# Bootstrap Inference of Level Relationships in the Presence of Serially Correlated Errors: A Large Scale Simulation Study and an Application in Energy Demand

- 216 Downloads
- 2 Citations

## Abstract

By undertaking a large scale simulation study, we demonstrate that the maximum entropy bootstrap (meboot) data generation process can provide accurate and narrow parameter confidence intervals in models with combinations of stationary and nonstationary variables, under both low and high degrees of autocorrelation. The relatively small sample sizes in which meboot performs particularly well make it a useful tool for rolling window estimation. As a case study, we analyze the evolution of the price and income elasticities of import demand for crude oil in Turkey by using quarterly data between 1996–2011. Our approach can be employed to tackle a wide range of macroeconometric estimation problems where small sample sizes are a common issue.

## Keywords

Meboot Bootstrap Simulation Rolling windows Oil demand## Notes

### Acknowledgments

We are grateful to H. D. Vinod and Ragnar Nymoen for their help and suggestions. We also would like to thank the anonymous reviewers for extremely useful comments.

## References

- Adeyemi, O. I., Broadstock, D. C., Chitnis, M., Hunt, L. C., & Judge, G. (2010). Asymmetric price responses and the underlying energy demand trend: Are they substitutes or complements? evidence from modelling OECD aggregate energy demand.
*Energy Economics*,*32*, 1157–1164.CrossRefGoogle Scholar - Altinay, G. (2007). Short-run and long-run elasticities of import demand for crude oil in Turkey.
*Energy Policy*,*35*, 5829–5835.CrossRefGoogle Scholar - Amarawickrama, H. A., & Hunt, L. C. (2008). Electricity demand for Sri Lanka: A time series analysis.
*Energy*,*33*, 724–739.CrossRefGoogle Scholar - Ames, A. J. (2005). Monte carlo experiments on maximum entropy constructive ensembles for time series analysis and inference. Master’s thesis, Virginia Polytechnic Institute and State University, Department of Agricultural and Applied Economics.Google Scholar
- Balat, M. (2010). Security of energy supply in Turkey: Challenges and solutions.
*Energy Conversion and Management*,*51*, 1998–2011.CrossRefGoogle Scholar - Berkowitz, J., & Kilian, L. (2000). Recent developments in bootstrapping time series.
*Econometric Reviews*,*19*, 1–48.CrossRefGoogle Scholar - Bühlmann, P. (1998). Sieve bootstrap for smoothing nonstationary time series.
*Annals of Statistics*,*26*, 48–83.CrossRefGoogle Scholar - Carlstein, E. (1986). The use of subseries methods for estimating the variance of a general statistic from a stationary time series.
*Annals of Statistics*,*14*, 1171–1179.CrossRefGoogle Scholar - Central Bank of the Republic of Turkey. (2012). Balance of Payments Report 2011-IV. Ankara.Google Scholar
- Darvas, Z., & Varga, B. (2012). Uncovering time-varying parameters with the Kalman-filter and the flexible least squares: A Monte Carlo study. Working Papers 12/04, Department of Mathematical Economics and Economic Analysis, Corvinus University of Budapest, Budapest. https://ideas.repec.org/p/mkg/wpaper/1204.html.
- Davidson, R., & MacKinnon, J. G. (1999). The size distortion of bootstrap tests.
*Econometric Theory*,*15*, 361–376.CrossRefGoogle Scholar - Davison, A. C., & Hinkley, D. V. (1997).
*Bootstrap methods and their application*(1st ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Dées, S., Karadeloglou, P., Kaufmann, R. K., & Sánchez, M. (2007). Modelling the world oil market: Assessment of a quarterly econometric model.
*Energy Policy*,*35*, 178–191.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 - Dimitropoulos, J., Hunt, L. C., & Judge, G. (2005). Estimating underlying energy demand trends using UK annual data.
