Testing for local covariate trend effects in volatility models. (English) Zbl 1450.62119
This article proposes a new nonparametric local covariate trend testing approach to statistically test the significance of an exogeneous covariate in the autoregressive conditional heteroscedastic volatility model, where the effect of the covariate can be nonlinear. The test statistic is based on an artificial high-dimensional one-way ANOVA where the number of factor levels increases with the sample size. The key idea is to measure the local effect of the covariate on the residuals of the null model in small neighborhoods of time, so that, if different neighborhoods exhibit significantly different average effects, then an overall covariate effect may be expected to exist. Asymptotic properties of the new test statistic are derived. As for the finite sample performance of the test, simulation studies are presented which indicate a competitive performance of the new method both in terms of size and power of the test. An application to volatility analysis of three major cryptoassets and their relationship with the prices of gold and the S&P500 index is presented
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62G10 | Nonparametric hypothesis testing |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62J10 | Analysis of variance and covariance (ANOVA) |
| 91B84 | Economic time series analysis |
| 62P20 | Applications of statistics to economics |
References:
| [1] | Abay, N. C., Akcora, C. G., Gel, Y. R., Kantarcioglu, M., Islambekov, U. D., Tian, Y., and Thuraisingham, B. (2019). Chainnet: Learning on blockchain graphs with topological features. In, 2019 IEEE International Conference on Data Mining (ICDM), pages 946-951. |
| [2] | Akritas, M. G. and Arnold, S. (2000). Asymptotics for analysis of variance when the number of levels is large., Journal of the American Statistical Association, 95:212-226. · Zbl 0996.62064 · doi:10.1080/01621459.2000.10473915 |
| [3] | Akritas, M. G. and Papadatos, N. (2004). Heteroscedastic one-way anova and lack-of-fit tests., Journal of the American Statistical Association, 99:368-382. · Zbl 1117.62481 · doi:10.1198/016214504000000412 |
| [4] | Beyaztas, B. H., Beyaztas, U., Bandyopadhyay, S., and Huang, W.-M. (2018). New and fast block bootstrap-based prediction intervals for garch(1,1) process with application to exchange rates., Sankhya A, 80(1):168-194. · Zbl 1387.62098 · doi:10.1007/s13171-017-0098-2 |
| [5] | Bickel, P. J., Götze, F., and van Zwet, W. R. (2012). Resampling fewer than n observations: gains, losses, and remedies for losses. In, Selected works of Willem van Zwet, pages 267-297. Springer. · Zbl 1373.62173 |
| [6] | Bickel, P. J. and Sakov, A. (2008). On the choice of m in the m out of n bootstrap and its application to confidence bounds for extreme percentiles., Statistica Sinica, 18(3):967-985. · Zbl 1534.62057 |
| [7] | Bitcoin (2018). Download bitcoin core., https://bitcoin.org/en/download. [Online; accessed 2018-12-31]. |
| [8] | Blau, B. M. (2018). Price dynamics and speculative trading in bitcoin., Research in International Business and Finance, 43:15-21. |
| [9] | Boos, D. and Brownie, C. (1995). Anova and rank tests when the number of treatments is large., Statistics & Probability Letters, 23:183-191. · Zbl 0819.62037 · doi:10.1016/0167-7152(94)00112-L |
| [10] | Brenner, R. J., Harjes, R. H., and Kroner, K. F. (1996). Another look at models of the short-term interest rate., The Journal of Financial and Quantitative Analysis, 31(1):85-107. |
| [11] | Cermak, V. (2017). Can bitcoin become a viable alternative to fiat currencies? an empirical analysis of bitcoin’s volatility based on a garch model., An Empirical Analysis of Bitcoin’s Volatility Based on a GARCH Model (May 2, 2017). |
