Simple models are presented for use in the modeling and generation of sequences of dependent discrete random variables. The models are essentially Markov Chains, but are structurally autoregressions, and so depend on only a few parameters. The marginal distribution is an intrinsic component in the specification of each model, and the Poisson, Geometric, Negative Binomial and Binomial distributions are considered. Details are also given for the introduction of time‐dependence into the means of the sequences so that seaonality can be treated simply.

Most time series methods assume that any trend will continue unabated, regardless of the forecast lead time. But recent empirical findings suggest that forecast accuracy can be improved by either damping or ignoring altogether trends which have a low probability of persistence. This paper develops an exponential smoothing model designed to damp erratic trends. The model is tested using the sample of 1,001 time series first analyzed by Makridakis et al. Compared to smoothing models based on a linear trend, the model improves forecast accuracy, particularly at long leadtimes. The model also compares favorably to sophisticated time series models noted for good long-range performance, such as those of Lewandowski and Parzen.forecasting: time series

Some simple models are described which may be used for the modelling or generation of sequences of dependent discrete random variates with negative binomial and geometric univariate marginal distributions. The models are developed as analogues of well-known continuous variate models for gamma and negative exponential variates. The analogy arises naturally from a consideration of self-decomposability for discrete random variables. An alternative derivation is also given wherein both the continuous and the discrete variate processes arise simultaneously as measures on a process of overlapping intervals. The former is the process of interval lengths and the latter is a process of counts on these intervals.

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

Observations made in the scientific and popular literature suggest that the characteristics of both marine and terrestrial ecosystems are changing rapidly due to increasing global air and sea temperatures. Here, we examine the hypothesis that fish species with more 'southern' distributions are increasing in the northern North Sea over time. In order to do this, 2 important databases on fish abundance collected by trawl on research cruises are interrogated. When combined, the databases cover both the entire North Sea and the Scottish west coast and span a period of 80 yr (1925 to 2004). The data take the form of length-frequencies for all species caught (> 300 different species), while additional information (e.g. age, sex, weight and stage of sexual maturity) is available for the commercially important component (e.g. cod). The trawl data suggest that the North Sea is experiencing waves of immigration by exotic, southern species (e.g. red mullet, anchovy and pilchard). The purpose of this paper is to describe and document these changes.KEY WORDS: Anchovy · Sardine · Horse mackerel · Mackerel · Long-term · North Sea · Climate Resale or republication not permitted without written consent of the publisherMar Ecol Prog Ser 284: [269][270][271][272][273][274][275][276][277][278] 2004 doliolids are connected to unusual incursions of oceanic water caused by changes in the North Atlantic Oscillation (Edwards et al. 1999).Higher than average sea temperatures are correlated with low recruitment of cod at the latitudinal limits of its range (Planque & Frédou 1999, O'Brien et al. 2000. Reid et al. (2001) related abrupt changes in the abundance and composition of the plankton and fish community ca. 1988 to recent increases in the North Sea horse mackerel fishery. Pronounced increases in tropical fish in the Bay of Biscay area have been noted (Quero et al. 1998) by scientists in France, while Swaby & Potts (1999) made the first British record of the sailfin dory Zenopsis conchifer, noting that the species is advancing northwards along the continental shelf west of the British Isles at a rate of 60 km per decade. Other studies show similar patterns. Information on first records of southerly fish species caught in Cornish waters has been collated and published (Stebbing et al. 2002), and nearly 20 completely new species have been recorded (by 2001). The fish species noted include bigeyed tunny Thunnus obesus, sailfin dory Zenopsis conchifer, short-nosed seahorse Hippocampus hippocampus and barracuda Sphyraena sphyraena. In the Irish Sea, the occurrence of the warm-water species, anchovy Engraulis encrasicolus, has increased between 1990 and 1998 according to trawl data from research surveys (Armstrong et al. 1999). British commercial fishermen have also noted change. The spider-crab Maia squinado fishery, for example, is advancing steadily further northwards (Anonymous 2003).In 1996, a paper was published describing the longterm variation in the abundance of southern species in the southern North Sea (Corten & van...

No abstract

This version is available at https://strathprints.strath.ac.uk/18569/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the ABSTRACTThe population of Calanus finmarchicus in the North Sea is replenished each spring by invasion from an overwintering stock located beyond the shelf edge. A combination of field observations, statistical analysis of Continuous Plankton Recorder (CPR) data, and particle tracking model simulations, was used to investigate the processes involved in the cross-shelf invasion. The results showed that the main source of overwintering animals entering the North Sea in the spring is at depths of greater than 600 m in the Faroe Shetland Channel, where concentrations of up to 620 m 73 are found in association with the overflow of Norwegian Sea Deep Water (NSDW) across the Iceland Scotland Ridge. The input of this water mass to the Faroe Shetland Channel, and hence the supply of overwintering C. finmarchicus, has declined since the late 1960s due to changes in convective processes in the Greenland Sea. Beginning in February, animals start to emerge from the overwintering state and migrate to the surface waters, where their transport into the North Sea is mainly determined by the incidence of north-westerly winds that have declined since the 1960s. Together, these two factors explain a high proportion of the 30-year trends in spring abundance in the North Sea as measured by the CPR survey. Both the regional winds and the NSDW overflow are connected to the North Atlantic Oscillation Index (NAO), which is an atmospheric climate index, but with different time scales of response. Thus, interannual fluctuations in the NAO can cause immediate changes in the incidence of northwesterly winds without leading to corresponding changes in C. finmarchicus abundance in the North Sea, because the NSDW overflow responds over longer (decadal) time scales.

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.