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VAR Models: Estimation, Inferences, and Applications

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Handbook of Financial Econometrics and Statistics

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Abstract

Vector autoregression (VAR) models have been used extensively in finance and economic analysis. This paper provides a brief overview of the basic VAR approach by focusing on model estimation and statistical inferences. Applications of VAR models in some finance areas are discussed, including asset pricing, international finance, and market microstructure. It is shown that such approach provides a powerful tool to study financial market efficiency, stock return predictability, exchange rate dynamics, and information content of stock trades and market quality.

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Notes

  1. 1.

    For further discussions on VAR techniques, see Watson (1994); Lutkepohl (1991), and Stock and Watson (2001), among others.

  2. 2.

    For more estimation details, refer to Hasbrouck (1993).

  3. 3.

    Whether options lead stocks in the price discovery process is still a question open to debate. Early studies in this literature present strong evidence in favor of the option lead in prices. For example, Latane and Rendleman (1976) and Beckers (1981) show that the volatility implied in option prices predicts future stock-price volatility. Consistently, Manaster and Renleman (1982) find that the option-implied stock prices contain valuable information about the equilibrium prices of the underlying stocks that has not been revealed in the stock market. However, Vijh (1988) questions the results in Manaster and Rendleman (1982), since using daily closing prices introduces a bias associated with the bid-ask spread and nonsynchronous trading. After purging the effects of bid-ask spreads, Stephan and Whaley (1990) find that the stock market leads the option market. Nevertheless, Chan et al. (1993) argue that the stock lead is due to the relative smaller stock tick. If the average of the bid and ask is used instead of transaction prices, neither market leads the other. Latter studies on the stock option lead-lag analysis have been focused more on the trading volume. Easley et al. (1998) show that “positive news option volumes” and “negative news option volumes” have predictive power for future stock-price changes. See also Pan and Poteshman (2006) and Cao et al. (2003). By measuring the relative share of price discovery occurring in the stock and option markets, Chakravarty et al. (2004) conclude that informed trading takes place in both stock and option markets, suggesting an important role for option volume.

  4. 4.

    Zhou’s (2009) analysis incorporates the option market trades in addition to the stock and bond market transactions. Chava and Tookes (2005) also incorporate the option markets and examine the volatility reaction of stock, bond, and options to macroeconomic and firm specific information, finding significant effects near announcements. Overall, they find that corporate bond and option trades have information content for future stock price movements.

  5. 5.

    For convertible bonds, Downing et al. (2009) find that these results also hold, but only for those with conversion options deep in the money. Kwan (1996) first examines the relation between individual stocks and bonds using weekly quote data and also finds evidence in support of stock leads.

References

  • Baillie, R., & Bollwerslev, T. (1989). Common stochastic trends in a system of exchange rates. Journal of Finance, 44, 167–181.

    Article  Google Scholar 

  • Beckers, S. (1981). Standard deviations implied in option prices as predictors of future stock price variability. Journal of Banking and Finance, 5, 363–381.

    Article  Google Scholar 

  • Bekaert, G., & Hodrick, R. (1992). Characterizing predictable components in excess returns on equity and foreign exchange markets. Journal of Finance, 47, 467–509.

    Article  Google Scholar 

  • Black, F. (1975). Fact and fantasy in the use of options. Financial Analysts Journal, 31(36–41), 61–72.

    Google Scholar 

  • Campbell, J., & Shiller, R. (1987). Cointegration and tests of present value models. Journal of Political Economy, 95, 1062–1088.

    Article  Google Scholar 

  • Campbell, J., & Shiller, R. (1989). The dividend-price ratio and expectations of future dividends and discount factors. Review of Financial Studies, 1, 195–228.

    Article  Google Scholar 

  • Campbell, J., & Viceira, L. (1999). Consumption and portfolio decisions when expected returns are time varying. Quarterly Journal of Economics, 114, 433–495.

    Article  Google Scholar 

  • Campbell, J., Chan, Y. L., & Viceira, L. (2003). A multivariate model of strategic asset allocation. Journal of Financial Economics, 67, 41–80.

