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An empirical study of break point detection for seasonal change in an external migration series

Authors

Guan Yu Zheng, Richard Penny, Marco Reale, Easaw Chacko

Abstract

Statistics New Zealand is interested in detection of structural breaks in its time series as these may indicate major changes in the data generating process which could affect the consistency of its outputs over time. As part of its time series outputs Statistics New Zealand produces the original time series but also often produces a seasonally adjusted series and trend estimate from the original series. To produce these outputs Statistics New Zealand uses the U.S. Bureau of the Census product X-12-ARIMA (X-12) to decompose the original series into a set of unobserved components; trend-cycle, seasonal, and irregular. Each individual component also provides useful information for the interpretation in the behaviour of the series so it is important that each component is estimated correctly.

There is a large literature on the identification of breaks in trends or levels. However a component of major interest to Statistics New Zealand is the seasonal pattern, so Statistics New Zealand needs to ensure that structural breaks in the seasonal component are identified properly and efficiently. For example, the school term changed to a four term year from three term year in 1996, thus altering the dates of school holidays. This could be reflected as an abrupt change in the seasonal pattern of the travel behaviour of New Zealand residents holidaying overseas. At present, Statistics New Zealand identifies these breaks by visual inspection of the individual monthly or quarterly SI charts.

We have investigated the use of two methods to identify the structural breaks, that of Bai and Perron (BP), and Atheoretical Regression Trees (ART). BP produces optimal solutions but at the cost of lengthy computation for long series and is also conservative in its identification of a break. ART uses regression trees which involves a nonparametric method for fitting piece-wise constant functions to a time series. ART, in contrast to BP, tends to overidentify the number of possible breaks. For Statistics New Zealand this is less of an issue, as not identifying a break is more an issue than identifying spurious breaks.

In our work we applied BP and ART to the SI series for each month produced by X-12 from the NZ short-term departures series. The SI series consists of a combination of the seasonal and irregular components for that particular month. We have found that BP and ART produce broadly similar results. Both methods identified a break in the August SI series in 1996 that could reflect the change of school holidays. They also showed range of possible breaks in the other months. We have found that the minimum allowed length of the segment between breaks is crucial to where breaks are identified. Statistics New Zealand would prefer to find a break in the seasonal pattern within 3 years of its occurrence, so we compared the results specifying minimum segment lengths of 3 and 10 and find that the results are similar.

pdf icon. An Empirical Study of Break Point Detection for Seasonal Change in an External Migration Series (PDF, 257KB)

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