相关论文: Antipersistent binary time series

In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…

A binary modified de Bruijn sequence is an infinite and periodic binary sequence derived by removing a zero from the longest run of zeros in a binary de Bruijn sequence. The minimal polynomial of the modified sequence is its unique…

We generalize the notion of a de Bruijn sequence to a "multi de Bruijn sequence": a cyclic or linear sequence that contains every k-mer over an alphabet of size q exactly m times. For example, over the binary alphabet {0,1}, the cyclic…

Generation and prediction of time series is analyzed for the case of a Bit-Generator: a perceptron where in each time step the input units are shifted one bit to the right with the state of the leftmost input unit set equal to the output…

The forward prediction problem for a binary time series $\{X_n\}_{n=0}^{\infty}$ is to estimate the probability that $X_{n+1}=1$ based on the observations $X_i$, $0\le i\le n$ without prior knowledge of the distribution of the process…

The well known prefer-one, prefer-opposite, and prefer-same binary de Bruijn sequences are all constructed using simple preference rules. We apply the technique of preference functions of span one to define q-ary sequences that generalize…

This article deals with detection of nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with constant long memory parameter, typically an I(d) series with d>-.5. The…

We extend previous work on anti-recurrence sequences of Kimberling and Moses, Zaslavsky, and Bosma et al. Kimberling and Moses have formulated several questions on these sequences, which can be combined into the meta-conjecture that…

We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…

A balanced generalized de Bruijn sequence with parameters $(n,l,k)$ is a cyclic sequence of $n$ bits such that (a) the number of 0's equals the number of 1's, and (b) each substring of length $l$ occurs at most $k$ times. We determine…

The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically,…

Negative orientable sequences, i.e. periodic sequences with elements from a finite alphabet of size at least three in which an n-tuple or the negative of its reverse appears at most once in a period of the sequence, were introduced by…

A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…

Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…

Analogously to de Bruijn sequences, Orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., recursive…

Given independent random variables $Y_1, \ldots, Y_n$ with $Y_i \in \{0,1\}$ we test the hypothesis whether the underlying success probabilities $p_i$ are constant or whether they are periodic with an unspecified period length of $r \ge 2$.…

Let $\widetilde{\alpha}$ be a length-$L$ cyclic sequence of characters from a size-$K$ alphabet $\mathcal{A}$ such that the number of occurrences of any length-$m$ string on $\mathcal{A}$ as a substring of $\widetilde{\alpha}$ is $\lfloor L…

P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…

We compare ordinary and symmetric variants of two classical measures of pseudorandomness for binary sequences, the $2$-adic complexity and the linear complexity. In the periodic setting, we show that for binary periodic sequences…

We consider the limitations of two techniques for detecting nonlinearity in time series. The first technique compares the original time series to an ensemble of surrogate time series that are constructed to mimic the linear properties of…