| [12] | Chatterjee, S. and Das, S. (2003). Parameter estimation in conditional heteroscedastic models., Communications in Statistics: Theory and Methods, 32:1135-1153. · Zbl 1104.62306 · doi:10.1081/STA-120021324 |
| [13] | Chu, J., Chan, S., Nadarajah, S., and Osterrieder, J. (2017). Garch modelling of cryptocurrencies., Journal of Risk and Financial Management, 10(4):17. |
| [14] | Chua, C. L. and Tsiaplias, S. (2019). Information flows and stock market volatility., Journal of Applied Econometrics, 34(1):129-148. |
| [15] | Collier, A. (2019). An ethereum package for r., github.com/BSDStudios/ethr. |
| [16] | Dedecker, J., Doukhan, P., Lang, G., Leon, J. R., louhichi, S., and Prieur, C. (2007)., Weak Dependence With Examples and Applications. Springer - Lecture Notes in Statistics. · Zbl 1165.62001 |
| [17] | Dey, A. K., Akcora, C. G., Gel, Y. R., and Kantarcioglu, M. (2020). On the role of local blockchain network features in cryptocurrency price formation., Canadian Journal of Statistics, https://doi.org/10.1002/cjs.11547. · Zbl 1492.62185 |
| [18] | Dixon, M. F., Akcora, C. G., Gel, Y. R., and Kantarcioglu, M. (2019). Blockchain analytics for intraday financial risk modeling., Digital Finance, 1(1-4):67-89. |
| [19] | Dyhrberg, A. H. (2016). Bitcoin, gold and the dollar-a garch volatility analysis., Finance Research Letters, 16:85-92. |
| [20] | Engle, R. and Patton, A. (2001). What good is a volatility model., Quantitative finance, 1:237-245. · Zbl 1405.91612 · doi:10.1088/1469-7688/1/2/305 |
| [21] | Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation., Econometrica, 50:987-1008. · Zbl 0491.62099 · doi:10.2307/1912773 |
| [22] | Fabozzi, F. J., Focardi, S. M., Rachev, S. T., and Arshanapalli, B. G. (2014)., Autoregressive Moving Average Models, chapter 9, pages 171-190. John Wiley & Sons, Ltd. |
| [23] | Francq, C. et al. (2019). Qml inference for volatility models with covariates., Econometric Theory, 35(1):37-72. · Zbl 1415.62078 · doi:10.1017/S0266466617000512 |
| [24] | Francq, C. and Sucarrat, G. (2017). An equation-by-equation estimator of a multivariate log-garch-x model of financial returns., Journal of Multivariate Analysis, 153:16-32. · Zbl 1351.62164 · doi:10.1016/j.jmva.2016.09.010 |
| [25] | Gidea, M., Goldsmith, D., Katz, Y., Roldan, P., and Shmalo, Y. (2020). Topological recognition of critical transitions in time series of cryptocurrencies., Physica A: Statistical Mechanics and its Applications, page 123843. · Zbl 07530523 |
| [26] | Hamadeh, T. and Zakoïan, J.-M. (2011). Asymptotic properties of ls and qml estimators for a class of nonlinear garch processes., Journal of Statistical Planning and Inference, 141(1):488-507. · Zbl 1197.62128 · doi:10.1016/j.jspi.2010.06.026 |
| [27] | Han, H. (2015). Asymptotic properties of garch-x processes., Journal of Financial Econometrics, 13(1):188-221. |
| [28] | Han, H. and Kristensen, D. (2014). Asymptotic theory for the qmle in garch-x models with stationary and nonstationary covariates., Journal of Business & Economic Statistics, 32(3):416-429. |
| [29] | Han, H. and Park, J. Y. (2008). Time series properties of arch processes with persistent covariates., Journal of Econometrics, 146(2):275-292. Honoring the research contributions of Charles R. Nelson. · Zbl 1429.62398 · doi:10.1016/j.jeconom.2008.08.016 |
| [30] | Hansen, P. R., Huang, Z., and Shek, H. H. (2012). Realized garch: a joint model for returns and realized measures of volatility., Journal of Applied Econometrics, 27(6):877-906. |
