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Signal Analysis currently features tests and procedures addressed at verifying certain hypotheses, such as linearity, stationarity, changes of regime, and the kind of information utilized in back/forecasting time series, possibly by calibration. In such context, methodological updates are required, especially when it comes to dealing with series characterized by high irregularities or when unobservable are involved as in the case of Kalman filtering.1,2 Many Regime-Switching techniques, for instance, are affected by strict requirements such as stationarity and single-point shift3,4 which require amelioration or updating. Similarly, time-varying parameters utilized for back/ forecasting purposes are better computed in a Bayesian context, in order to exploit prior pieces of evidence based on their known distribution. Finally, current stationarity tests5,6 in a nonlinear setting with dramatic changes in trend and subsample variances may require substantial corrections. Section 1 is devoted to defining random signals, whereas Section 2 tackles the issue of Regime-Switch testing. Section 3 produces a novel technique in the field of signal smoothing. The following two sections illustrate the steps for implementing Bayesian Monte Carlo simulation and calibration, whereas the final section is addressed at supplying corrected stationarity tests. Section 7 concludes.

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