Skip to main content
SpringerLink
Log in

Are standard asset pricing factors long-range dependent?

  • Published:
Journal of Economics and Finance Aims and scope Submit manuscript

Abstract

Factor portfolios derived from phenomena identified in the cross-section of stock returns have become vital parts of modern investment products and financial models. Even though much has been learned about the properties of these portfolios in recent years, one issue still remains unaddressed. Are factor returns long-range dependent (LRD)? We seek to answer this important research question because if factor returns were LRD, optimal portfolio decisions and traditional asset pricing methods/tests based on these factors would be severely biased and the validity of a large strand of prior research would be compromised. Specifically, using Hurst exponent approaches within rescaled range and detrended fluctuation frameworks, we analyse the presence of LRD in the returns of factor portfolios formed based on size, book-to-market, momentum and beta characteristics. For the periods from 1931 to 2014 (US market) and 1990 to 2014 (20 international markets) and supported by several robustness checks, we find no systematic evidence of persistence or anti-persistence in the factor returns. This implies that the factor use can be considered unproblematic in both asset management and asset pricing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. 1 We use the term ‘factor returns’ because we do not wish to take sides in the debate about whether they are anomalous returns or represent premia compensating for certain types of risk.

  2. 2 Also, note that the conclusions of some tests of the efficient market hypothesis or stock market rationality also hang precariously on the presence or absence of long-term memory (see Merton 1987).

  3. 3 A typical example of LRD is given by Granger-type fractionally differenced (FD) time-series models (see Campbell et al. 1997). Consider an AR(1) series with slope ϕ=0.5 and a FD series with differencing parameter κ=1/3. Although both series have first-order autocorrelation of 0.500, at lag 5 (10, 25) the AR(1) correlation is 0.031 (0.001, 0.000) whereas the FD series has correlation 0.295 (0.235, 0.173), declining to only 0.109 at lag 100.

  4. 4 Recent applications show that they are useful as standards that can distinguish emerging capital markets from mature capital markets (see Eom et al. 2008; Auer, 2016b).

  5. 5 There are some online sources offering international factor returns (e.g., the data library of Kenneth French). However, they often do not provide the beta factor and also do not cover as many countries as we do.

  6. 6 Individual issues are assigned to markets based on the location of the primary exchange. For companies traded in multiple markets, the primary trading vehicle identified by Compustat/XpressFeed is used.

  7. 7 Book equity is obtained as shareholders’ equity minus the preferred stock value (PSTKRV, PSTKL or PSKT depending on availability). Shareholders’ equity is measured by stockholders’ equity (SEQ) or, if not available, the sum of common equity (CEQ) and preferred stocks (PSTK). If both SEQ and CEQ are unavailable, shareholders’ equity is proxied by total assets (TA) minus the sum of total liability (LT) and minority interest (MIB).

  8. 8 For firms with fiscal year ending in December this approach of Asness et al. (2013a) delivers the same measure as in Fama and French (1992). For firms with fiscal year not ending in December, prices at the fiscal year end date are used while Fama and French (1992) use December prices for all firms.

  9. 9 This definition is in line with recent evidence that short-term prior returns contribute little to momentum profits (see Novy-Marx 2012). Its slightly different from the seminal momentum studies of Jegadeesh and Titman (1993, 2001) using returns over the past 3 to 12 months.

  10. 10 For US securities, the size breakpoint is the median NYSE market equity. For international securities, it is the 80th percentile by country.

  11. 11 The book-to-market breakpoints are the 70th and 30th percentiles. Also note that Fama and French (1992, 1993, 1996, 2012) use independent sorts. However, we prefer conditional sorts, as proposed by Asness et al. (2013a), because they ensure a balanced number of stocks in each portfolio.

  12. 12 The momentum breakpoints are the 70th and 30th percentiles.

  13. 13 This choice of countries is motivated by a focus on developed markets listed in the MSCI market classification (see https://www.msci.com/market-classification). Some developed markets (Israel and Portugal), emerging markets and frontier markets in the MSCI classification cannot be considered because of insufficient sample sizes.