    Article  Google Scholar 

  • Cao, C., Chen, Z., & Griffin, J. M. (2003). The informational content of option volume prior to takeovers. Journal of Business, 78, 1071–1109.

    Google Scholar 

  • Chakravarty, S., Gulen, H., & Mayhew, S. (2004). Informed trading in stock and option markets. Journal of Finance, 59, 1235–1258.

    Article  Google Scholar 

  • Chan, K., Chung, P., & Johnson, H. (1993). Why option prices lag stock prices: A trading-based explanation. Journal of Finance, 48, 1957–1967.

    Article  Google Scholar 

  • Chan, K., Chung, Y. P., & Fong, W.-M. (2002). The informational role of stock and option volume. Review of Financial Studies, 15, 1049–1075.

    Article  Google Scholar 

  • Chava, S., & Tookes, H. (2005). Where (and how) does news impact trading? (Unpublished working paper). Texas A&M University/Yale School of Management.

    Google Scholar 

  • Cochrane, J. (1992). Explaining the variance of price-dividend ratios. Review of Financial Studies, 5, 243–280.

    Article  Google Scholar 

  • De Long, B., Shleifer, A., Summers, L., & Waldman, R. (1990). Noise trader risk in financial markets. Journal of Political Economy, 98, 703–738.

    Article  Google Scholar 

  • Diebold, F., Gardeazabai, J., & Yilmaz, K. (1994). On cointegration and exchange rate dynamics. Journal of Finance, 49, 727–735.

    Article  Google Scholar 

  • Downing, C., Underwood, S., & Xing, Y. (2009). An intraday analysis of the relative informational efficiency of stocks and bonds. Journal of Financial and Quantitative Analysis, 44, 1081–1102.

    Article  Google Scholar 

  • Easley, D., O’Hara, M., & Srinivas, P. S. (1998). Option volume and stock prices: Evidence on where informed traders trade. Journal of Finance, 53, 431–466.

    Article  Google Scholar 

  • Fama, E., & French, K. (1988). Dividend yields and expected stock returns. Journal of Financial Economics, 22, 3–26.

    Article  Google Scholar 

  • Flood, R., Hodrick, R., & Kaplan, P. (1986). An evaluation of recent evidence on stock market bubbles (NBER working paper).

    Google Scholar 

  • Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross spectral methods. Econometrica, 37, 424–438.

    Article  Google Scholar 

  • Gurun, U. G., Johnston, R., & Markov, S. (2011). Sell-side debt analysts and market efficiency (Working paper).

    Google Scholar 

  • Hai, W., Mark, N., & Wu, Y. (1997). Understanding spot and forward exchange rate regressions. Journal of Applied Econometrics, 12, 715–734.

    Article  Google Scholar 

  • Hamilton, J. D. (1994). Time series analysis. Princeton: Princeton University Press.

    Google Scholar 

  • Hasbrouck, J. (1991). Measuring the information content of stock trades. Journal of Finance, 46, 179–207.

    Article  Google Scholar 

  • Hasbrouck, J. (1993). Assessing the quality of a security market: A new approach to transaction-cost measurement. Review of Financial Studies, 6, 191–212.

    Article  Google Scholar 

  • Hodrick, R. (1992). Dividend yields and expected stock returns: Alternative procedures for inference and measurement. Review of Financial Studies, 5, 357–386.

    Article  Google Scholar 

  • Hotchkiss, E. S., & Ronen, T. (2002). The informational efficiency of the corporate bond market: An intraday analysis. Review of Financial Studies, 15, 1325–1354.

    Article  Google Scholar 

  • Kwan, S. H. (1996). Firm-specific information and the correlation between individual stocks and bonds. Journal of Financial Economics, 40, 63–80.

    Article  Google Scholar 

  • Latane, H., & Rendleman, R. J. (1976). Standard deviation of stock price ratios implied in option prices. Journal of Finance, 31, 369–381.

    Article  Google Scholar 

  • Lee, B.-S. (1996). Time-series implications of aggregate dividend behavior. Review of Financial Studies, 9, 589–618.