*Applied Economics Letters*,*12*, 239–244.CrossRefGoogle Scholar - Ediger, V. S., & Berk, I. (2011). Crude oil import policy of Turkey: Historical analysis of determinants and implications since 1968.
*Energy Policy*,*39*, 2132–2142.CrossRefGoogle Scholar - Efron, B. (1979). Bootstrap methods: Another look at the jackknife.
*The Annals of Statistics*,*7*, 1–26.CrossRefGoogle Scholar - Efron, B., & Tibshirani, R. J. (1993).
*An introduction to the bootstrap*(1st ed.). New York: Chapman and Hall.CrossRefGoogle Scholar - Fong, W. M. (2013). Footprints in the market: Hedge funds and the carry trade.
*Journal of International Money and Finance*,*33*, 41–59.CrossRefGoogle Scholar - Ghosh, S. (2009). Import demand of crude oil and economic growth: Evidence from India.
*Energy Policy*,*37*, 699–702.CrossRefGoogle Scholar - Gómez, V., & Maravall, A. (1997). Guide for Using the Programs TRAMO and SEATS. Madrid: Banco de España. http://www.bde.es/webbde/en/secciones/servicio/software/programas.html.
- Hall, P. (1985). Resampling a coverage process.
*Stochastic Process Applications*,*19*, 259–269.CrossRefGoogle Scholar - Hardle, W., Horowitz, J., & Kreiss, J. P. (2003). Bootstrap methods for time series.
*International Statistical Review*,*71*, 435–459.CrossRefGoogle Scholar - Horowitz, J. L. (2001). The bootstrap. In J. J. Heckman & E. E. Leamer (Eds.),
*Handbook of econometrics*(Vol. 5, Chap. 5). Amsterdam: North-Holland.Google Scholar - Horowitz, J. L. (2003). The bootstrap in econometrics.
*Statistical Science*,*18*, 211–218.CrossRefGoogle Scholar - Hughes, J. E., Knittel, C. R., & Sperling, D. (2008). Evidence of a shift in the short-run price elasticity of gasoline demand.
*The Energy Journal*,*29*, 93–114.CrossRefGoogle Scholar - Hunt, L. C., & Ninomiya, Y. (2003). Unravelling trends and seasonality: A structural time series analysis of transport oil demand in the UK and Japan.
*The Energy Journal*,*24*, 63–96.CrossRefGoogle Scholar - Hyndman, R. J. (1996). Computing and graphing highest density regions.
*American Statistician*,*50*, 120–126.Google Scholar - Hyndman, R. J. (2012). Package ‘hdrcde’. R Package version 2.16. http://cran.r-project.org/web/packages/hdrcde/index.html.
- International Energy Agency. (2010).
*Turkey 2009 Review*. Paris: International Energy Agency.Google Scholar - Judson, R. A., Schmalensee, R., & Stoker, T. M. (1999). Economic development and the structure of the demand for commercial energy.
*The Energy Journal*,*20*, 29–57.CrossRefGoogle Scholar - Kalaba, R., & Tesfatsion, L. (1988). The flexible least squares approach to time-varying linear regression.
*Journal of Economic Dynamics and Control*,*12*, 43–48.CrossRefGoogle Scholar - Kalaba, R., & Tesfatsion, L. (1989). Time-varying linear regression via flexible least squares.
*Computers and Mathematics with Applications*,*17*, 1215–1245.CrossRefGoogle Scholar - Kalaba, R., & Tesfatsion, L. (1990). Flexible least squares for approximately linear systems.
*IEEE Transactions on Systems, Man, and Cybernetics*,*20*, 978–989.CrossRefGoogle Scholar - Kalman, R. E. (1960). A new approach to linear filtering and prediction problems.
*Journal of Basic Engineering*,*82*, 35–45.CrossRefGoogle Scholar - Kladroba, A. (2005). Flexible least squares estimation of state space models: An alternative to Kalman filtering? Working Paper 149. Universitat Duisburg-Essen. https://ideas.repec.org/p/zbw/udewwd/149.html.
- Koutris, A., Heracleous, M. S., & Spanos, A. (2008). Testing for nonstationarity using maximum entropy resampling: A misspecification testing perspective.
*Econometric Reviews*,*27*, 363–384.CrossRefGoogle Scholar - Kunsch, H. R. (1989). The jackknife and the bootstrap for general stationary observations.
*Annals of Statistics*,*17*, 1217–1241.CrossRefGoogle Scholar - Li, H., & Maddala, G. S. (1996). Bootstrapping time series models.
