Abstract
Spectral analysis is a statistical approach for analysing stationary time series data in which the series is decomposed into cyclical or periodic components indexed by the frequency of repetition. Spectral analysis falls within the frequency domain approach to time series analysis. The spectral density function plays the central role and it summarizes the contributions of cyclical components to the variation of a stationary time series. The spectral density at frequency zero is particularly important because of its direct link to the variance of a time series sample average, that is, the long-run variance.
Keywords
- Alias effect
- ARMA models
- Autocovariances
- Autoregressive spectral density estimator
- Bandwidth
- Bartlett kernel
- Bias
- Cross-spectral densities
- Cycles
- Econometric methodology
- Fixed-b asymptotics
- Frequency
- Frequency domain
- Generalized method of moments
- Granger causality
- Heteroskedasticity and autocorrelation covariance matrix estimation
- Kernel estimators
- Long-run variance
- Mean square error
- Nonparametric estimators
- Probability
- Quadratic spectral kernel
- Spectral analysis
- Spectral density
- Spectral density matrix
- Spectral representation theorem
- Time domain
- Time series analysis
- Truncation lag
- Variance
- White noise
JEL classifications
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Andrews, D.W.K. 1991. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59: 817–854.
Berk, K. 1974. Consistent autoregressive spectral estimates. Annals of Statistics 2: 489–502.
Blanchard, O., and D. Quah. 1989. The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79: 655–673.
Cochrane, J.H. 1988. How big is the random walk in GNP? Journal of Political Economy 96: 893–920.
Engle, R. 1974. Band spectrum regression. International Economic Review 15: 1–11.
Geweke, J., and S. Porter-Hudak. 1983. The estimation and application of long memory time series. Journal of Time Series Analysis 4: 221–238.
Goncalves, S., and T.J. Vogelsang. 2006. Block bootstrap puzzles in HAC robust testing: The sophistication of the naive bootstrap. Working paper, Department of Economics, Michigan State University.
Granger, C. 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37: 424–438.
den Haan, W.J., and A. Levin. 1997. A practictioner’s guide to robust covariance matrix estimation. In Handbook of statistics: Robust inference, ed. G. Maddala and C. Rao, vol. 15. New York: Elsevier.
Hamilton, J.D. 1994. Time series analysis. Princeton: Princeton University Press.
Hansen, L.P. 1982. Large sample properties of generalized method of moments estimators. Econometrica 50: 1029–1054.
Hashimzade, N., and T.J. Vogelsang. 2007. Fixed-b asymptotic approximation of the sampling behavior of nonparametric spectral density estimators. Journal of Time Series Analysis.
Hashimzade, N., N.M. Kiefer, and T.J. Vogelsang. 2005. Moments of HAC robust covariance matrix estimators under fixed-b asymptotics. Working paper, Department of Economics, Cornell University.
Hong, Y. 1996. Consistent testing for serial correlation of unknown form. Econometrica 64: 837–864.
Jansson, M. 2004. The error rejection probability of simple autocorrelation robust tests. Econometrica 72: 937–946.
Kiefer, N.M., and T.J. Vogelsang. 2005. A new asymptotic theory for heteroskedasticity autocorrelation robust tests. Econometric Theory 21: 1130–1164.
King, R., C. Plosser, J. Stock, and M. Watson. 1991. Stochastic trends and economic fluctuations. American Economic Review 81: 819–840.
Neave, H.R. 1970. An improved formula for the asymptotic variance of spectrum estimates. Annals of Mathematical Statistics 41: 70–77.
Neave, H.R. 1971. The exact error in spectrum estimates. Annals of Mathematical Statistics 42: 901–975.
Newey, W.K., and K.D. West. 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703–708.
Newey, W.K., and K.D. West. 1994. Automatic lag selection in covariance estimation. Review of Economic Studies 61: 631–654.
Ng, S., and P. Perron. 1996. The exact error in estimating the spectral density at the origin. Journal of Time Series Analysis 17: 379–408.
Parzen, E. 1957. On consistent estimates of the spectrum of a stationary time series. Annals of Mathematical Statistics 28: 329–348.
Perron, P., and S. Ng. 1998. An autoregressive spectral density estimator at frequency zero for nonstationarity tests. Econometric Theory 14: 560–603.
Phillips, P.C.B., and B.E. Hansen. 1990. Statistical inference in instrumental variables regression with i(1) processes. Review of Economic Studies 57: 99–125.
Phillips, P.C.B., and P. Perron. 1988. Testing for a unit root in time series regression. Biometrika 75: 335–346.
Phillips, P.C.B., Y. Sun, and S. Jin. 2005. Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing. Working Paper No. 2005–12, Department of Economics, UCSD.
Phillips, P.C.B., Y. Sun, and S. Jin. 2006. Spectral density estimation and robust hypothesis testing using steep origin kernels without truncation. International Economic Review 47: 837–894.
Priestley, M.B. 1981. Spectral analysis and time series, vol. 1. New York: Academic.
Robinson, P. 1991. Automatic frequency domain inference on semiparametric and nonparametric models. Econometrica 59: 1329–1363.
Stock, J., and M. Watson. 1988. Testing for common trends. Journal of the American Statistical Association 83: 1097–1107.
Velasco, C., and P.M. Robinson. 2001. Edgeworth expansions for spectral density estimates and studentized sample mean. Econometric Theory 17: 497–539.
Watson, M.W. 1993. Measures of fit for calibrated models. Journal of Political Economy 101: 1011–1041.
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Vogelsang, T.J. (2018). Spectral Analysis. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1275
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DOI: https://doi.org/10.1057/978-1-349-95189-5_1275
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