| [31] | Kurbucz, M. T. (2019). Predicting the price of bitcoin by the most frequent edges of its transaction network., Economics Letters, 184:108655. |
| [32] | Li, Y., Islambekov, U., Akcora, C., Smirnova, E., Gel, Y. R., and Kantarcioglu, M. (2020). Dissecting ethereum blockchain analytics: What we learn from topology and geometry of the ethereum graph? In, Proceedings of the 2020 SIAM International Conference on Data Mining, pages 523-531. |
| [33] | Litecoin (2018). Money for the internet age., https://litecoin.com/. [Online; accessed 2018-12-31]. |
| [34] | Lyubchich, V. and Gel, Y. R. (2016). A local factor nonparametric test for trend synchronism in multiple time series., Journal of Multivariate Analysis, 150:91-104. · Zbl 1347.62198 · doi:10.1016/j.jmva.2016.05.004 |
| [35] | Lyubchich, V., Gel, Y. R., and El-Shaarawi, A. (2013). On detecting non-monotonic trends in environmental time series: A fusion of local regression and bootstrap., Environmetrics, 24(4):209-226. · Zbl 1525.62171 |
| [36] | May, H. and Herce, M. A. (2002). Endogenous exchange rate volatility, trading volume and interest rate differentials in a model of portfolio selection., Review of International Economics, 7(2):202-218. |
| [37] | Mcquad, D. (2017). Bitcoin sends price of gold fallen as investors dump secure investment for cryptocurrency., http://fortune.com/2018/02/08/litecoin-monero-cryptocurrency-bitcoin/. |
| [38] | Nakamoto, S. (2008). Bitcoin: A peer-to-peer electronic cash system., Working paper. |
| [39] | Pedersen, R. S. and Rahbek, A. (2019). Testing garch-x type models., Econometric Theory, 35(5):1012-1047. · Zbl 1432.62310 · doi:10.1017/S026646661800035X |
| [40] | Peligrad, M. (1987). On the central limit theorem for i-mixing sequences of random variables., The Annals of Probability, 15(4):1387-1394. · Zbl 0638.60032 · doi:10.1214/aop/1176991983 |
| [41] | PerthMint (2019). The perth mint., https://www.perthmint.com. |
| [42] | Rice, J. (1984). Bandwidth choice for nonparametric regression., Ann. Statist., 12(4):1215-1230. · Zbl 0554.62035 · doi:10.1214/aos/1176346788 |
| [43] | Robert, E. (2002). New frontiers for arch models., Journal of Applied Econometrics, 17(5):425-446. |
| [44] | Roberts, J. (2018). Litecoin is now a surprise favorite of criminals tired of bitcoin., https://fortune.com/2018/02/08/litecoin-monero-cryptocurrency-bitcoin/. |
| [45] | Sadik, Z. A., Date, P. M., and Mitra, G. (2018). News augmented garch (1, 1) model for volatility prediction., IMA Journal of Management Mathematics, 30(2):165-185. · Zbl 07110063 · doi:10.1093/imaman/dpy004 |
| [46] | Sidorov, S. P., Revutskiy, A., Faizliev, A., Korobov, E., and Balash, V. (2014). Garch model with jumps: testing the impact of news intensity on stock volatility. In, Proceedings of the World Congress on Engineering, volume 1, pages 189-210. |
| [47] | Sucarrat, G., Grønneberg, S., and Escribano, A. (2016). Estimation and inference in univariate and multivariate log-garch-x models when the conditional density is unknown., Computational Statistics & Data Analysis, 100:582-594. · Zbl 1466.62199 · doi:10.1016/j.csda.2015.12.005 |
| [48] | Wang, L., Akritas, M., and Van Keilegom, I. (2008). An anova-type nonparametric diagnostic test for heteroscedastic regression models., Journal of Nonparametric Statistics, 20(5):365-382. · Zbl 1142.62025 · doi:10.1080/10485250802066112 |
| [49] | Wang, L. and Keilegom, I. V. (2007). Nonparametric test for the form of parametric regression with time series errors., Statistica Sinica, 17:369-386. · Zbl 1145.62033 |
| [50] | Yahoo (2019). Yahoo finance., https://finance.yahoo.com. |
| [51] | Zambom, A. · Zbl 1480.62080 |
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