Universal Codes as a Basis for Nonparametric Testing of Serial Independence for Time Series
<|reference_start|>Universal Codes as a Basis for Nonparametric Testing of Serial Independence for Time Series: We consider a stationary and ergodic source $p$ generated symbols $x_1 ... x_t$ from some finite set $A$ and a null hypothesis $H_0$ that $p$ is Markovian source with memory (or connectivity) not larger than $m, (m >= 0).$ The alternative hypothesis $H_1$ is that the sequence is generated by a stationary and ergodic source, which differs from the source under $H_0$. In particular, if $m= 0$ we have the null hypothesis $H_0$ that the sequence is generated by Bernoully source (or the hypothesis that $x_1 ...x_t$ are independent.) Some new tests which are based on universal codes and universal predictors, are suggested.<|reference_end|>
@article{ryabko2005universal,
    title={Universal Codes as a Basis for Nonparametric Testing of Serial
  Independence for Time Series},
    author={Boris Ryabko and Jaakko Astola},
    journal={arXiv preprint arXiv:cs/0506094},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0506094},
    primaryClass={cs.IT math.IT}
}