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SPECTRAL FINANCIAL ECONOMETRICS

Published online by Cambridge University Press:  06 April 2022

Federico M. Bandi  and
Andrea Tamoni
Federico M. Bandi*
Affiliation:
Carey Business School, Johns Hopkins University
Andrea Tamoni
Affiliation:
Rutgers Business School, Rutgers University
*
Address correspondence to Federico M. Bandi, Carey Business School, Johns Hopkins University, Baltimore, MD, USA; e-mail: [email protected].
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Abstract

We survey the literature on spectral regression estimation. We present a cohesive framework designed to model dependence on frequency in the response of economic time series to changes in the explanatory variables. Our emphasis is on the statistical structure and on the economic interpretation of time-domain specifications needed to obtain horizon effects over frequencies, over scales, or upon aggregation. To this end, we articulate our discussion around the role played by lead-lag effects in the explanatory variables as drivers of differential information across horizons. We provide perspectives for future work throughout.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 6: YALE 2018 CONFERENCE IN HONOR OF PETER C. B. PHILLIPS: PART II , December 2022 , pp. 1175 - 1220
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

We dedicate this article to Peter C.B. Phillips on the occasion of the conference “A Celebration of Peter Phillips’ 40 Years at Yale,” New Haven, October 19–20, 2018. We thank Peter and conference participants for their useful comments. We are especially grateful to the Editor, Guido Kuersteiner, and two anonymous reviewers for their careful reading and many helpful suggestions.

References

REFERENCES

Andersen, T.G. & Varneskov, R.T. (2021) Consistent inference for predictive regressions in persistent economic systems. Journal of Econometrics 224, 215–244.CrossRefGoogle Scholar
Bandi, F.M., Chaudhuri, S., Lo, A.W., & Tamoni, A. (2021) Spectral factor models. Journal of Financial Economics 142, 214–238.CrossRefGoogle Scholar
Bandi, F.M. & Perron, B. (2006) Long memory and the relation between implied and realized volatility. Journal of Financial Econometrics 4, 636–670.CrossRefGoogle Scholar
Bandi, F.M., Perron, B., Tamoni, A., & Tebaldi, C. (2019) The scale of predictability. Journal of Econometrics 208, 120–140.CrossRefGoogle Scholar
Bandi, F.M. & Su, Y. (2022) Conditional Spectral Methods. Working paper, Johns Hopkins University.CrossRefGoogle Scholar
Bandi, F.M. & Tamoni, A. (2021) Business-Cycle Consumption Risk and Asset Prices. Working paper, Johns Hopkins University and Rutgers University.Google Scholar
Bansal, R. & Yaron, A. (2004) Risks for the long run: A potential resolution of asset pricing puzzles. Journal of Finance 59, 1481–1509.CrossRefGoogle Scholar
Baxter, M. & King, R.G. (1999) Measuring business cycles: Approximate band-pass filters for economic time series. Review of Economics and Statistics 81, 575–593.Google Scholar
Berkowitz, J. (2001) Generalized spectral estimation of the consumption-based asset pricing model. Journal of Econometrics 104, 269–288.CrossRefGoogle Scholar
Beveridge, S. & Nelson, C.R. (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the “business cycle”. Journal of Monetary Economics 7, 151–174.CrossRefGoogle Scholar
Burns, A.F. & Mitchell, W.C. (1946) Measuring Business Cycles . National Bureau of Economic Research.Google Scholar
Campbell, J.Y. & Mankiw, G. (1987) Are output fluctuations transitory? Quarterly Journal of Economics 102, 857–880.CrossRefGoogle Scholar
Chaudhuri, S.E. & Lo, A.W. (2015) Spectral analysis of stock-return volatility, correlation, and beta. In 2015 IEEE Signal Processing and Signal Processing Education Workshop , pp. 232–236.CrossRefGoogle Scholar
