II, 15-30. [25] Hassapis, C.; Kalyvitis, S., Investigating the links between growth and real stock price changes with empirical evidence from the G-7 Countries, Quarterly Rev. Econom. Finance, 42, 543-575 (2002) [26] Hosking, J. R.M., Fractional differencing, Biometrika, 68, 165-176 (1981) · Zbl 0464.62088 [27] Jensen, M. J., Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter, J. Forecasting, 18, 17-32 (1999) [28] Kim, S., In, F.H., 2003. The relationship between financial variables and real economic activity: evidence from spectral and wavelet analyses. Stud. Nonlinear Dynamics Econometrics 7-4 (Art. 4).; Kim, S., In, F.H., 2003. The relationship between financial variables and real economic activity: evidence from spectral and wavelet analyses. Stud. Nonlinear Dynamics Econometrics 7-4 (Art. 4). · Zbl 1080.91535 [29] Lee, B. S., Causal relations among stock returns, interest rates, real activity and inflation, J. Finance, 47, 591-603 (1992) [30] Lindsay, R.; Percival, D. B.; Rothrock, D. A., The discrete wavelet transform and the scale analysis of the surface properties of sea ice, IEEE Trans. Geosci. Remote Sensing, 34, 771-787 (1996) [31] Lo, A. W., Long-term memory in stock market prices, Econometrica, 59, 1279-1313 (1991) · Zbl 0781.90023 [32] Mallat, S., A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Mach. Intell., 11, 674-693 (1989) · Zbl 0709.94650 [33] Michelacci, C.; Zaffaroni, P., (Fractional) Beta convergence, J. Monetary Econom., 45, 129-153 (2000) [34] McCoy, E. J.; Walden, A. T., Wavelet analysis and synthesis of stationary long-memory processes, J. Comput. Graph. Statist., 5, 26-56 (1996) [35] Nason, G. P.; Silverman, B. W., The stationary wavelet transform and some statistical applications, (Antoniadis, A.; Oppenheim, G., Wavelets and Statistics (1995), Springer: Springer New York), 281-300 · Zbl 0828.62038 [36] Nasseh, A.; Strauss, J., Stock prices and domestic and international macroeconomic activity: a cointegration approach, Quarterly Rev. Econom. Finance, 40, 229-245 (2000) [37] Percival, D. B., On estimation of the wavelet variance, Biometrika, 82, 619-631 (1995) · Zbl 0830.62083 [38] Percival, D. B.; Walden, A. T., Wavelet Methods for Time Series Analysis (2000), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 0963.62079 [39] Pollock, D. S.G., Introduction to the special issue on statistical signal extraction and filtering, Comput. Statist. Data Anal., 50, 2137-2145 (2006) · Zbl 1445.00018 [40] R Development Core Team, 2006. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN \(3-900051-07-0. \langle;\) http://www.R-project.org \(\rangle;\); R Development Core Team, 2006. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN \(3-900051-07-0. \langle;\) http://www.R-project.org \(\rangle;\) [41] Ramsey, J.B., 2002. Wavelets in economics and finance: past and future. C.V. Starr Center for Applied Economics 11, 2002-02.; Ramsey, J.B., 2002. Wavelets in economics and finance: past and future. C.V. Starr Center for Applied Economics 11, 2002-02. [42] Ramsey, J. B.; Lampart, C., The decomposition of economic relationship by time scale using wavelets: money and income, Macroeconon. Dynamics, 2, 49-71 (1998) · Zbl 0920.90024 [43] Ramsey, J.B., Lampart, C., 1998b. The decomposition of economic relationship by time scale using wavelets: expenditure and income. Stud. Nonlinear Dynamics Econometrics 3-1, (Art. 2).; Ramsey, J.B., Lampart, C., 1998b. The decomposition of economic relationship by time scale using wavelets: expenditure and income. Stud. Nonlinear Dynamics Econometrics 3-1, (Art. 2). · Zbl 1078.91572 [44] Rapach, D. E., Macro shocks and real stock prices, J. Econom. Business, 53, 5-26 (2001) [45] Schwert, G. W., Stock returns and real activity: a century of evidence, J. Finance, 45, 1237-1257 (1990) [46] Serroukh, A.; Walden, A. T.; Percival, D. B., Statistical properties of the wavelet variance estimator for non-gaussian/non-linear time series, J. Amer. Statist. Assoc., 95, 184-196 (2000) · Zbl 0996.62085 [47] Silverberg, G., Verspagen, B., 1999. Long memory in time series of economic growth and convergence. Research Memoranda 015 Maastricht: MERIT, Maastricht Economic Research Institute on Innovation and Technology.; Silverberg, G., Verspagen, B., 1999. Long memory in time series of economic growth and convergence. Research Memoranda 015 Maastricht: MERIT, Maastricht Economic Research Institute on Innovation and Technology. · Zbl 1157.91020 [48] Sowell, F., Maximum likelihood estimation of stationary univariate fractionally integrated time series models, J. Econometrics, 53, 165-188 (1992) [49] Strang, G., Wavelets and dilation equations: a brief introduction, SIAM Rev., 31, 614-627 (1989) · Zbl 0683.42030 [50] Whitcher, B., Guttorp, P., Percival, D.B., 1999. Mathematical backgroundfor wavelet estimators for cross covariance and cross correlation. Technical Report 38, National Research Centre for Statistics and the Environment, Seattle.; Whitcher, B., Guttorp, P., Percival, D.B., 1999. Mathematical backgroundfor wavelet estimators for cross covariance and cross correlation. Technical Report 38, National Research Centre for Statistics and the Environment, Seattle. [51] Whitcher, B.; Guttorp, P.; Percival, D. B., Wavelet analysis of covariance with application to atmospheric series, J. Geophys. Res. Atmosph., 105, 14941-14962 (2000) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.