  14. 14 Note that the tail behaviour of this kind of GARCH specifications often remains too short (see Bollerslev and Wooldridge 1992). However, this is no disadvantage for our analysis because RRA is robust to heavy tails.

  15. 15 While this is the most frequently used procedure, there are also versions that differ in the sub-sample (distinct vs. overlapping) and scatter-plot construction (averages vs. all points) (see Mielniczuk and Wojdyłło 2007).

  16. 16 For more details and potential drawbacks of Eq. 9, see Sánchez Granero et al. (2008). Also note that our results do not change significantly when the correction concerning (9) is omitted.

  17. 17 Interestingly, in our application, this simple procedure yields results similar to the bootstrap test proposed by Grau-Carles (2005) and recently used by Cajueiro and Tabak (2008, 2010) and Souza et al. (2008).

  18. 18 These intervals refer to minimum sub-sample sizes of n m i n >50. However, they are also good approximations for smaller n m i n . Detailed values for other sizes and confidence levels are tabulated in Weron (2002).

  19. 19 This is why a new strand of the literature seeks to construct new types of size factors that may revive the size effect. One prominent example in this field is the size factor of Asness et al. (2015). Its main idea is to control for ‘junk’, i.e., stocks of companies that are small, have low average returns and are typically distressed or illiquid.

  20. 20 For the sake of brevity, we do not report the filter results. However, they are available upon request.

  21. 21 Switching to a 95 % confidence interval causes a few breaches. However, a picture of insignificant LRD in most time-windows remains.

  22. 22 Note that Weron (2002) also constructs his simulated confidence intervals for the PRM and finds that the resulting values are close to the classic normality-based interval of the method.

  23. 23 Similar arguments hold when we follow Kang et al. (2009) and Mohammadi and Su (2010) by using alternative GARCH types, namely the TGARCH, EGARCH, CGARCH, IGARCH and FIGARCH models.

  24. 24 To back up this result, we have extended the study of Kristoufek (2012), which compares the performance of various Hurst exponent approaches in a variety of different memory and distribution settings, by our filtered procedure. Our results show that (i) non-normal GARCH residuals do not bias the H estimator and that (ii) the application of the filter leads to more precise estimates (in terms of a lower mean absolute error) of the population H than the estimator of Lo (1991).

  25. 25 If one interprets cross-sectional effects as market anomalies, absence of long memory in factor returns does not imply efficient markets because the performance of the portfolios still originates from abnormal predictability.

References

  • Alvarez J, Rodriguez E (2008) Short-Term Predictability of Crude Oil Markets: A Detrended Fluctuation Analysis Approach. Energy Econ 30(5):2645–2656

    Article  Google Scholar 

  • Amenc N, El Bied S, Martellini L (2003) Predictability in Hedge Fund Returns. Financ Anal J 59(5):32–46

    Article  Google Scholar 

  • Andrews D, Guggenberger P (2003) A Bias-Reduced Log-Peridogram Regression Estimator for the Long-Memory Parameter. Econometrica 71(2):675–712

    Article  Google Scholar 

  • Anis A, Lloyd E (1976) The Expected Value of the Adjusted Rescaled Rescaled Hurst Range of Independent Normal Summands. Biometrika 63(1):111–116

    Article  Google Scholar 

  • Artmann S, Finter P, Kempf A, Koch S, Theissen E (2012) The Cross-Section of German Stock Returns: New Data and New Evidence. Schmalenbach Bus Rev 64(1):20–43

    Article  Google Scholar 

  • Asness C, Frazzini A, Israel R, Moskowitz T, Pedersen L (2015) Size Matters, If You Control For Junk. Unpublished Manuscript, AQR Capital Management, Greenwich

  • Asness C, Frazzini A, Pedersen L (2013a) Quality Minus Junk. Unpublished Manuscript, AQR Capital Management, Greenwich

