## Binary Time SeriesBasic concepts of stationary processes; Sufficient statistics for binary Markov chains; The distribution of the number of axis-crossing; Upcrossings of a high level by a stationary process; Clipping a gaussian process; Estimation in ar(1) after hard limiting; Estimation in ar(p); Runs and estimates of correlations; Spectral analysis after clipping; Extremes in stationary time series; A central limit (ACL); Prediction in binary data. |

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Algebras analysis analytic function assume assumption asymptotic distribution Bernoulli trials BIBLI0GRAPHICAL REMARKS binary process binary series binary time series C0NDITI0NS F0R REGULAR Chapter characteristic function condition dH constant coefficients covariance defines a regular denotes elliptic elliptic operator equation equivalent follows ft u u fundamental solution Gaussian process Gevrey class given hard limiting hence HYP0ELLIPTIC B0UNDARY PR0BLEMS HYP0ELLIPTIC DIFFERENTIAL 0PERAT0RS hypoelliptic operator implies independent inequality integer joint distribution Kedem l-runs Markov chain Mathematics n-tuple normal distribution number of axis-crossings obtained by clipping open set operator P(D parameters parametrix partial differential operator pf.T Poisson Poisson distribution Pr(X Pr(Z probability Proof prove random variables real number satisfies semielliptic boundary-value problem semihomogeneous of degree sequence stationary binary stationary Gaussian process stationary process stationary time series sufficient statistics Suppose Theorem l.l Theory tion value problem zero mean stationary