    Article  Google Scholar 

  • Lee, B.-S. (1998). Permanent, temporary and non-fundamental components of stock prices. Journal of Financial and Quantitative Analysis, 33, 1–32.

    Article  Google Scholar 

  • Lutkepohl, H. (1991). Introduction to multiple time series analysis. Berlin: Springer.

    Book  Google Scholar 

  • Manaster, S., & Rendelman, R. J. (1982). Option prices as predictors of equilibrium stock prices. Journal of Finance, 37, 1043–1057.

    Article  Google Scholar 

  • Mankiw, N. G., Romer, D., & Shapiro, M. D. (1991). Stock market forecastability and volatility: A statistical appraisal. Review of Economic Studies, 58, 455–477.

    Article  Google Scholar 

  • Mark, N. (1995). Exchange rates and fundamentals: Evidence on long-horizon predictability. American Economic Review, 85, 201–218.

    Google Scholar 

  • Mark, N., & Sul, D. (2001). Nominal exchange rates and monetary fundamentals: Evidence from a small post-Bretton Woods panel. Journal of International Economics, 53, 29–52.

    Article  Google Scholar 

  • Mark, N., & Wu, Y. (1998). Rethinking deviations from uncovered interest parity: The role of covariance risk and noise. Economic Journal, 108, 1686–1706.

    Article  Google Scholar 

  • Meese, R. A., & Rogoff, K. (1983). Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics, 14, 3–24.

    Article  Google Scholar 

  • Pan, J., & Poteshman, A. (2006). The information in option volume for stock prices. Review of Financial Studies, 19, 871–908.

    Article  Google Scholar 

  • Ronen, T., & Zhou, X. (2012). Trade and information in the corporate bond market. Journal of Financial Markets, 16, 61–103.

    Google Scholar 

  • Shiller, R. (1984). Stock prices and social dynamics. Brookings Papers on Economic Activity, 2, 457–498.

    Google Scholar 

  • Sims, C. A. (1972). Money, income, and causality. American Economic Review, 62, 540–552.

    Google Scholar 

  • Sims, C. A. (1980). Macroeconomics and reality. Econometrica, 48, 1–48.

    Article  Google Scholar 

  • Stephan, J., & Whaley, R. (1990). Intraday price changes and trading volume relations in the stock and stock option markets. Journal of Finance, 45, 191–220.

    Article  Google Scholar 

  • Stock, J., & Watson, M. (2001). Vector autoregressions. Journal of Economic Perspectives, 15, 101–115.

    Article  Google Scholar 

  • Viceira, L. (2001). Optimal portfolio choice for long-horizon investors with nontradable labor income. Journal of Finance, 56, 433–470.

    Article  Google Scholar 

  • Vijh, A. M. (1988). Potential biases from using only trade prices of related securities on different exchanges. Journal of Finance, 43, 1049–1055.

    Article  Google Scholar 

  • Watson, M. (1994). Vector autoregressions and cointegration. In R. F. Engle & D. McFadden (Eds.), Handbook of econometrics (Vol. IV). Amsterdam: Elsevier.

    Google Scholar 

  • Zhou, X. (2009). Information-based trading in the junk bond market (Working paper), Cornell University.

    Google Scholar 

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Authors and Affiliations

  1. Rutgers Business School – Newark and New Brunswick, Rutgers, The State University of New Jersey, New Brunswick, NJ, USA

    Yangru Wu & Xing Zhou

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  1. Yangru Wu
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  2. Xing Zhou
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Correspondence to Yangru Wu .

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Editors and Affiliations

  1. Department of Finance and Economics, Rutgers Business School, Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA

    Cheng-Few Lee

  2. Center for PBBEF Research, North Brunswick, New Jersey, USA

    John C. Lee

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Wu, Y., Zhou, X. (2015). VAR Models: Estimation, Inferences, and Applications. In: Lee, CF., Lee, J. (eds) Handbook of Financial Econometrics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7750-1_76

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  • DOI: https://doi.org/10.1007/978-1-4614-7750-1_76

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