Residents tended to rate the units in a more positive direction than staff on some sub-scales. Participants rated the 'low' secure unit in a more positive direction than the 'medium' secure unit on two sub-scales of the CIES. However, on selected sub-scales there were differences. The findings of this study suggest that the CIES may be a valid instrument for use within forensic services for people with ID, and further suggests that residents and staff have different perceptions of the shared social climate, which may have implications for service development.
We propose a model for non-normal times series in which we regard the series as an instantaneous transformation of an underlying 'generating' series which is normal. We describe a procedure which simultaneously estimates both the transformation to normality and the time series structure of the underlying series. This model has several advantages; in particular several alternative types of forecast can easily be calculated. The relative merits of these forecasts are considered.
We propose a model for time series with a general marginal distribution given by the Johnson family of distributions. We investigate for which Johnson distributions forecasting using the model is likely to be most effective compared to using a linear model. Monte Carlo simulation is used to assess the reliability of methods for determining which of the three Johnson forms is most appropriate for a given series. Finally, we give model fitting and forecasting results using the modelling procedure on a selection of simulated and real time series.KEY WORDS Johnson Non-normal ARMA models Slifker-Shapiro Consider an autocorrelated time series which, on inspection, does not appear to have a normal marginal distribution. Conventional techniques (see, for instance, Box and Jenkins, 1976) cope with correlated data but usually assume a normal marginal distribution. Typical occurences of such data are river flow, wind velocities, speech waves, or output from an industrial process.Janacek and Swift (1990) and Swift and Janacek (1991) postulate a model whereby the data are regarded as an instantaneous transformation of a time series with a standard normal marginal distribution. The model can be estimated via maximum likelihood and forecasts are readily calculable. Janacek and Swift (1991, p. 504) explain that in practice the model is appropriate when the data are stationary, autocorrelated, and do not exhibit strong directionality. The main difficulty in the model's use is that the practitioner must specify a particular family of marginal distributions (beta, gamma, etc.) in advance.In this paper we propose adopting the Johnson system of distributions (Johnson, 1949) as a general family of marginal distributions for the Janacekt-Swift model. This has two main advantages. First, it allows the first four moments of the marginal distribution to be represented. Second, a Johnson random variable can be generated by one of three transformations of a standard normal variate, so the transformation for the Janacek-Swift model is available in closed analytic form.The Janacek-Swift model has a greater forecasting advantage for models in which there are negative correlations and/or which are highly non-linear as measured by the Linearity Factor or LFl (Swift and Janacek, 1991). We investigate which Johnson distributions are most useful by looking at the relationship between the parameters and the LE We use Monte Carlo simulation to assess the reliability of methods for determining which of the three Johnson transformations
We look at the problem of forecasting time series which are not normally distributed. An overall approach is suggested which works both on simulated data and on real data sets. The idea is intuitively attractive and has the considerable advantage that it can readily be understood by nonspecialists. Our approach is based on ARMA methodology and our models are estimated via a likelihood procedure which takes into account the non-normality of the data. We examine in some detail the circumstances in which taking explicit account of the nonnormality improves the forecasting process in a significant way. Results from several simulated and real series are included.KEY WORDS ARMA models Marginal distributions Hermite polynomials Likelihood Non-normalSuppose we have a series of sequential data ( Y , ) which, on examination, is clearly autocorrelated and not normally distributed. Such data arise as, for example, the correlated inter-arrival times of queuing systems, river flow over short time periods, wind velocities or speech waves. It is obviously desirable to model the data so that forecasts can be made. If the data were normally distributed Gaussian ARMA models could be used, or if they were uncorrelated and non-normal then the parameters of a class of marginal distributions could be estimated using likelihood. No standard procedure is available which can cope with both non-normality and serial correlation. Of course, for long series one could fit a linear model using least squares and rely on asymptotic results. This, however, provides no information on the distribution of the errors (or, equivalently, the marginal distribution) so that prediction intervals of the forecasts cannot be calculated and the usefulness of such a procedure is questionable.Several explicit models have been developed to simulate data with special types of autocorrelation structure and marginal distribution. Lawrence and Lewis (1981, 1985, 1987) have considered linear models with non-normal noise inputs. The models allow the third and higher cross moments of the series to be represented while limiting the correlation structure, usually to an AR( 1) or AR(2) type. These can be regarded as model structures for appropriate data series. Very little work, however, has been done on model fitting. Lawrence and Lewis (1985) fit a model to a very long wind-velocity series, but use moment estimates and a rather ad hoc procedure to estimate the parameters. Smith (1986) considers the likelihood of one of the Lawrence and Lewis models NEAR(2), and describes difficulties in maximization which
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