In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

[1] Meaningful quantification of data and structural uncertainties in conceptual rainfall-runoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes ill-posed unless sufficiently precise prior knowledge of data uncertainty is supplied; this ill-posedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfall-runoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.

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Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors

Author Posting. © Oceanography Society, 2007. This article is posted here by permission of Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 20, 3 (2007): 22-39.

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Larval transport and dispersal in the coastal ocean and consequences for population connectivity

Mangrove macrobenthos: Assemblages, services, and linkages

[1] This study explores the decomposition of predictive uncertainty in hydrological modeling into its contributing sources. This is pursued by developing data-based probability models describing uncertainties in rainfall and runoff data and incorporating them into the Bayesian total error analysis methodology (BATEA). A case study based on the Yzeron catchment (France) and the conceptual rainfall-runoff model GR4J is presented. It exploits a calibration period where dense rain gauge data are available to characterize the uncertainty in the catchment average rainfall using geostatistical conditional simulation. The inclusion of information about rainfall and runoff data uncertainties overcomes ill-posedness problems and enables simultaneous estimation of forcing and structural errors as part of the Bayesian inference. This yields more reliable predictions than approaches that ignore or lump different sources of uncertainty in a simplistic way (e.g., standard least squares). It is shown that independently derived data quality estimates are needed to decompose the total uncertainty in the runoff predictions into the individual contributions of rainfall, runoff, and structural errors. In this case study, the total predictive uncertainty appears dominated by structural errors. Although further research is needed to interpret and verify this decomposition, it can provide strategic guidance for investments in environmental data collection and/or modeling improvement. More generally, this study demonstrates the power of the Bayesian paradigm to improve the reliability of environmental modeling using independent estimates of sampling and instrumental data uncertainties.

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Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation

Physical processes that force transport of planktonic larvae of invertebrates are responsible for some of the spatial and temporal variability in recruit- ment. We investigated the influence of tide- and wind- driven circulation on intra-year variability of megalopal supply to populations of the crab Carcinus maenas in 2 estuaries on the Portuguese west coast. Daily data on physical variables and on supply and settlement of megalopae were subjected to time series analysis and mul- tiple regression techniques in order to identify periodicity in the variables as well as time lags between larval supply and physical variables. Relaxation of northerly winds, which favor upwelling, was associated with temperature increase and subtidal sea level rise at the coast, which are indicative of coastal convergence of the surface layer. Supply of megalopae to the estuaries, as measured with passive plankton nets, followed a fortnightly cycle with maximum larval supply at the time of maximum tidal am- plitude. Supply was enhanced by southerly winds, with delays of 0 to -2 d. Settlement of megalopae on artificial settlement substrates deployed on the bottom was uncou- pled to supply at both estuaries. Therefore, transport of C. maenas megalopae to the nearshore is accomplished by onshore advection following downwelling winds, and supply to the estuaries occurs by selective tidal stream transport. Involvement of internal waves and internal tidal bores cannot be be ruled out, but very particular periodicities of the generating mechanisms would have to be assumed to account for the observed time lags.

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Tide and wind control of megalopal supply to estuarine crab populations on the Portuguese west coast

The development of statistical methodologies based on spatial and temporal hydrological data is a very important tool in the monitoring of surface water quality in a river basin. This paper uses cluster analysis and linear models to describe hydrological space–time series of quality variables and to detect changes in surface water quality data collected in the River Ave hydrological basin, located in the north-west region of Portugal. This area receives many untreated effluent discharges from textile industries, which result in extreme pollution. Because of this problematic environmental situation, local authorities installed a network of 20 monitoring sites, producing monthly measurements of quality variables and later began to operate three wastewater treatment plants (WTP) at the end of the 1998 hydrological year. In this work, we propose a two-step methodology to analyse these data which use cluster analysis to classify the quality monitoring sites into spatial homogeneous groups. Then we adjust linear models to the quality variables associated with the clusters, taking into account the seasonal variations throughout the year, different trends for each period of time (before and after the installation of WTPs), and the hydro-meteorological factor. Finally, statistical tests are performed to evaluate the effective role of the WTPs' performance. Copyright © 2011 John Wiley & Sons, Ltd.

Water quality monitoring using cluster analysis and linear models

Parameter estimation of state space models for univariate observations

In this paper we will consider a linear regression model with the sequence of error terms following an autoregressive stationary process. The statistical properties of the maximum likelihood and least squares estimators of the regression parameters will be summarized. Then, it will be proved that, for some typical cases of the design matrix, both methods produce asymptotically equivalent estimators. These estimators are also asymptotically efficient. Such cases include the most commonly used models to describe trend and seasonality like polynomial trends, dummy variables and trigonometric polynomials. Further, a very convenient asymptotic formula for the covariance matrix will be derived. It will be illustrated through a brief simulation study that, for the simple linear trend model, the result applies even for sample sizes as small as 20.

On the efficiency of regression analysis with AR(p) errors

Since area precipitation measurements are difficult to obtain because of the large spatial and time variability of the precipitation field, the development of statistical methods for the optimal combination of weather radar and rain gauge measurements is a matter of great importance. This work presents area rainfall prediction methods based on kriging and cokriging techniques modified to account for the autoregressive temporal structure of the gauge measurement process. Hence, the suggested kriging-type predictor includes spatial observations both at the present time and at k lagged time instants. Such predictors are called of kth-order. Cokriging-type predictors developed in this article include the mixed cokriging and linkage cokriging predictors. Mixed cokriging combines 1st-order prediction and observations of a co-process. The linkage cokriging predictor is appropriate to deal with observations from any two different processes with proportional, yet unknown, expected values. This will be the case for the spatiotemporal models adopted in this work to describe rain gauges and radar measurements. Its expression is the same as the simple cokriging, but the usual conditions are replaced by a single linkage condition. Finally, we apply these methods to a storm of mixed type that occurred in 1992, for 99 h, over the Alenquer River basin region located north of Lisbon. Copyright © 2005 John Wiley & Sons, Ltd.

Teresa Alpuim

Papers

Tide and wind control of megalopal supply to estuarine crab populations on the Portuguese west coast

Water quality monitoring using cluster analysis and linear models

Parameter estimation of state space models for univariate observations

On the efficiency of regression analysis with AR(p) errors

Spatiotemporal models in the estimation of area precipitation