*Econometric Reviews*,*15*, 115–158.CrossRefGoogle Scholar - MacKinnon, J. G. (2002). Bootstrap inference in econometrics.
*Canadian Journal of Economics*,*35*, 615–645.CrossRefGoogle Scholar - MacKinnon, J. G. (2006). Bootstrap methods in econometrics.
*The Economic Record*,*82*, S2–S18.CrossRefGoogle Scholar - Ministry of Energy and Natural Resources. (2012). Statistical reports—May 2012. http://www.enerji.gov.tr.
- Monteiro, A., Carvalho, A., Ribeiro, I., Scotto, M., Barbosa, S., Alonso, A., et al. (2012). Trends in ozone concentrations in the iberian peninsula by quantile regression and clustering.
*Atmospheric Environment*,*56*, 184–193.CrossRefGoogle Scholar - Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships.
*Journal of Applied Econometrics*,*16*, 289–326.CrossRefGoogle Scholar - Plasil, M. (2011). Potential product, output gap and uncertainty rate associated with their determination while using the Hodrick-Prescott filter.
*Politicka Ekonomie*,*59*, 490–507.CrossRefGoogle Scholar - Politis, D. N., & Romano, J. P. (1993). The stationary bootstrap.
*Journal of the American Statistical Association*,*89*, 1303–1313.CrossRefGoogle Scholar - PwC Turkey. (2011).
*Nice work if you can get it!*. İstanbul: Developments in the Turkish Petroleum Market.Google Scholar - Rajarshi, M. B. (1990). Bootstrap in markov-sequences based on estimates of transition density.
*Annals of the Institute of Statistical Mathematics*,*42*, 253–268.CrossRefGoogle Scholar - Turkish Petroleum Industry Association. (2008). The Lubricant No. 10. Problem in the fuel oil sector and solution proposals. Istanbul (in Turkish).Google Scholar
- Turkish Petroleum Industry Association. (2010). The calorific values of petroleum and energy goods and the effect of taxes. Istanbul (in Turkish).Google Scholar
- Turkish Petroleum Industry Association. (2012). 2011 Sector Report. Istanbul.Google Scholar
- Turkish Statistical Institute. (2012). Official statistics programme—May 2012. http://www.turkstat.gov.tr/Start.do.
- Vinod, H. D. (1993). Bootstrap methods: Applications in econometrics. In G. S. Maddala, C. R. Rao, & H. D. Vinod (Eds.),
*Handbook of statistics: Econometrics*(Vol. 11, pp. 629–661). New York: North Holland, Elsevier.Google Scholar - Vinod, H. D. (2004). Ranking mutual funds using unconventional utility theory and stochastic dominance.
*Journal of Empirical Finance*,*11*, 353–377.CrossRefGoogle Scholar - Vinod, H. D. (2006). Maximum entropy ensembles for time series inference in economics.
*Journal of Asian Economics*,*17*, 955–978.CrossRefGoogle Scholar - Vinod, H. D. (2008).
*Hands-on intermediate econometrics using R*(1st ed.). Singapore: World Scientific Publishing Ltd.CrossRefGoogle Scholar - Vinod, H. D. (2010). New solution to time series inference in spurious regression problems. SSRN Working Paper Series. http://ssrn.com/paper=1560074.
- Vinod, H. D. (2012). Constructing scenarios of time heterogeneous series for stress testing. SSRN Working Paper Series. http://ssrn.com/paper=1987879.
- Vinod, H. D., & de Lacalle, J. L. (2009). Maximum entropy bootstrap for time series: The meboot R package.
*Journal of Statistical Software*,*29*(5), 1–19.CrossRefGoogle Scholar - Word Bank. (2012). Global economic monitor (commodities) database—May 2012. http://data.worldbank.org/data-catalog/commodity-price-data.
- Yalta, A. T. (2011). Analyzing energy consumption and gdp nexus using maximum entropy bootstrap: The case of Turkey.
*Energy Economics*,*33*, 453–460.CrossRefGoogle Scholar - Yalta, A. T., & Cakar, H. (2012). Energy consumption and economic growth in China: A reconciliation.
*Energy Policy*,*41*, 666–675.CrossRefGoogle Scholar - Ziramba, E. (2010). Price and income elasticities of crude oil import demand in South Africa: A cointegration analysis.
*Energy Policy*,*38*, 7844–7849.CrossRefGoogle Scholar