Chaudhuri, S.E. & Lo, A.W. (2018) Dynamic alpha: A spectral decomposition of investment performance across time horizons. Management Science 65, 4440–4450.CrossRefGoogle Scholar
Choi, I. & Phillips, P.C.B. (1993) Testing for a unit root by frequency domain regression. Journal of Econometrics 59, 263–286.CrossRefGoogle Scholar
Christensen, B.J. & Nielsen, M.Ø. (2006) Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting. Journal of Econometrics 133, 343–371.CrossRefGoogle Scholar
Christiano, L.J. & Fitzgerald, T.J. (2003) The band pass filter. International Economic Review 44, 435–465.CrossRefGoogle Scholar
Christiano, L.J. & Vigfusson, R.J. (2003) Maximum likelihood in the frequency domain: The importance of time-to-plan. Journal of Monetary Economics 50, 789–815.CrossRefGoogle Scholar
Cogley, T. (2001) A frequency decomposition of approximation errors in stochastic discount factor models. International Economic Review 42, 473–503.CrossRefGoogle Scholar
Cohen, L. & Frazzini, A. (2008) Economic links and predictable returns. Journal of Finance 63, 1977–2011.Google Scholar
Cohen, K.J., Hawawini, G.A., Maier, S.F., Schwartz, R.A., & Whitcomb, D.K. (1983) Friction in the trading process and the estimation of systematic risk. Journal of Financial Economics 12, 263–278.CrossRefGoogle Scholar
Cohen, R.B., Polk, C., & Vuolteenaho, T. (2009) The price is (almost) right. Journal of Finance 64, 2739–2782.CrossRefGoogle Scholar
Comin, D. & Gertler, M. (2006) Medium-term business cycles. American Economic Review 96, 523–551.CrossRefGoogle Scholar
Corbae, D., Ouliaris, S., & Phillips, P.C.B. (1994) A reexamination of the consumption function using frequency domain regressions. Empirical Economics 19, 595–609.CrossRefGoogle Scholar
Corbae, D., Ouliaris, S., & Phillips, P.C.B. (2002) Band spectral regression with trending data. Econometrica 70, 1067–1109.Google Scholar
Corsi, F. (2009) A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics 7, 174–196.CrossRefGoogle Scholar
Croux, C., Forni, M., & Reichlin, L. (2001) A measure of comovement for economic variables: Theory and empirics. Review of Economics and Statistics 83, 232–241.Google Scholar
Daubechies, I. (1992) Ten Lectures on Wavelets . Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Bondt, D., Werner, F.M., & Thaler, R. (1985) Does the stock market overreact? Journal of Finance 40, 793–805.CrossRefGoogle Scholar
Dew-Becker, I. & Giglio, S. (2016) Asset pricing in the frequency domain: Theory and empirics. Review of Financial Studies 29, 2029–2068.CrossRefGoogle Scholar
Diebold, F.X., Ohanian, L.E., & Berkowitz, J. (1998) Dynamic equilibrium economies: A framework for comparing models and data. Review of Economic Studies 65, 433–451.CrossRefGoogle Scholar
Dimson, E. (1979) Risk measurement when shares are subject to infrequent trading. Journal of Financial Economics 7, 197–226.CrossRefGoogle Scholar
Engle, R.F. (1974) Band spectrum regression. International Economic Review 15, 1–11.CrossRefGoogle Scholar
Engle, R.F. (1978) Testing price equations for stability across spectral frequency bands. Econometrica 46, 869–881.CrossRefGoogle Scholar
Englund, P., Persson, T., & Svensson, L.E.O. (1992) Swedish business cycles: 1861–1988. Journal of Monetary Economics 30, 343–371.CrossRefGoogle Scholar
Fama, E.F. & French, K.R. (1992) The cross-section of expected stock returns. Journal of Finance 47, 427–465.Google Scholar
Faria, G. & Verona, F. (2018) Forecasting stock market returns by summing the frequency-decomposed parts. Journal of Empirical Finance 45, 228–242.CrossRefGoogle Scholar
Faria, G. & Verona, F. (2020) Time-frequency forecast of the equity premium. Quantitative Finance 21, 1–17.Google Scholar
Feng, G., Giglio, S., & Xiu, D. (2020) Taming the factor zoo: A test of new factors. Journal of Finance 75, 1327–1370.CrossRefGoogle Scholar
