# Does the price of crude oil help predict the conditional distribution of aggregate equity return?

- 82 Downloads

## Abstract

Contrary to point predictions that only convey information about the central tendency of the target variable, or the best prediction, density predictions take into account the whole shape of the conditional distribution, which means that they provide a characterization of prediction uncertainty. They can also be used to assess out-of-sample predictive power when specific regions of the conditional distribution are emphasized, such as the center or the left tail. We carry out an out-of-sample density prediction study for monthly returns on the Standard & Poor’s 500 index from 1859*m*9 through 2017*m*12 with a stochastic volatility benchmark and alternatives to it that include the West Texas Intermediate price of crude oil. Results suggest that models employing certain nonlinear transformations of the price of crude oil help deliver statistically significant density prediction improvements relative to the benchmark. The biggest payoff occurs when predicting the left tail of the conditional distribution. They also generate the earliest signal of a market downturn around the 2008 financial crisis.

## Keywords

Crude oil price Density prediction Stochastic volatility## JEL Classification

C22 C53 G10 Q40## Notes

### Compliance with ethical standards

### Conflict of interest

The author declares that he/she has no conflict of interest.

### Human and animal rights

This article does not contain any studies with human participants or animals performed by the author.

## References

- Alessi L, Ghysels E, Onorante L, Peach R, Potter S (2014) Central bank macroeconomic forecasting during the global financial crisis: the European Central Bank and Federal Reserve Bank of New York experiences. J Bus Econ Stat 32:483–500Google Scholar
- Alquist R, Kilian L, Vigfusson RJ (2013) Forecasting the price of oil. In: Timmermann A, Elliott G (eds) Handbook of economic forecasting. Elsevier, AmsterdamGoogle Scholar
- Amihud Y, Hurvich CM (2004) Predictive regressions: a reduced-bias estimation method. J Financ Quant Anal 39:813–841Google Scholar
- Andrews DWK, Monahan JC (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60:953–966Google Scholar
- Balcilar M, Gupta R, Miller SM (2015) Regime switching model of US crude oil and stock market prices: 1859 to 2013. Energy Econ 49:317–327Google Scholar
- Britton E, Fisher P, Whitley J (1998) The Inflation Report projections: understanding the fan chart. Bank Engl Q Bull 38:30–37Google Scholar
- Carter C, Kohn R (1994) On gibbs sampling for state-space models. Biometrika 81:541–553Google Scholar
- Chan J (2013) Moving average stochastic volatility models with application to inflation forecast. J Econom 176:162–172Google Scholar
- Chan J (2017) The stochastic volatility in mean model with time-varying parameters: an application to inflation modeling. J Bus Econ Stat 35:17–28Google Scholar
- Chan J, Grant AL (2016) Modeling energy price dynamics: GARCH versus stochastic volatility. Energy Econ 54:182–189Google Scholar
- Chen SS (2010) Do higher oil prices push the stock market into bear territory? Energy Econ 32:490–495Google Scholar
- Chen NF, Roll R, Ross S (1986) Economic forces and the stock market. J Bus 59:383–403Google Scholar
- Clark TE, McCracken MW (2012) Advances in forecast evaluation. In: Timmermann A, Elliott G (eds) Handbook of economic forecasting. Elsevier, AmsterdamGoogle Scholar
- Dangl T, Halling M (2012) Predictive regressions with time-varying coefficients. J Financ Econ 106:157–181Google Scholar
- Dickey DA, Fuller WA (1981) Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49:1057–1072Google Scholar
- Diebold FX, Mariano RS (1995) Comparing predictive accuracy. J Bus Econ Stat 13:253–63Google Scholar
- Driesprong G, Jacobsen B, Maat B (2008) Striking oil: another puzzle? J Financ Econ 89:307–327Google Scholar
- Durbin J, Koopman SJ (2002) A simple and efficient simulation smoother for state space time series analysis. Biometrika 89:603–615Google Scholar
- Elliot G, Stock JH (1994) Inference in time series regression when the order of integration of a regressor is unknown. Econom Theory 10:672–700Google Scholar
- Engle RF (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50:987–1007Google Scholar
- Foster FD, Smith T, Whaley RE (1997) Assessing goodness-of-fit of asset pricing models: the distribution of the maximal $R^{2}$. J Finance 53:591–607Google Scholar
- Geweke J (1992) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Berger J, Bernardo J, Dawid A, Smith A (eds) Bayesian statistics. Oxford University Press, OxfordGoogle Scholar
- Giacomini R, Rossi B (2010) Forecast comparisons in unstable environments. J Appl Econom 25:595–620Google Scholar
- Gil-Alana LA, Gupta R (2014) Persistence and cycles in historical oil price data. Energy Econ 45:511–516Google Scholar
- Gil-Alana LA, Gupta R, Olubusoye OE, Yaya OS (2016) Time series analysis of persistence in crude oil price volatility across bull and bear regimes. Energy 109:29–37Google Scholar
