Apple, Alphabet or Microsoft: Which Is the Most Efficient Share?

  • Paulo Ferreira Center for Advanced Studies in Management and Economics, Universidade de Évora, Portugal
Keywords: Detrended Fluctuation Analysis, Return Rates, Efficiency, Apple, Alphabet, Microsoft


Studying the efficiency of financial assets is important because, if they are not efficient, this means that investors have some capacity to predict the behavior of those assets. In this paper, we use detrended fluctuation analysis to assess the efficiency of the three most valuable American companies, which, curiously, all happen to be from the same economic sector: Apple, Alphabet, and Microsoft. The results point to the efficiency of Apple’s shares and to similar results regarding Alphabet. Only Microsoft shares show evidence of deviations from efficiency. Our results also suggest that moments of crisis could have an impact on the efficiency pattern of shares.


Anagnostidis, P., Varsakelis, C., and Emmanouilides, C. (2016). Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone. Physica A: Statistical Mechanics and its Applications, 447:116–128.

Ausloos, M. (2000). Statistical physics in foreign exchange currency and stock markets. Physica A: Statistical Mechanics and its Applications, 285(1-2):48–65.

Ausloos, M., Vandewalle, N., Boveroux, P., Minguet, A., and Ivanova, K. (1999). Applications of statistical physics to economic and financial topics. Physica A: Statistical Mechanics and its Applications, 274(1-2):229–240.

Bachelier, L. (1900). Theorie de la speculation. Annales scientifiques de l’Ecole Normale Superieure, 3(17):21–86.

Bai, J. and Perron, P. (1998). Estimating and Testing Linear Models with Multiple Structural Changes. Econometrica, 66(1):47–78.

Bai, J. and Perron, P. (2003a). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1):1–22.

Bai, J. and Perron, P. (2003b). Critical values for multiple structural change tests. Econometrics Journal, 6(1):72–78.

Barkoulas, J. T. and Baum, C. F. (1996). Long-term dependence in stock returns. Economics Letters, 53(3):253–259.

Bonanno, G., Lillo, F., and Mantegna, R. N. (2001). Levels of complexity in financial markets. Physica A: Statistical Mechanics and its Applications, 299(1-2):16–27.

Cao, G. and Zhang, M. (2015). Extreme values in the Chinese and American stock markets based on detrended fluctuation analysis. Physica A: Statistical Mechanics and its Applications, 436:25–35.

Chow, G. C. (1960). Tests of Equality Between Sets of Coefficients in Two Linear Regressions. Econometrica, 28(3):591–605.

Christodoulou-Volos, C. and Siokis, F. M. (2006). Long range dependence in stock market returns. Applied Financial Economics, 16(18):1331–1338.

Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, 1(2):223–236.

Darbellay, G. A. (1998). Predictability: An Information-Theoretic Perspective. In Prochazka, A., Uhlır, J., Rayner, P. W. J., and Kingsbury, N. G., editors, Signal Analysis and Prediction, pages 249–262. Birkhauser Boston, Boston, MA.

Di Matteo, T., Aste, T., and Dacorogna, M. M. (2005). Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development. Journal of Banking and Finance, 29(4):827–851. Risk Measurement.

Ferreira, P. and Dionısio, A. (2014). Revisiting serial dependence in the stock markets of the G7 countries, Portugal, Spain and Greece. Applied Financial Economics, 24(5):319–331.

Ferreira, P. and Dionısio, A. (2016). How long is the memory of the US stock market? Physica A: Statistical Mechanics and its Applications, 451:502–506.

Granger, C. W., Maasoumi, E., and Racine, J. (2004). A Dependence Metric for Possibly Nonlinear Processes. Journal of Time Series Analysis, 25(5):649–669.

Granger, C. W. J. and Morgenstern, O. (1964). Spectral analysis of New York stock market prices. In Cootner, P., editor, The random character of stock market prices, pages 162–188. Cambridge, MA: MIT Press.

Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116:770–808.

Kantelhardt, J. W., Koscielny-Bunde, E., Rego, H. H., Havlin, S., and Bunde, A. (2001). Detecting long-range correlations with detrended fluctuation analysis. Physica A: Statistical Mechanics and its Applications, 295(3-4):441–454.

Kendall, M. G. and Hill, A. B. (1953). The Analysis of Economic Time-Series-Part I: Prices. Journal of the Royal Statistical Society. Series A (General), 116(1):11–34.

Kristoufek, L. (2015). Detrended fluctuation analysis as a regression framework: Estimating dependence at different scales. Physical Review E, 91:022802.

Liu, Y., Cizeau, P., Meyer, M., Peng, C.-K., and Stanley, H. E. (1997). Correlations in economic time series. Physica A: Statistical Mechanics and its Applications, 245(3):437–440.

Malkiel, B. G. and Fama, E. F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. The Journal of Finance, 25(2):383–417.

Mandelbrot, B. (1977). The fractal geometry of nature. New York, NY: W. H. Freeman and Company.

Osborne, M. F. M. (1964). Brownian motion in the stock market. In Cootner, P., editor, The random character of stock market prices, pages 262–296. Cambridge, MA: MIT Press.

Parisi, D. R., Sornette, D., and Helbing, D. (2013). Financial price dynamics and pedestrian counterflows: A comparison of statistical stylized facts. Physical Review E, 87:012804.

Peng, C.-K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., and Goldberger, A. L. (1994). Mosaic organization of DNA nucleotides. Physical Review E, 49:1685–1689.

Quandt, R. E. (1960). Tests of the Hypothesis That a Linear Regression System Obeys Two Separate Regimes. Journal of the American Statistical Association, 55(290):324–330.

Sadique, S. and Silvapulle, P. (2001). Long-term memory in stock market returns: international evidence. International Journal of Finance & Economics, 6(1):59–67.

Sewell, M. (2011). History of the efficient market hypothesis. Research Note No. RN/11/04, London, UK: UCL Department of Computer Science.

How to Cite
Ferreira, P. (2016). Apple, Alphabet or Microsoft: Which Is the Most Efficient Share?. Econometric Research in Finance, 1(2), 67 - 79.
Bookmark and Share