  • Asness C, Moskowitz T, Pedersen L (2013b) Value and Momentum Everywhere. J Financ 68(3):929–985

  • Auer B (2016a) On the Performance of Simple Trading Rules Derived From the Fractal Dynamics of Gold and Silver Price Fluctuations. Financ Res Lett 16:255–267

  • Auer B (2016b) On Time-Varying Predictability of Emerging Stock Market Returns. Emerg Mark Rev 27:1–13

  • Auer B (2016c) Pure Return Persistence, Hurst Exponents, and Hedge Fund Selection - A Practical Note. J Asset Manag 17(5):319–330

  • Auer B, Hoffmann A (2016) Do Carry Trades Show Signs of Long Memory?. Q Rev Econ Financ 61:201–208

    Article  Google Scholar 

  • Ausloos M (2000) Statistical Physics in Foreign Exchange Currency and Stock Markets. Physica A 285(1-2):48–65

    Article  Google Scholar 

  • Baillie R (1996) Long Memory Processes and Fractional Integration in Econometrics. J Econ 73(1):5–59

    Article  Google Scholar 

  • Bali T, Cakici N, Whitelaw R (2011) Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns. J Financ Econ 99(2):427–446

    Article  Google Scholar 

  • Barkoulas J, Baum C (1996) Long-Term Dependence in Stock Returns. Econ Lett 53(3):253–259

    Article  Google Scholar 

  • Barunik J, Kristoufek L (2010) On Hurst Exponent Estimation Under Heavy-Tailed Distributions. Physica A 389(18):3844–3855

    Article  Google Scholar 

  • Batten J, Ciner C, Lucey B, Szilagyi P (2013) The Structure of Gold and Silver Spread Returns. Quant Finan 13(4):561–570

    Article  Google Scholar 

  • Batten J, Ellis C, Fethertson T (2008) Sample Period Selection and Long-Term Dependence: New Evidence from the Dow Jones Index. Chaos, Solitons Fractals 36(5):1126–1140

  • Batten J, Hamada M (2009) The Compass Rose Pattern in Electricity Prices. Chaos 19(4):043106

    Article  Google Scholar 

  • Bollerslev T, Wooldridge J (1992) Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances. Econ Rev 11 (2):143–172

    Article  Google Scholar 

  • Cajueiro D, Tabak B (2004a) Ranking Efficiency for Emerging Markets. Chaos, Solitons Fractals 22(2):349–352

  • Cajueiro D, Tabak B (2004b) The Hurst Exponent Over Time: Testing the Assertion that Emerging Markets Are Becoming More Efficient. Physica A 336 (3-4):521–537

  • Cajueiro D, Tabak B (2005a) Ranking Efficiency for Emerging Equity Markets II. Chaos, Solitons Fractals 23(2):671–675

  • Cajueiro D, Tabak B (2005b) Testing for Time-Varying Long-Range Dependence in Volatility for Emerging Markets. Physica A 346(3-4):577–588

  • Cajueiro D, Tabak B (2008) Testing for Long-Range Dependence in World Stock Markets. Chaos, Solitons Fractals 37(3):918–927

    Article  Google Scholar 

  • Cajueiro D, Tabak B (2010) Fluctuation Dynamics in US Interest Rates and the Role of Monetary Policy. Financ Res Lett 7(3):163–169

    Article  Google Scholar 

  • Campbell J, Lo A, MacKinlay A (1997) The Econometrics of Financial Markets. Princeton University Press, Princeton

    Google Scholar 

  • Carbone A, Castelli G, Stanley H (2004) Time-Dependent Hurst Exponent in Financial Time Series. Physica A 344(1-2):267–271

    Article  Google Scholar 

  • Carhart M (1997) On Persistence in Mutual Fund Performance. J Financ 52 (1):57–82

    Article  Google Scholar 

  • Chamoli A, Bansal A, Dimri V (2007) Wavelet and Rescaled Range Approach for the Hurst Coefficient for Short and Long Time Series. Comput Geosci 33(1):83–93

