Leverage, skewness and amplitude asymmetric cycles

Artiach, Miguel (2012): Leverage, skewness and amplitude asymmetric cycles.

Abstract

The leverage parameter is shown to turn up as part of the third-order moment when a stochastic volatility process is linearly filtered. If the filter is of the autoregressive class and possesses complex-valued roots or is a Gegenbauer long-memory filter, the leverage effect plays a determinant role in producing Amplitude Asymmetric Cycles, in which the degree of asymmetry depends on the persistence of the process at both levels (conditional mean and variance), the variance of the shocks to the volatility and the value of their inter-temporal correlation with the shocks to the levels.

• Item Type: MPRA Paper
• Language: English
• Keywords: Leverage, stochastic volatility, skewness, amplitude asymmetric cycles
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E37 - Forecasting and Simulation: Models and Applications

References

Arteche, J. (2011). Standard and seasonal long memory in volatility: an application to Spanish inflation. Empirical Economics, pages 1–20.

Arteche, J. and Velasco, C. (2005). Trimming and tapering semi-parametric estimates in asymmetric long memory time series. Journal of Time Series Analysis, 26(4):581–611.

Black, F. (1976). Studies of stock price volatility changes. In Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics Statistics Section, pages 177–181.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3):307–327.

Breidt, F., Crato, N., and De Lima, P. (1998). The detection and estimation of long memory in stochastic volatility. Journal of Econometrics, 83(1-2):325–348.

Candelon, B. and Gil-Alaña, L. (2004). Fractional integration and business cycle features. Empirical economics, 29(2):343–359.

Caporale, G. and Gil-Alaña, L. (2006). Long memory at the long run and at the cyclical frequencies: modelling real wages in england, 1260–1994. Empirical Economics, 31(1):83–93.

Caporale, G. and Gil-Alaña, L. (2007). Nonlinearities and fractional integration in the US unemployment rate. Oxford Bulletin of Economics and Statistics, 69(4):521–544.

Collard, F. (1998). Spectral and persistence properties of cyclical growth. Journal of Economic Dynamics and Control, 23(3):463–488.

Engle, R. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, pages 987–1007.

Ferrara, L. and Guegan, D. (2008). Business surveys modelling with seasonal-cyclical long memory models. Universit´e Paris1 Panth´eon-Sorbonne (Post-Print and Working Papers).

Giraitis, L., Kokoszka, P., and Leipus, R. (2000). Stationary ARCH models: dependence structure and central limit theorem. Econometric theory, 16(1):3–22.

Hamilton, J. (1994). Time series analysis. Princeton Univ Pr.

Hamori, S. (2000). Volatility of real GDP: some evidence from the united states, the united kingdom and japan. Japan and the World Economy, 12(2):143–152.

Hansen, L. (1982). Large sample properties of generalized method of moments estimators. Econometrica: Journal of the Econometric Society, pages 1029–1054.

Harvey, A. (1998). Long memory in stochastic volatility. In Forecasting volatility in the financial markets, page 351. Butterworth-Heinemann.

Harvey, A. and Shephard, N. (1996). Estimation of an asymmetric stochastic volatility model for asset returns. Journal of Business & Economic Statistics, 14(4):429–434.

Ho, K. and Tsui, A. (2003). Asymmetric volatility of real GDP: Some evidence from canada, japan, the united kingdom and the united states. Japan and the World Economy, 15(4):437–445.

Ho, K., Tsui, A., and Zhang, Z. (2009). Modelling volatility asymmetry of business cycles in the US. Mathematics and Computers in Simulation, 79:2856–2868.

Jacquier, E., Polson, N., and Rossi, P. (2004). Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics, 122(1):185–212.

Kramer, W. and Runde, R. (1994). Some pitfalls in using empirical autocorrelations to test for zero correlation among common stock returns. Econometric Analysis of financial Markets, pages 1–10.

Maravall, A. and del Rio, A. (2001). Time aggregation and the Hodrick-Prescott filter. Working paper 0108, Banco de España.

Milhøj, A. (1985). The moment structure of ARCH processes. Scandinavian Journal of Statistics, pages 281–292.

Pérez, A. (2000). Estimación e identificación de modelos de volatilidad estocástica con memoria larga. PhD thesis, Universidad de Valladolid.

Sichel, D. E. (1993). Business cycle asymmetry: a deeper look. Economic Inquiry, 31:224–236.

Taylor, S. (1986). Modeling financial time series. Wiley, New York, NY.

Welsh, A. and Jernigan, R. (1983). A statistic to identify asymmetric time series. American Statistical Association 1983 Proceedings of the Business and Economics Statistics Section, pages 390–395.

Yang, M. (2008). Normal log-normal mixture, leptokurtosis and skewness. Applied Economics Letters, 15(9):737–742.

Yu, J. (2005). On leverage in a stochastic volatility model. Journal of Econometrics, 127(2):165–178.

Yule, G. (1927). On a method of investigating periodicities in disturbed series, with special reference to wolfer’s sunspot numbers. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 226:636–646.

Zaffaroni, P. (2003). Gaussian inference on certain long-range dependent volatility models. Journal of Econometrics, 115(2):199–258.