This paper considers the effects of seasonal adjustment on transformed time series which are then transformed back to provide seasonally adjusted series in the original scale of the observations. It is shown that this approach can lead to ambiguities in terms of the definition of trend, particularly where there is significant variation about the trend, due to either or both of the seasonal and irregular components. General adjustment and bias correction methods are given. Results are illustrated by simulation and with reference to NZ official time series.

This work is joint with Professor Tohru Ozaki, Institute of Statistical Mathematics, Tokyo, Japan.

This work is joint with Professor Tohru Ozaki, Institute of Statistical Mathematics, Tokyo, Japan.

For any given central moving-average trend filter, a family of end filters is constructed using a minimum revisions criterion and a local dynamic model operating within the span of the central filter. These end filters are equivalent to evaluating the central filter with unknown observations replaced by constrained optimal linear predictors. Two prediction methods are considered; best linear unbiased prediction (BLUP) and best linear biased prediction where the bias is time invariant (BLIP). The BLIP end filters generalise those developed by Musgrave for the central X-11 Henderson filters and include the BLUP end filters as a special case.

The properties of these end filters are determined both in theory and practice. In particular, they are compared to the Musgrave end filters used by X-11 and to the case where the central filter is evaluated with unknown observations predicted by global ARIMA models. The latter parallels the forecast extension method used in X-11-ARIMA.

This work is joint with Mr Alistair Gray, Statistics New Zealand.

A selection of the more commonly used models are reviewed and their time series properties explored. Particular issues addressed include stationarity and the specification of the volatility or diffusion function. Parametric and non-parametric estimation methods are also applied to both simulated data and New Zealand interest rate data. The results of this analysis are used to highlight areas for further research.

This work is joint with Mr Darren Upton (Mathematical and Computing Sciences) and Dr Martin Lally (Economics and Finance) both from the Victoria University of Wellington.

The stochastic properties of the CEV model are reviewed together with various methods of estimation. In particular, a semi-parametric maximum likelihood estimation method is proposed and its properties explored through simulation. This method is then used to fit CEV models to a selection of Australian stock price series. The results of this exploratory analysis are reported together with other work in progress.

This work is joint with Mr John Randal (Statistics and Operations Research) and Dr Martin Lally (Economics and Finance) both from the Victoria University of Wellington.

A hidden semi-Markov model for breakpoint rainfall data is proposed which builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the breakpoint data the transformed observations are modelled as mixtures of normals within unobserved states where the states evolve over time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions.

Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture distribution over disjoint ranges providing a flexible choice. The methods are also extended to deal with censored data. An application of the model to large-scale bivariate data sets of breakpoint rainfall measurements at selected New Zealand locations is discussed.

This work is joint with Dr John Sansom, National Institute of Water and Atmospheric Research, New Zealand.

Spectral estimation procedures are developed for the case of independent jitter and autocovariance estimation procedures for both independent and dependent jitter. These are typically modifications of general estimation procedures proposed elsewhere, but tailored to the particular jittered sampling scheme considered. However the results available for dependent jitter are mixed. These issues will be discussed as well as possible multivariate extensions of this work to oceanographic array data.

The findings of this exploratory research are reported and promising new forecasting methods identified. However further research and development remains to be done to refine these methods to the point where they can be used operationally in practice.

This work is joint with Mr Simon Jurke (Core Management Systems Ltd, New Zealand) and Dr Jonathan Lermit (Transpower New Zealand Ltd).

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