    Article  Google Scholar 

  • Chordia T, Subrahmanyam A, Tong Q (2014) Have Capital Market Anomalies Attenuated in the Recent Era of High Liquidity and Trading Activitiy?. J Account Econ 58(1):41–58

    Article  Google Scholar 

  • Clark A (2005) The Use of Hurst and Effective Return in Investing. Quant Finan 5(1):1–8

    Article  Google Scholar 

  • Crato N, Ray B (2000) Memory in Returns and Volatilities of Futures’ Contracts. J Futur Mark 20(6):525–543

    Article  Google Scholar 

  • De Santis G, Gérard B (1997) International Asset Pricing and Portfolio Diversification with Time-Varying Risk. J Financ 52(5):1881–1912

    Article  Google Scholar 

  • De Souza C, Gokcan S (2004) Hedge Fund Investing: A Quantitative Aproach to Hedge Fund Manager Selection and De-Selection. J Wealth Manag 6(4):52–73

    Article  Google Scholar 

  • Di Matteo T (2007) Multi-Scaling in Finance. Quant Finan 7(1):21–36

    Article  Google Scholar 

  • Ellis C, Hudson C (2007) Scale-Adjusted Volatility and the Dow Jones Index. Physica A 378(2):374–386

    Article  Google Scholar 

  • Eom C, Choi S, Oh G, Jung W (2008) Hurst Exponent and Prediction Based Weak-Form Efficient Market Hypothesis of Stock Markets. Physica A 387 (18):4630–4636

    Article  Google Scholar 

  • Fama E, French K (1992) The Cross-Section of Expected Stock Returns. J Financ 47(2):427–465

    Article  Google Scholar 

  • Fama E, French K (1993) Common Risk Factors in the Returns on Stocks and Bonds. J Financ Econ 33(1):3–56

    Article  Google Scholar 

  • Fama E, French K (1996) Multifactor Explanations of Asset Pricing Anomalies. J Financ 51(1):55–84

    Article  Google Scholar 

  • Fama E, French K (1998) Value versus Growth: The International Evidence. J Financ 53(6):1975–1999

    Article  Google Scholar 

  • Fama E, French K (2012) Size, Value, and Momentum in International Stock Returns. J Financ Econ 105(3):457–472

    Article  Google Scholar 

  • Fama E, French K (2015) A Five-Factor Asset Pricing Model. J Financ Econ 116(1):1–22

    Article  Google Scholar 

  • Fernandez V (2011) Alternative Estimators of Long-Range Dependence. Stud Nonlinear Dyn Econ 15(2):1–37

    Google Scholar 

  • Frazzini A, Pedersen L (2014) Betting Against Beta. J Financ Econ 111 (1):1–25

    Article  Google Scholar 

  • Geweke J, Porter-Hudak S (1983) The Estimaton and Application of Long Memory Time Series Models. J Time Ser Anal 4(4):221–238

    Article  Google Scholar 

  • Giraitis L, Kokoszka P, Leipus R, Teyssière G (2003) Rescaled Variance and Related Tests for Long Memory in Volatility and Levels. J Econ 112(2):265–294

    Article  Google Scholar 

  • Grau-Carles P (2000) Empirical Evidence of Long-Range Correlations in Stock Returns. Physica A 287(3-4):396–404

    Article  Google Scholar 

  • Grau-Carles P (2005) Tests of Long Memory: A Bootstrap Approach. Comput Econ 25(2):103–113

    Article  Google Scholar 

  • Grech D, Mazur Z (2004) Can One Make Any Crash Prediction in Finance Using the Local Hurst Exponent Idea? Physica A 336(1-2):133–145

    Article  Google Scholar 

  • Grech D, Pamula G (2008) The Local Hurst Exponent of the Financial Time Series in the Vicinity of Crashes on the Polish Stock Exchange Market. Physica A 387(16-17):4299–4308

