Eddie McKenzie

University of Strathclyde · Department of Mathematics and Statistics

Mortality monitoring systems are important for gauging the effect of influenza and other wide ranging health threats. We present the daily all-cause mortality monitoring system routinely used in Scotland, which differs from others by using two different statistical models for calculating expected mortality. The first model is an extended Serfling m...

The damped trend method of exponential smoothing is a benchmark that has been difficult to beat in empirical studies of forecast accuracy. One explanation for this success is the flexibility of the method, which contains a variety of special cases that are automatically selected during the fitting process. That is, when the method is fitted, the op...

Over the past twenty years, damped trend exponential smoothing has performed well in numerous empirical studies, and it is now well established as an accurate forecasting method. The original motivation for this method was intuitively appealing, but said very little about why or when it provided an optimal approach. The aim of this paper is to prov...

Bacon, P. J., Gurney, W. S. C., McKenzie, E., Whyte, B., Campbell, R., Laughton, R., Smith, G., and MacLean, J. 2011. Objective determination of the sea age of Atlantic salmon from the sizes and dates of capture of individual fish. – ICES Journal of Marine Science, 68: 130–143. The sea ages of Atlantic salmon indicate crucial differences between oc...

Marine protected areas (MPAs) are attaining increasing importance in the management of marine ecosystems. They are effective for conservation in tropical and subtropical areas (mainly coral and rocky reefs), but it is debated whether they are useful in the management of migratory fish stocks in open temperate regions. World War II created a large m...

Fishery management policies need to be based on historical summaries of stock status which are well correlated with the size of the group of individuals who will be affected by any harvest. This paper is motivated by the problem of managing stocks of Atlantic salmon, which can be accurately monitored during the riverine stages of their life-history...

This paper reports an investigation of stock-recruitment relations for Atlantic salmon (Salmo salar). We regard these relations as stochastic functions characterized by an expected stock-recruitment relation and deviations from this expectation driven by observational error and uncharacterised environmental variability. We estimate model parameters...

Age at length keys (ALKs), which give the probability of age given length, are a fundamental component of many age-based fish stock assessment methods. Usually, ALKs are compiled from readings of otoliths or scales taken from length-stratified sub-samples of fishery landings or research vessel trawls catches. The assessment process is data intensiv...

Egg mortality is a key parameter for understanding early life histories of fish. Small variations in estimated mortality cause large differences on adult fish biomass estimates. Therefore, the assumption of a constant egg mortality rate may be misleading. Here, we show how to estimate mortality rates for the individual egg stages of Atlantic macker...

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, Geome...

Despite novel medicines for the control of sea lice on farmed Atlantic salmon, infections remain a threat to the health of fish and the commercial viability of farms throughout European, North American and South American waters. In Scotland the dynamics of sea lice populations, and in particular the species Lepeophtheirus salmonis and Caligus elong...

Ideally, mortality is estimated over a single population observed for enough time to see them all die. Unfortunately such observation resolution is not possible in the field. Mortality is generally estimated on data combined in time and space. In order to enhance mortality rates over a population, during the 2004 mackerel egg survey, sampling took...

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 orde...

Patterns of mature cod and haddock abundance in the North Sea were estimated from International Council for the Exploration of the Seas (ICES) International Bottom Trawl Survey (IBTS) data acquired from 1980 to 1999 in the first quarter of each year. Relationships between abundances and environmental properties (water depth, bottom temperature and...

Summary • Attempts to understand the demography of natural populations from time-series can be hampered by the fact that changes due to births and deaths may be confounded with those due to movement in and out of the sampling area. • We illustrate the problem using a stage-structured time-series of the marine copepod Calanus finmarchicus sampled in...

Most lice infestations on salmon farmed in the North Atlantic are attributed to Caligus elongatus and Lepeophtheirus salmonis. This study reports findings from time-series analysis conducted on observations of the lesser-studied C. elongatus, in four farms on the west coast of Scotland over the period 1996–2000. Least-squares and Poisson regression...

Trawl data from Scottish research vessels dating from January 1925 show that catches of the warm water pelagic species, anchovy (Engraulis encrasicholus) and sardine (Sardina pilchardus), increased suddenly after 1995. Most were observed in the first quarter of each year, with 1998 and 2003 having the largest numbers, although few data are availabl...

Modeling discrete variate time series is the most challenging and, as yet, least well developed of all areas of research in time series. The fact that variate values are integer renders most traditional representations of dependence either impossible or impractical. Discrete variate time series occur in many contexts, often as counts of events, obj...

This paper is concerned with historical changes in domestic ventilation rates, relative humidity and the associated risk of house dust mite colonization. A controlled trial evaluated allergen and water vapour control measures on the level of house dust mite (HDM) Der p1 allergen and indoor humidity, concurrently with changes in lung function in 54...

The Continuous Plankton Recorder survey provides pan-oceanic data on geographic distribution, species composition, seasonal cycles of abundance, and long-term change during the last 70 years. In this paper we compare and contrast some of the historic data-analytic protocols of the survey, focusing primarily on the various means by which spatio-temp...