Freyberger, J., Neuhierl, A., & Weber, M. (2020) Dissecting characteristics nonparametrically. Review of Financial Studies 33, 2326–2377.CrossRefGoogle Scholar
Friedman, M. (1957) A Theory of the Consumption Function . Princeton University Press.CrossRefGoogle Scholar
Friedman, M. & Kuznets, S. (1954) Income from Independent Professional Practice . National Bureau of Economic Research.Google Scholar
Fuster, A., Laibson, D., & Mendel, B. (2010) Natural expectations and macroeconomic fluctuations. Journal of Economic Perspectives 24, 67–84.CrossRefGoogle ScholarPubMed
Gençay, R., Selçuk, F., & Whitcher, B.J. (2001) An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Elsevier.Google Scholar
Gençay, R., Selçuk, F., & Whitcher, B.J. (2003) Systematic risk and timescales. Quantitative Finance 3, 108–116.CrossRefGoogle Scholar
Gençay, R., Selçuk, F., & Whitcher, B.J. (2005) Multiscale systematic risk. Journal of International Money and Finance 24, 55–70.CrossRefGoogle Scholar
Gilbert, T., Hrdlicka, C., Kalodimos, J., & Siegel, S. (2014) Daily data is bad for beta: Opacity and frequency-dependent betas. Review of Asset Pricing Studies , 4, 78–117.CrossRefGoogle Scholar
Granger, C.W.J. & Lin, J.-L. (1995) Causality in the long run. Econometric Theory 11, 530–536.Google Scholar
Granger, C.W.J. & Watson, M.W. (1984) Time series and spectral methods in econometrics. In Griliches, Z. & Intriligator, M.D. (eds). Handbook of Econometrics , vol. 2, pp. 979–1022. Elsevier.CrossRefGoogle Scholar
Haar, A. (1910) Zur theorie der orthogonalen funktionensysteme. Mathematische Annalen 69, 331–371.CrossRefGoogle Scholar
Hamilton, J.D. (2018) Why you should never use the Hodrick-Prescott filter. Review of Economics and Statistics 100, 831–843.CrossRefGoogle Scholar
Handa, P., Kothari, S.P., & Wasley, C. (1989) The relation between the return interval and betas: Implications for the size effect. Journal of Financial Economics 23, 79–100.CrossRefGoogle Scholar
Handa, P., Kothari, S.P., & Wasley, C. (1993) Sensitivity of multivariate tests of the capital asset-pricing model to the return measurement interval. Journal of Finance 48, 1543–1551.CrossRefGoogle Scholar
Hannan, E.J. (1963a) Regression for time series. In Rosenblatt, M. (ed). Time Series Analysis , pp. 17–37. Wiley.Google Scholar
Hannan, E.J. (1963b) Regression for time series with errors of measurement. Biometrika 50, 293–302.CrossRefGoogle Scholar
Hannan, E.J. (1969) The estimation of mixed moving average autoregressive systems. Biometrika 56, 579–593.CrossRefGoogle Scholar
Hannan, E.J. (1970) Multiple Time Series . Wiley.CrossRefGoogle Scholar
Hannan, E.J. & Robinson, P.M. (1973) Lagged regression with unknown lags. Journal of the Royal Statistical Society, Series B 35, 252–267.Google Scholar
Hannan, E.J. & Thomson, P.J. (1971) Spectral inference over narrow bands. Journal of Applied Probability 8, 157–169.CrossRefGoogle Scholar
Harvey, A.C. (1978) Linear regression in the frequency domain. International Economic Review 19, 507–512.CrossRefGoogle Scholar
Harvey, C.R., Liu, Y., & Zhu, H. (2016) … and the cross-section of expected returns. Review of financial studies 29, 5–68.CrossRefGoogle Scholar
Hawawini, G. (1983) Why beta shifts as the return interval changes. Financial Analysts Journal 39, 73–77.CrossRefGoogle Scholar
Heston, S.L. & Sadka, R. (2008) Seasonality in the cross-section of stock returns. Journal of Financial Economics 87, 418–445.CrossRefGoogle Scholar
Hodrick, R.J. (2020) An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data. Working paper, Columbia University.CrossRefGoogle Scholar
Hodrick, R.J. & Prescott, E.C. (1997) Postwar US business cycles: An empirical investigation. Journal of Money, Credit, and Banking 29, 1–16.CrossRefGoogle Scholar
Hong, H. & Stein, J.C. (1999) A unified theory of underreaction, momentum trading, and overreaction in asset markets. Journal of Finance 54, 2143–2184.CrossRefGoogle Scholar