    Article  Google Scholar 

  • Griffin J (2002) Are the Fama and French Factors Global or Country Specific?. Rev Financ Stud 15(3):783–803

    Article  Google Scholar 

  • Hamori S (1992) Test of C-CAPM for Japan: 1980-1988. Econ Lett 38(1):67–72

    Article  Google Scholar 

  • Harvey C, Liu Y, Zhu H (2016) ... and the Cross-Section of Expected Returns. Rev Financ Stud 29(1):5–68

    Article  Google Scholar 

  • Hull M, McGroarty F (2014) Do Emerging Markets Become More Efficient As They Develop? Long Memory Persistence in Equity Indices. Emerg Mark Rev 18:45–61

    Article  Google Scholar 

  • Hurst H (1951) Long Term Storage Capacity of Reservoirs. Trans Am Soc Civ Eng 116:770–799

    Google Scholar 

  • Ivanova K, Ausloos M (2002) Are EUR and GBP Different Words For the Same Currency?. Eur Phys J B 27:239–247

    Google Scholar 

  • Jacobs H (2015) What Explains the Dynamics of 100 Anomalies?. J Bank Financ 57:65–85

    Article  Google Scholar 

  • Jacobsen B (1996) Long Term Dependence in Stock Returns. J Empir Financ 3(4):393–417

    Article  Google Scholar 

  • Jegadeesh N, Titman S (1993) Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. J Financ 48(1):65–91

    Article  Google Scholar 

  • Jegadeesh N, Titman S (2001) Profitability of Momentum Strategies: An Evaluation of Alternative Explanations. J Financ 56(2):699–720

    Article  Google Scholar 

  • Kang S, Kang S, Yoon S (2009) Forecasting Volatility of Crude Oil Markets. Energy Econ 31(1):119–125

    Article  Google Scholar 

  • Kantelhardt J (2009) Fractal and Multifractal Time Series. In: Meyers R (ed) Encyclopedia of Complexity and Systems Science. Springer, New York, pp 3754-3779

  • Kristoufek L (2012) How Are Rescaled Range Analyses Affected by Different Memory and Distributional Properties? A Monte Carlo Study. Physica A 391 (17):4252–4260

    Article  Google Scholar 

  • Kristoufek L, Vosvrda M (2013) Measuring Capital Market Efficiency: Global and Local Correlations Structure. Physica A 392(1):184–193

    Article  Google Scholar 

  • Ledoit O, Wolf M (2008) Robust Performance Hypothesis Testing with the Sharpe Ratio. J Empir Financ 15(5):850–859

    Article  Google Scholar 

  • Liew J, Vassalou M (2000) Can Book-to-Market, Size and Momentum be Risk Factors that Predict Economic Growth?. J Financ Econ 57(2):221–245

    Article  Google Scholar 

  • Lo A (1991) Long-Term Memory in Stock Market Prices. Econometrica 59 (5):1279–1313

    Article  Google Scholar 

  • Lo A, MacKinlay C (1988) Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test. Rev Financ Stud 1(1):41–66

    Article  Google Scholar 

  • Lucey B (2004) Robust Estimates of Daily Seasonality in the Irish Equity Market. Appl Financ Econ 14(7):517–523

    Article  Google Scholar 

  • Maheswaran S, Sims C (1993) Empirical Implications of Arbitrage-Free Asset Markets. In: Phillips P (ed) Models, Methods and Applications of Econometrics. Blackwell, Oxford, pp 301-316

  • Mandelbrot B (1971) When Can Price be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models. Rev Econ Stat 53(3):225–236

    Article  Google Scholar 

  • Mandelbrot B (1972) Statistical Methodology for Nonperiodic Cycles: From the Covariance to R/S Analysis. Ann Econ Soc Meas 1(3):259–290

    Google Scholar 

  • Mandelbrot B (1975) Limit Theorems on the Self-Normalized Range for Weakly and Strongly Dependent Processes. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 31(4):271–285