This study investigates whether pelagic fish schools of different species or groupings (e.g. herring, "surface herring", "gadoids", mackerel, sprat and sandeels) were positively or negatively associated with each other in time and space. To do this, statistical models were fitted to pre-processed acoustic fisheries data to reveal how pelagic school...

The abundance of Calanus finmarchicus is known to have fallen between the present and the late 1950s in north-eastern Atlantic shelf waters. Further west in deeper water, however, long-term abundance of the copepod has risen.

The use of Generalized Additive Models in the analysis of Continuous Plankton Recorder (CPR) distribution and abundance data for Calanus finmarchicus and C. helgolandicus is demonstrated. Strong emphasis is placed on the influence of long-term trend, seasonality and location. The preponderance of zeros in the data, as well as the particular problem...

Generalized linear models were used to assess the influence of diel vertical migration (DVM) on Continuous Plankton Recorder data for adult (stages V and VI) Calanus finmarchicus. To simplify interpretation, the data were first divided into individual months and modelled using a Generalized Linear Model incorporating factors for long-term trend and...

The results of Lamoureux and Lastrapes (1990) are extended to the UK stock market, and the study examines, in particular, their finding that GARCH modelling captures the serial dependence in volume of trade. Using data on 50 UK companies, we find that although the parameter estimates of the GARCH model become insignificant when volume of trade is u...

A summary of the Icelandic Spring Survey zooplankton data for May and June is presented for the years 1960–1996, along with time-series information on sea surface temperature. Changes in zooplankton abundance are assessed using displacement volumes and simple index numbers modelled as various functions of temporal (year) and location (latitude and...

Patterns in the temporal abundance of Calanus finmarchicus and C. helgolandicus in 3 sub-regions of the northern North Sea are described from Continuous Plankton Recorder data, updating earlier studies with information from 3 more years (1994, 1995 and 1996). Abundances are considered using time-series techniques that allow the annual seasonal cycl...

The paper investigates the proposition that the UK FTSE All-share index returns, during the period from January 2nd, 1970, to October 17th, 1997, are covariance stationary. The null hypothesis of variance constancy is rejected by using the Loretan and Phillips test statistic. An intervention model in the spirit of Box and Tiao is used to filter the...

The 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...

Seasonal variation in the abundance of marine plankton taxa is commonly expressed in the form of ‘mean annual cycles', in which the mean abundance over several years for a particluar season is plotted against the time of year. Typically, such mean annual cycles are used to compare patterns between different spatial locations. We wish to argue, howe...

Simulating a stationary AR(p), Xt = ∑pi=1αiXt−i + Zt, when the innovations {Zt} are assumed to be i.i.d. is straightforward. Starting the process in the stationary state, however, requires generation of (X1,X2,…,Xp) from the stationary p-dimensional distribution. When Zt is normal this may be achieved by generating Xi as a linear function of X1,X2,...

"Transition matrix techniques are used to relate the past and present performance of pension fund portfolios. In particular, funds are ranked to study the tendency of portfolios to remain in the same quartile of the ranking as they were in the previous period. For raw returns, funds in both of the top quartiles are found to be more likely to remain...

The growth of herring Clupea harengus larvae within a patch tracked for approximately 20 d in the Orkney-Shetland area (north of Scotland) was investigated using otolith microstructure and, in a supporting role, condition factor analyses. Daily otolith growth responded conservatively to external factors, there being significant autocorrelation with...

We present a time series analysis of 34 yr of continuous plankton recorder (CPR) data for 2 taxa: 'total small copepods' and Calanus copepodite stages 5 and 6 in the North Sea. Each was resolved into spatial averages over areas which correspond to the hydrographic regimes of the North Sea as defined by ICES. An iterative method which enables reliab...

A statistical method is described which enables comparisons to be made between two sets of data where each datum can only be expressed as a positive or negative value. The method is based upon logistic regression analysis. It has been applied to patterns of positive and negative responses to chromatographic analyses carried out on hand swabs taken...

Some new distribution theoretic results are presented for non negative integer random variables using an alternative and more sutiable form of linear combination. In particular, characterizations based on the behaviour of such linear combinations are considered. Discrete analogues of the Cramer-Wold and Skitovich-Darmois theorems are derived. They...

It is shown that the stationary, autoregressive, Markovian minification processes introduced by Tavares and Sim can be extended to give processes with marginal distributions other than the exponential and Weibull distributions. Necessary and sufficient conditions on the hazard rate of the marginal distributions are given for a minification process...

It is shown that the stationary, autoregressive, Markovian minification processes introduced by Tavares and Sim can be extended to give processes with marginal distributions other than the exponential and Weibull distributions. Necessary and sufficient conditions on the hazard rate of the marginal distributions are given for a minification process...

A simple time series model for bivariate exponential variables having first-order autoregressive structure is presented, the BEAR(1) model. The linear random coefficient difference equation model is an adaptation of the New Exponential Autoregressive model (NEAR(2)). The process is Markovian in the bivariate sense and has correlation structure anal...