- Gjerde O, Saettem F (1999) Causal relations among stock returns and macroeconomic variables in a small, open economy. J Int Financ Mark Inst Money 9:61–74Google Scholar
- Gneiting T, Ranjan R (2011) Comparing density forecasts using threshold- and quantile-weighted scoring rules. J Bus Econ Stat 29:411–422Google Scholar
- Groen JJJ, Richard P, Ravazzolo F (2013) Real-time inflation forecasting in a changing world. J Bus Econ Stat 1:29–44Google Scholar
- Hamilton JD (2003) What is an oil shock? J Econom 113:363–398Google Scholar
- Hamilton JD (2011) Nonlinearities and the macroeconomic effects of oil prices. Macroecon Dyn 15:472–497Google Scholar
- Huang R, Masulis R, Stoll H (1996) Energy shocks and financial markets. J Futures Mark 16:1–27Google Scholar
- Hull J, White A (1987) The pricing of options on assets with stochastic volatilities. J Finance 42:281–300Google Scholar
- Inoue A, Kilian L (2004) In-sample or out-of-sample tests of predictability: which one should we use? Econom Rev 23:371–402Google Scholar
- Jansson M, Moreira M (2006) Optimal inference in regression models with nearly integrated regressors. Econometrica 74:681–714Google Scholar
- Johannes M, Korteweg A, Polson N (2014) Sequential learning, predictability, and optimal portfolio returns. J Finance 69:611–644Google Scholar
- Jones CM, Kaul G (1996) Oil and stock markets. J. Finance 51:463–491Google Scholar
- Jurado K, Ludvigson SC, Ng S (2015) Measuring uncertainty. Am Econ Rev 105:1177–1216Google Scholar
- Kilian L, Manganelli S (2008) The central banker as a risk manager: estimating the Federal Reserve’s preferences under Greenspan. J Money Credit Bank 40:1103–1129Google Scholar
- Kilian L, Vigfusson RJ (2013) Do oil prices help forecast U.S. real GDP? The role of nonlinearities and asymmetries. J Bus Econ Stat 31:78–93Google Scholar
- Kim S, Shephard N, Chib S (1998) Stochastic volatility: likelihood inference and comparison with ARCH models. Rev Econ Stud 65:361–393Google Scholar
- Koop G (2003) Bayesian econometrics. Wiley, New YorkGoogle Scholar
- Koopman SJ, Lucas A, Scharth M (2016) Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models. Review of Economics and Statistics 98:97–110Google Scholar
- Lewellen J (2004) Predicting returns with financial ratios. J Financ Econ 74:209–235Google Scholar
- Liu L, Ma F, Wang Y (2015) Forecasting excess stock returns with crude oil market data. Energy Econ 48:316–324Google Scholar
- Lo AW, MacKinlay AC (1990) Data-snooping biases in tests of financial asset pricing models. Rev Financ Stud 3:431–467Google Scholar
- Lux T, Segnon M, Gupta R (2016) Forecasting crude oil price volatility and value-at-risk: evidence from historical and recent data. Energy Econ 56:117–133Google Scholar
- Miller J, Ratti R (2009) Crude oil and stock markets: stability, instability and bubbles. Energy Econ 31:559–568Google Scholar
- Narayan PK, Gupta R (2015) Has oil price predicted stock returns for over a century? Energy Econ 48:18–23Google Scholar
- Narayan PK, Narayan S (2010) Modelling the impact of oil prices on Vietnam’s stock prices. Appl Energy 87:356–361Google Scholar
- Narayan PK, Sharma SS (2011) New evidence on oil price and firm returns. J Bank Finance 5:3253–3262Google Scholar
- Naser H, Alaali F (2018) Can oil prices help predict US stock market returns? Evidence using a dynamic model averaging (DMA) approach. Empir Econ 55:1757–1777Google Scholar
- Nelson CR, Kim M (1993) Predictable stock returns: the role of small sample bias. J Finance 48:641–661Google Scholar
- Park J, Ratti RA (2008) Oil price shocks and stock markets in the U.S. and 13 European countries. Energy Econ 30:2587–2608Google Scholar
- Phan DHB, Sharma SS, Narayan PK (2015) Stock return forecasting: some new evidence. Int Rev Financ Anal 40:38–51Google Scholar
- Rapach DE, Wohar ME (2006) In-sample vs. out-of-sample tests of stock return predictability in the context of data mining. J Empir Finance 13:231–247Google Scholar
- Sadorsky P (1999) Oil price shocks and stock market activity. Energy Econ 21:449–469Google Scholar
- Stambaugh RF (1999) Predictive regressions. J Financ Econ 54:375–421Google Scholar
- Stock JH, Watson MW (1996) Evidence on structural instability in macroeconomic time series relations. J Bus Econ Stat 14:11–30Google Scholar
- Swanson NR (1998) Money and output viewed through a rolling window. J Monet Econ 41:455–474Google Scholar
- Tourus W, Valkanov R, Yan S (2004) On predicting stock returns with nearly integrated explanatory variables. J Bus 77:937–966Google Scholar
- Wei C (2003) Energy, the stock market, and the putty-clay investment model. Am Econ Rev 93:311–23Google Scholar
- Welch I, Goyal A (2008) A comprehensive look at the empirical performance of equity premium prediction. Rev Financ Stud 21:1455–1508Google Scholar
- Westerlund J, Narayan PK (2012) Does the choice of estimator matter when forecasting returns? J Bank Finance 36:2632–2640Google Scholar