    Article  Google Scholar 

  • Mandelbrot B (1997) Fractals and Scaling in Finance. Springer, Berlin

    Book  Google Scholar 

  • Mandelbrot B, Wallis J (1969) Some Long-Run Properties of Geophysical Records. Water Resour Res 5(2):321–340

    Article  Google Scholar 

  • McLean R, Pontiff J (2016) Does Academic Research Destroy Stock Return Predictability?. J Financ 71(1):5–32

    Article  Google Scholar 

  • Merton R (1987) On the Current State of the Stock Market Rationality Hypothesis. In: Dornbusch R, Fischer F (eds) Macroeconomics and Finance: Essays in Honor of Franco Modigliani. MIT Press, Cambridge, pp 93-124

  • Mielniczuk J, Wojdyłło P (2007) Estimation of Hurst Exponent Revisited. Comput Stat Data Anal 51(9):4510–4525

    Article  Google Scholar 

  • Mohammadi H, Su L (2010) International Evidence on Crude Oil Price Dynamics: Applications of ARIMA-GARCH Models. Energy Econ 32(5):1001–1008

    Article  Google Scholar 

  • Moreira J, Silva J, Kamphorst S (1994) On the Fractal Dimension of Self-Affine Profiles. J Phys A Math Gen 27(24):8079–8089

    Article  Google Scholar 

  • Mulligan R (2004) Fractal Analysis of Highly Volatile Markets: An Application to Technology Equities. Q Rev Econ Financ 44(1):155–179

    Article  Google Scholar 

  • Rahmani B (2006) A Multifractal Detrended Fluctuation Description of Iranian Rial-US Dollar Exchange Rate. Physica A 367:328–336

    Article  Google Scholar 

  • Novy-Marx R (2012) Is Momentum Really Momentum?. J Financ Econ 103 (3):429–453

    Article  Google Scholar 

  • Novy-Marx R (2013) The Other Side of Value: The Gross Profitability Premium. J Financ Econ 108(1):1–28

    Article  Google Scholar 

  • Ohanissian A, Russell J, Tsay R (2004) True or Spurious Long Memory in Volatility: Does it Matter for Pricing Options?. Unpublished Manuscript, University of Chicago

  • Pastor L, Stambaugh R (2003) Liquidity Risk and Expected Stock Returns. J Polit Econ 111(3):642–685

    Article  Google Scholar 

  • Peng C, Buldyrev S, Havlin S, Simons M, Stanley H, Goldberger A (1994) Mosaic Organization of DNA Nucleotides. Phys Rev E 49(2):1685–1689

    Article  Google Scholar 

  • Peters E (1992) R/S Analysis Using Logarithmic Returns. Financ Anal J 48 (6):81–82

    Article  Google Scholar 

  • Peters E (1994) Fractal Market Analysis: Applying Chaos Theory to Investment and Economics. Wiley, New York

    Google Scholar 

  • Petkova R (2006) Do the Fama-French Factors Proxy for Innovations in Predictive Variables?. J Financ 61(2):581–612

    Article  Google Scholar 

  • Qian B, Rasheed K (2004) Hurst Exponent and Financial Market Predictability. In: Proceedings of the 2nd IASTED Inernational Conference on Financial Engineering and Applications, pp 203–209

  • Qian B, Rasheed K (2006) Stock Market Prediction With Multiple Classifiers. Appl Intell 26(1):25–33

    Article  Google Scholar 

  • Sánchez Granero M, Trinidad Segovia J, García Pérez J (2008) Some Comments on Hurst Exponent and the Long Memory Processes on Capital Markets. Physica A 387(22):5543–5551

    Article  Google Scholar 

  • Schwert W, Seguin P (1990) Heteroskedasticity in Stock Returns. J Financ 45(4):1129–1155

    Article  Google Scholar 

  • Sensoy A, Tabak B (2015) Time-Varying Long Term Memory in the European Union Stock Markets. Physica A 436:147–158

