Degree Name

Doctor of Philosophy


School of Mathematics and Applied Statistics


Many important economic and social time series are based on repeated sample surveys. A key element in the design of a repeated sample survey is the rotation pattern, which affects the sample overlap, and hence the correlation between estimates at different lags. Seasonally adjusted and trend estimates can be calculated to aid in the interpretation of the time series. Most national statistical agencies use the XI1 and X11ARIMA seasonal adjustment packages. The rotation pattern affects the variability of the time series of survey estimates and the trend and seasonally adjusted estimates produced from them. This thesis considers the choice of rotation pattern for trend estimation from a repeated survey.

The implications of different rotation patterns on the sampling variance of seasonally adjusted and trend estimates is considered. An important issue in analysing trend estimates is that estimates at the very end of a time series are revised. The impact of different rotation patterns on the mean square error of the revisions of trend estimates is assessed.

As well as altering the rotation pattern, the filters used to estimate trend can be changed. Theory is developed to allow optimal trend filters to be generated for series having a known correlation structure. This is used to investigate rotation patterns and optimal filter combinations. The use of a design means that the sample consists of a number of rotation groups. In some cases it will be possible to obtain separate estimates for each rotation group. Optimal trend estimates can then be found depending on whether the individual rotation group or overall estimates are available. The properties of trend estimates obtained directly from the separate rotation group estimates, those obtained from the simple average of the rotation group estimates and using best linear unbiased estimates are compared for different rotation patterns.