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Elucidating Easter's economic effects

Authors

John Crequer and Barbara Clendon

Abstract

Statistics New Zealand not only provides users the measured time series, but also the series with identifiable seasonal and calendar effects removed. Although these effects are easily modelled, they are not easy to estimate because of the volatility of New Zealand's time series. To remove seasonal variation Statistics New Zealand uses X-12-ARIMA. Possible calendar effects are trading day and moving holidays (eg Easter). Regular calendar effects are easily modelled and are thus relatively straight-forward to estimate. However, estimating the effect of moving holidays is more difficult because the period over which they affect the series needs to be quantified, and there is only one measurement per year. Statistics New Zealand has been investigating using GenHol to estimate the effect of Easter on its time series.

Easter is of particular interest because it moves between both months and quarters. Were it not for this behaviour the effect could simply be subsumed into the usual seasonal factors. On the other hand, this movement allows us to estimate its effect. Historically it has been difficult to estimate the effect of Easter due to it shifting both
between and within March and April, affecting both monthly and quarterly statistics. This reduces the number of observations available on the same economic basis for estimating the effect. Nevertheless, the effect is much more discernable in a monthly series while in a quarterly series the effect is less easy to distinguish from the irregular or noise component. The new methodology available through using GenHol allows us to make better use of all observations to estimate the overall effect.

GenHol is a supplementary tool for X-12-ARIMA which creates variables linked to the time periods of interest. GenHol has potential application to any moving holiday that has an effect on a particular series. Examples of such moving holidays are Easter, Chinese New Year, and school holidays. In this paper we are concentrating on the Easter moving holiday. Each economic series is affected in different ways by Easter. GenHol allows us to specify three time periods of variable length in which an effect occurs. These are the before, during and after time intervals. For each interval the effect is estimated, which may also vary in direction and magnitude. The coefficients are estimated as a part of the usual seasonal adjustment process, in a similar fashion to trading day coefficients. Our interest in this tool has arisen partly because the built in Easter effect available with X-12-ARIMA is based on the U.S and Canada models which are not strictly applicable to the New Zealand situation.

The expected gain from a better specification of the holiday is a reduction in the magnitude of the irregular and hence better estimates of trend and seasonal components. We investigated series for retail trade, building consents and accommodation guest nights. Overall, the results indicated an improvement in the adjustment of the series for regular effects, allowing greater confidence in the interpretation of our published series. The current state of our analysis is presented.

pdf icon. Elucidating Easter's economic effects (PDF, 321KB)

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