Real-time supervision of shifts in inflation expectations is an important issue for monetary policy makers, especially in the presence of economic uncertainty. In this paper, we elaborate tools for on-line monitoring of such shifts by extracting valuable information from noisy daily financial market data. For this purpose, first, we suggest a new risk adjustment for observable proxies of medium and long run inflation expectations assuming that the latter are well-anchored. Second, we propose an econometric methodology for sequential monitoring of level changes in the associated proxies at daily frequency. Our empirical evidence shows that the on-line surveillance of risk adjusted US forward breakeven inflation rates by means of the cumulative sum (CUSUM) detector appears to be helpful to extract timely signals on potential shifts. In particular, the obtained signals indicate important turning points in market-based measures of inflation expectations, which also tend to materialize in lower frequency experts' surveys.

The problem of detecting an abrupt change in the distribution of an arbitrary, sequentially observed, continuous-path stochastic process is considered and the optimality of the CUSUM test is established with respect to a modified version of Lorden's criterion. We apply this result to the case that a random drift emerges in a fractional Brownian motion and we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H+1/2.

Quantitative analysis of the spatial patterns in age-structured fish populations provides a useful complement to stock assessment methods. The spatial distribution of an age-structured population is characterized by indicators for location, dispersion and aggregation, which are estimated from survey data. The times series of spatial indicators are organised in a 3D data structure with dimensions along indicators, age classes and years. Multi factor analysis (MFA) is applied to quantify the reproducibility in time of the multivariate structure between age classes and indicators. MFA computes the mean annual pattern over the age classes. The deviation around that pattern in each year is also quantified. A multivariate indicator that characterise the spatial pattern over all age classes is developed. Its variation in time is evaluated with quality control methods. The multivariate indicator is shown to be $\chi ^{2}$ distributed and a CUSUM control chart is used to detect any significant changes in time. Software for implementing the method is presented and described. To illustrate this new method, North Sea cod data are analysed, and changes in the spatial patterns of the age-structured population are detected and interpreted.

One method to assess fish stocks using a suite of indicators is the traffic light approach. In this approach, the time series of the different indicators are mapped on a common colour scale to highlight alerts that occur when indicators cross reference limit values. Until now, however, the procedure has lacked a statistical framework. Here, we propose the cumulative sum (CUSUM) monitoring scheme as a suitable statistical framework. CUSUM is a statistical process control method that detects deviations from a reference mean, according to defined performance criteria. With the CUSUM monitoring scheme, alarm signals can be triggered when indicators cross defined in-control limits that correspond to defined probabilities of false alarm and non-alarm (i.e., precision and power of the CUSUM monitoring scheme). A table of CUSUM out-of-control deviations is constructed to serve as a diagnostics table. In this table, the deviations in the different indicators are quantitative and given in similar units of variance, which facilitates their integrated assessment. The CUSUM out-of-control table also shows how deviations accumulate over time and thus provides a view of the stock history. The procedure was applied to the North Sea cod stock to illustrate how a fishery-independent integrated assessment can be achieved using a suite of indicators derived from research survey data. The indicators used were related to the spatial distribution, abundance, length structure, length at maturity and apparent mortality. The stock was found to be outside its reference limits from 2001 and has shown a continued degradation in status since this time.

Statistical Process Control (SPC) methods are extensively used in manufacturing contexts to monitor production processes. This article illustrates their potential utility for monitoring the state of marine ecosystems, using survey indicators. We exemplify the use of one SPC tool, the cumulative sum (CUSUM) control chart, to detect persistent changes in the state of a system as new observations are collected, using simulated and real data. Practical guidelines are given on how the chart parameters can be tuned to achieve an acceptable compromise between the ability to detect anomalies quickly and keeping the risk of false alarms low. The common performance measures associated with control charts depend on some key assumptions being met, and the potential impact of their violation is indicated.

This work employs the Brownian motion model in which observations are taken sequentially. The objective is to detect a two-sided change in the constant drift by means of a stopping rule. As a performance measure, an extended Lorden criterion is used. The goal is to minimize the worst-case detection delay subject to a constraint in the frequency of false alarms. In a companion paper, attention is drawn to a first category of 2-CUSUM rules for which the harmonic mean rule holds. It is further seen that a special class of 2-CUSUM stopping rules within this category, called drift equalizer rules, perform strictly better than non-equalizer rules, according to this specific performance measure.

The necessary and sufficient conditions for various modes of interactions of the upper and lower schemes with headstarts are derived. The expression for the Laplace transform of the run-length distribution (for both interacting and non-interacting schemes) is obtained and used to develop a method of analysis for general two-sided cumulative sum schemes with headstarts. The results are shown to be relevant in the case when the schemes are supplemented by Shewhart’s control limits.