Peter Thomson & Tohru Ozaki (1998): Transformation & Seasonal Adjustment
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 trend and seasonal biases, particularly where there is significant variation about the trend due to either or both of the seasonal or irregular components. Bias correction methods are given and results are illustrated by simulation and with reference to New Zealand official time series.
Keywords: seasonal adjustment; trend estimation; transformation; bias correction.
Format: pdf 4 -- File length: 250 kb --
Tohru Ozaki & Peter Thomson (2000): A nonlinear dynamic model for multiplicative seasonal-trend decomposition
A nonlinear dynamic model is introduced for multiplicative seasonal time series that follows and extends the X-11 paradigm where the observed time series is a product of trend, seasonal and irregular factors. A selection of standard seasonal and trend component models used in additive dynamic time series models are adapted for the multiplicative framework and a nonlinear filtering procedure is proposed. The results are illustrated and compared to X-11 and log-additive models using real data. In particular it is shown that the new procedures do not suffer from the trend bias present in log-additive models.
Keywords: nonlinear dynamic models; X-11; seasonal time series; seasonal adjustment.
Format: pdf 4 -- File length: 258 kb --
Alistair Gray & Peter Thomson (2000): On a family of finite moving-average trend filters for the ends of series
A family of finite end filters is constructed using a minimum revisions criterion and based on a local dynamic model operating within the span of a given finite central filter. These end filters are equivalent to evaluating the central filter with unavailable future observations replaced by constrained optimal linear predictions. Two prediction methods are considered; best linear unbiased prediction and best linear biased prediction where the bias is time invariant. The properties of these end filters are determined. In particular, they are compared to X-11 end filters and to the case where the central filter is evaluated with unavailable future observations predicted by global ARIMA models as in X-11-ARIMA or X-12-ARIMA.
Keywords: local dynamic model; minimum revisions; best linear unbiased prediction; best linear biased prediction.
Format: pdf 4 -- File length: 306 kb --
Robert Davies (2002): Hypothesis testing when a parameter is present only under the alternative - linear model case
The results of Davies (1977, 1987) are extended to a linear model situation with unknown residual variance.
Keywords: change point; F-process; frequency component; hypothesis test; nuisance parameter; t-process; two-phase regression; up-crossing.
Format: pdf 4 -- File length: 166 kb --
Robert Davies (2001): Integrated processes and the discrete cosine transform
A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalised by a discrete cosine transform (DCT-II). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.
Keywords: beta-optimal test; Brownian motion; DCT-II; discrete cosine transform; integrated process; random walk; spectrum; time-series; unit root.
Format: pdf 4 -- File length: 298 kb --
David Harte (2002): Non Asymptotic Binomial Confidence Intervals
Non asymptotic confidence intervals for a binomial proportion p can be calculated by the use of the F distribution, which is related to the binomial distribution via the incomplete beta function. These confidence intervals were tabulated and/or plotted by Pearson & Hartley (1962, Pages 33 and 77) and Neave (1978). Such confidence intervals can be easily calculated using modern statistical software. In this technical note, we derive the formulae for these confidence intervals.
Keywords: binomial distribution; confidence interval; F distribution
Format: pdf 4 -- File length: 126 kb --
Peter Cenek & Robert Davies (2004): Crash risk relationships for improved safety management of roads
This paper presents the results of a first attempt to combine detailed information on road geometry (horizontal curvature, gradient and cross-fall), road surface condition (roughness, rut depth, texture depth and skid resistance), carriageway characteristics (region, urban/rural environment, and traffic flow) and crashes. Such a study was only made possible because of annual surveys of the entire 22,000 lane-km of New Zealandís State Highway network made with SCRIM+ since 1997, which involves simultaneous measurement of road condition and road geometry. Four subsets of road crashes were investigated: all reported injury and fatal crashes; selected injury and fatal crashes covering loss of control events; reported injury and fatal crashes occurring in wet conditions; and selected injury and fatal crashes occurring in wet conditions. One and two-way tables and Poisson regression modelling were employed to identify critical variables and the form of their relationship with crash risk. The critical variables common to all crash types investigated were horizontal curvature, traffic flow, skid resistance and to a lesser extent lane roughness. The resulting Poisson regression model uses 2nd or 3rd order polynomial functions of these variables to allow for the observed non-linear responses. Therefore, the model can be incorporated in existing road asset management systems. A comparison of observed and predicted crash numbers for different segments of the State Highway network showed that the model can provide estimates of crash numbers that are sufficiently accurate for safety management purposes. For example, the predicted effect of increasing the level of skid resistance was in line with the results from a paired crash site analysis, which considered changes in the number of crashes and road surface skid resistance at two different points in time at specific crash sites.
Keywords: crash rates, crash risk modelling, road surface condition, road geometry, roughness, texture, skid resistance
Format: pdf 4 -- File length: 123kb --