Hong, H., Torous, W., & Valkanov, R. (2007) Do industries lead stock markets? Journal of Financial Economics 83, 367–396.CrossRefGoogle Scholar
Hosoya, Y. (1991) The decomposition and measurement of the interdependency between second-order stationary processes. Probability Theory and Related Fields 88, 429–444.CrossRefGoogle Scholar
Hou, K. & Moskowitz, T.J. (2005) Market frictions, price delay, and the cross-section of expected returns. Review of Financial Studies 18, 981–1020.CrossRefGoogle Scholar
Jegadeesh, N. (1990) Evidence of predictable behavior of security returns. Journal of Finance 45, 881–898.CrossRefGoogle Scholar
Jordà, Ò. (2005) Estimation and inference of impulse responses by local projections. American Economic Review 95, 161–182.CrossRefGoogle Scholar
Kamara, A., Korajczyk, R.A., Lou, X., & Sadka, R. (2016) Horizon pricing. Journal of Financial and Quantitative Analysis 51, 1769–1793.CrossRefGoogle Scholar
Kang, B.U., In, F., & Kim, T.S. (2017) Timescale betas and the cross section of equity returns: Framework, application, and implications for interpreting the Fama–French factors. Journal of Empirical Finance 42, 15–39.CrossRefGoogle Scholar
Keim, D.B. (1983) Size-related anomalies and stock return seasonality: Further empirical evidence. Journal of Financial Economics 12, 13–32.CrossRefGoogle Scholar
Kelly, B.T., Pruitt, S., & Su, Y. (2019) Characteristics are covariances: A unified model of risk and return. Journal of Financial Economics 134, 501–524.CrossRefGoogle Scholar
Kim, S., Korajczyk, R.A., & Neuhierl, A. (2021) Arbitrage portfolios. Review of Financial Studies 34, 2813–2856.CrossRefGoogle Scholar
King, R.G. & Watson, M.W. (1996) Money, prices, interest rates and the business cycle. Review of Economics and Statistics 78, 35–53.CrossRefGoogle Scholar
Kothari, S.P., Shanken, J., & Sloan, R.G. (1995) Another Look at the Cross-Section of Expected Stock Returns. Journal of Finance 50, 185–224.CrossRefGoogle Scholar
Kozak, S., Nagel, S., & Santosh, S. (2020) Shrinking the cross-section. Journal of Financial Economics 135, 271–292.CrossRefGoogle Scholar
Lettau, M. & Pelger, M. (2020) Factors that fit the time series and cross-section of stock returns. Review of Financial Studies 33, 2274–2325.CrossRefGoogle Scholar
Levhari, D. & Levy, H. (1977) The capital asset pricing model and the investment horizon. Review of Economics and Statistics 59, 92–104.CrossRefGoogle Scholar
Lintner, J. (1965) The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47, 13–37.CrossRefGoogle Scholar
Lo, A.W. & MacKinlay, A. Craig (1990) An econometric analysis of nonsynchronous trading. Journal of Econometrics 45, 181–211.CrossRefGoogle Scholar
Mallat, S.G. (1989) A Theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 674–693.CrossRefGoogle Scholar
Marinucci, D. (2000) Spectral regression for cointegrated time series with long-memory innovations. Journal of Time Series Analysis 21, 685–705.CrossRefGoogle Scholar
Marinucci, D. & Robinson, P.M. (2001) Semiparametric fractional cointegration analysis. Journal of Econometrics 105, 225–247.CrossRefGoogle Scholar
Marinucci, D. & Robinson, P.M. (2003) Semiparametric frequency domain analysis of fractional cointegration. In Robinson, P.M. (ed.), Time Series with Long Memory , pp. 334–371. Oxford University Press.Google Scholar
Markowitz, H. (1952) Portfolio selection. Journal of Finance 7, 77–91.Google Scholar
Müller, U.K. & Watson, M.W. (2008) Testing models of low-frequency variability. Econometrica 76, 979–1016.Google Scholar
Müller, U.K. & Watson, M.W. (2016) Measuring uncertainty about long-run predictions. Review of Economic Studies 83, 1711–1740.CrossRefGoogle Scholar
Müller, U.K. & Watson, M.W. (2017) Low-Frequency Econometrics. In Honoré, B., Pakes, A., Piazzesi, M., & Samuelson, L. (eds.), Advances in Economics and Econometrics , vol. 2, pp. 53–94. Cambridge University Press.CrossRefGoogle Scholar