In this paper we apply the strategy of trend-damping to the popular Winters exponential smoothing systems for seasonal time series. Efficient model formulations are derived for both multiplicative and additive seasonal patterns. An algorithm is given to test the stability of the models in cases where predetermined smoothing parameters are used. Emp...

The Beta-Gamma transformation is described and is used to define a very simple first-order autoregressive Beta-Gamma process, BGAR(l). Maximum likelihood estimation is discussed for this model, as well as moment estimators. The first-order structure is extended to include moving average processes and mixed first-order autoregressive, pth-order movi...

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 beha...

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 beha...

Model identification has traditionally been ignored in forecasting via exponential smoothing. The usual practice is to apply the same model to every time-series in a collection. This paper develops a procedure for model identification in large forecasting applications based on an examination of variances of differences of the time-series. The order...

Analysis of time-series models has, in the past, concentrated mainly on secondorder properties, i.e. the covariance structure. Recent interest in non-Gaussian and non-linear processes has necessitated exploration of more general properties, even for standard models. We demonstrate that the powerful Markov property which greatly simplifies the distr...

Forecasts of ARIMA processes are generally made using the Difference Equation form. This is the approach favoured by Box and Jenkins and most subsequent authors. The purpose of this note is to emphasise that the Integrated Form of the forecast enjoys some important advantages derived from its explicit use of the Eventual Forecast Function (EFF). A...

In many practical cases in time series analysis, marginal distributions in stationary situations are not Gaussian. It is therefore necessary to be able to generate and analyze non-Gaussian time series. Several non-Gaussian time series models are discussed in this paper. The marginal distributions are Laplace or l-Laplace distributions, and the corr...

A procedure for deriving the variance of the forecast error for Winters' additive seasonal forecasting system is given. Both point and cumulative T-step ahead forecasts are dealt with. Closed form expressions are given in the cases when the model is (i) trend-free and (ii) non-seasonal. The effects of renormalization of the seasonal factors is also...

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 na...

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 na...

Derivation of the theoretical autocovariances of an ARMA model is important for anumber of purposes associated with the estimation and testing of the model. Onecommon algorithm, due to McLeod (1975), involves solving a systems of linear equations. By deriving the determinant of the matrix of coefficients in these equations we can ascertain the beha...

Normalizing the initial estimates of the seasonal factors in Winters’ seasonal forecasting systems is a universally recommended practice. Once forecasting begins, however, the seasonal factors lose their normalization. It is often recommended that these factors be renormalized either seasonally or continuously, i.e., with every observation. We show...

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 err...

Two stationary first-order autoregressive processes with Beta marginal distributions are presented. They are both linear, additive processes but the coefficients are Beta random variables. Their autocorrelation functions are investigated: one is positive and the other alternates in sign. The usefulness of the models in simulation is discussed. The...

Although the basic principles of exponential smoothing and discounted least squares are easily understood, the full power of the technique is only rarely exploited. The reason for this failure lies in the complexity of the standard procedures. Often they require fairly complex mathematical models and use a variety of cumbersome algebraic manipulati...

The autorun function is a tool proposed and applied by Z. Şen for examining the nature of dependence in hydrologic time-series. Unfortunately, the statistical properties which he attributes to the function are incorrect. The purpose of this paper is to give the correct mean and variance for the autorun function estimates and to derive an entirely e...

Time series models for positive-valued and discrete-valued input processes are discussed, with the emphasis on the simulation problems which arise in generating time series from these models.

A non-linear stationary stochastic process left brace X//t right brace is derived and shown to have the property that both the processes left brace X//t right brace and left brace log X//t right brace have the same correlation structure, viz. the Markov or first-order autoregressive correlation structure. The generation of such processes is discuss...

A non-linear stationary stochastic process {Xt } is derived and shown to have the property that both the processes {Xt } and {log Xt } have the same correlation structure, viz. the Markov or first-order autoregressive correlation structure. The generation of such processes is discussed briefly and a characterization of the gamma distribution is obt...

Some recent constructions for the generation of dependent sequences of identically distributed negative exponential random variables with specific correlation structures are generalized. This is achieved by attributing a correlation structure to the binary sequence which controls the generation of the exponentials. The procedure causes the autocorr...

By considering equivalences between various forecasting systems, the exact stochastic process followed by the one-step-ahead errors may be found. This process, the error process, is important for any monitoring scheme, and is a function of the forecasting system and the underlying data process. The error process is obtained for the most general for...

In discussing the equivalence of certain polynomial predictors, Godolphin and Harrison (1975) note a matrix U employed in Multiple Exponential Smoothing whose inverse has not been obtained explicitly. The inverse of a related matrix p is obtained here and the relationship between the two matrices U and p reveals why no inverse has been obtained in...

General exponential smoothing and adaptive smoothing are terms used to describe the application of discounted least squares to the fitting of certain mathematical functions to time series data. The technique yields forecasts satisfying simple recursive equations that generally contain fairly complex terms. We obtain the transfer function of such fo...

The project described was initiated to obtain information concerning medium to large boilers with modulating burners and to develop a method by which the optimum number, sizes and control policy of boilers for heating large buildings could be determined. This involved a research procedure which was based on the measurable facts of boiler efficiency...