    Article  Google Scholar 

  • Sharpe W (1966) Mutual Fund Performance. J Bus 39(1):119–138

    Article  Google Scholar 

  • Souza S, Tabak B, Cajueiro D (2008) Long-Range Dependence in Exchange Rates: The Case of the European Monetary System. Int J Theor Appl Financ 11 (2):199–223

    Article  Google Scholar 

  • Szilagyi P, Batten J (2007) Covered Interest Parity Arbitrage and Temporal Long-Term Dependence Between the US Dollar and the Yen. Physica A 376:409–421

    Article  Google Scholar 

  • Tabak B, Cajueiro D (2007) Are the Crude Oil Markets Becoming Weakly Efficient Over Time? A Test for Time-Varying Long-Range Dependence in Prices and Volatility. Energy Econ 29(1):28–36

    Article  Google Scholar 

  • Taqqu M, Teverovsky V, Willinger W (1995) Estimators for Long-Range Dependence: An Empirical Study. Fractals 3(4):785–798

    Article  Google Scholar 

  • Teverovsky V, Taqqu M, Willinger W (1999) A Critical Look at Lo’s Modified R/S Statistic. J Stat Plan Inf 80(1-2):211–227

    Article  Google Scholar 

  • Tofallis C (2008) Investment Volatility: A Critique of Standard Beta Estimation and a Simple Way Forward. Eur J Oper Res 187(3):1358–1367

    Article  Google Scholar 

  • Tsay R (2005) Analysis of Financial Time Series, 2nd Edn. Wiley, Hoboken

    Book  Google Scholar 

  • van Dijk M (2011) Is Size Dead? A Review of the Size Effect in Equity Returns. J Bank Financ 35(12):3263–3274

  • Vandewalle N, Ausloos M, Boveroux P (1997) Detrended Fluctuation Analysis of the Foreign Exchange Market. In: Kertesz J, Kondor I (eds) Econophysics - An Emergent Science: Proccedings of the 1st Workshop on Econophysics. Budapest University of Technology and Economics, Budapest, pp 36–49

  • Wallis J, Matalas N (1970) Small Sample Properties of H and K-Estimators of the Hurst Coefficient h. Water Resour Res 6(6):1583–1594

    Article  Google Scholar 

  • Wang Y, Liu L (2010) Is WTI Crude Oil Market Becoming Weakly Efficient Over Time? New Evidence From Multiscale Analysis Based on Detrended Fluctuation Analysis. Energy Econ 32(5):987–992

    Article  Google Scholar 

  • Wang Y, Wei Y, Wu C (2011) Detrendet Fluctuation Analysis on Spot and Futures Markets of West Texas Intermediate Crude Oil. Physica A 390(5):864–875

    Article  Google Scholar 

  • Weron R (2002) Estimating Long-Range Dependence: Finite Sample Properties and Confidence Intervals. Physica A 312(1-2):285–299

    Article  Google Scholar 

  • Willinger W, Taqqu M, Teverovsky V (1999) Stock Market Prices and Long-Range Dependence. Finance Stochast 3:1–13

    Article  Google Scholar 

Download references

Acknowledgments

The author thanks an anonymous reviewer for valuable comments and suggestions.

Author information

Authors and Affiliations

  1. University of Leipzig, Department of Finance, Grimmaische Straße 12, 04109, Leipzig, Germany

    Benjamin Rainer Auer

  2. University of Bremen, Chair of Financial Services, Hochschulring 4, 28359, Bremen, Germany

    Benjamin Rainer Auer

  3. CESifo Munich, Research Network Area Macro, Money and International Finance, Schackstraße 4, 80539, Munich, Germany

    Benjamin Rainer Auer

Authors
  1. Benjamin Rainer Auer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Benjamin Rainer Auer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Auer, B.R. Are standard asset pricing factors long-range dependent?. J Econ Finan 42, 66–88 (2018). https://doi.org/10.1007/s12197-017-9385-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12197-017-9385-y

Keywords

JEL Classification

Search

Navigation