Müller, U.K. & Watson, M.W. (2018) Long-run covariability. Econometrica 86, 775–804.CrossRefGoogle Scholar
Neuhierl, A. & Varneskov, R.T. (2021) Frequency dependent risk. Journal of Financial Economics 140, 644–675.CrossRefGoogle Scholar
Ortu, F., Severino, F., Tamoni, A., & Tebaldi, C. (2020) A persistence-based Wold-type decomposition for stationary time series. Quantitative Economics 11, 203–230.CrossRefGoogle Scholar
Ortu, F., Tamoni, A., & Tebaldi, C. (2013) Long-run risk and the persistence of consumption shocks. Review of Financial Studies 26, 2876–2915.CrossRefGoogle Scholar
Otrok, C., Ravikumar, B., & Whiteman, C.H. (2002) Habit formation: A resolution of the equity premium puzzle? Journal of Monetary Economics 49, 1261–1288.CrossRefGoogle Scholar
Phillips, P.C.B. (1991) Spectral regression for cointegrated time series. In Barnett, W., Powell, J., & Tauchen, G. (eds.), Nonparametric and Semiparametric Methods in Economics and Statistics, pp. 413–435. Cambridge University Press.Google Scholar
Phillips, P.C.B. (1998) New tools for understanding spurious regressions. Econometrica 66, 1299–1325.CrossRefGoogle Scholar
Phillips, P.C.B. (2005) HAC estimation by automated regression. Econometric Theory 21, 116–142.CrossRefGoogle Scholar
Phillips, P.C.B. & Jin, S. (2020) Business cycles, trend elimination, and the HP filter. International Economic Review 62, 469–520.CrossRefGoogle Scholar
Phillips, P.C.B. & Loretan, M. (1991) Estimating long-run economic equilibria. Review of Economic Studies 58, 407–436.CrossRefGoogle Scholar
Phillips, P.C.B. & Shi, Z. (2020) Boosting: Why you can use the HP filter. International Economic Review 62, 521–570.CrossRefGoogle Scholar
Robinson, P.M. (1977) The construction and estimation of continuous-time models and discrete approximations in econometrics. Journal of Econometrics 6, 173–197.CrossRefGoogle Scholar
Roll, R. (1977) A critique of the asset pricing theory’s tests Part I: On past and potential testability of the theory. Journal of Financial Economics 4, 129–176.CrossRefGoogle Scholar
Rozeff, M.S. & Kinney, W.R. (1976) Capital market seasonality: The case of stock returns. Journal of Financial Economics 3, 379–402.CrossRefGoogle Scholar
Sarno, L., Thornton, D.L., & Wen, Y. (2007) What’s unique about the federal funds rate? Evidence from a spectral perspective. Oxford Bulletin of Economics and Statistics 69, 293–319.CrossRefGoogle Scholar
Scholes, M. & Williams, J. (1977) Estimating betas from nonsynchronous data. Journal of Financial Economics 5, 309–327.CrossRefGoogle Scholar
Schwartz, R.A. & Whitcomb, D.K. (1977) Evidence on the presence and causes of serial correlation in market model residuals. Journal of Financial and Quantitative Analysis 12, 291–313.CrossRefGoogle Scholar
Sharpe, W.F. (1964) Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19, 425–442.Google Scholar
Shensa, M.J. (1992) The discrete wavelet transform: Wedding the à trous and Mallat algorithms. IEEE Transactions on Signal Processing 40, 2464–2482.CrossRefGoogle Scholar
Smith, K.V. (1978) The effect of intervaling on estimating parameters of the capital asset pricing model. Journal of Financial and Quantitative Analysis 13, 313–332.CrossRefGoogle Scholar
Thomson, P.J. (1986) Band-limited spectral estimation of autoregressive-moving-average processes. Journal of Applied Probability 23, 143–155.CrossRefGoogle Scholar
Watson, M.W. (1993) Measures of fit for calibrated models. Journal of Political Economy 101, 1011–41.CrossRefGoogle Scholar
Xiao, Z. & Phillips, P.C.B. (1998) Higher-order approximations for frequency domain time series regression. Journal of Econometrics 86, 297–336.CrossRefGoogle Scholar
Yu, J. (2012) Using long-run consumption-return correlations to test asset pricing models. Review of Economic Dynamics 15, 317–335.CrossRefGoogle Scholar