The problem of aggregation in macroeconomic variables: Theory and practice

Most of the time series are formed by various aggregation methods. The most common aggregation form is temporal aggregation. Low frequency series are obtained from high frequency series in the temporal aggregation. Hence, after the temporal aggregation, the observed frequency does not overlap with the assumed time unit. This leads to difference between individual characteristics of the aggregated series, model selection, and forecasting outcomes; and the results obtained from the original frequency series. Therefore, for time series analysis it is important to see the effects of temporal aggregation on econometric analysis. In the current study, systematic sampling and average sampling aggregations which are different approaches of temporal aggregation is used and the impact of these approaches on different econometric analysis, such as normal distribution, autocorrelation, unit root, structural break unit root, seasonal unit root, deterministic seasonality, cointegration and causality. In order to meet this purpose, M1, price, reserve and exchange rate series are used for the periods of 1990-2015. Both quarterly and yearly frequencies are obtained by using both types of aggregations with regard to the logarithmic transformed and untransformed monthly frequency series. Whether or not to take the logarithms of the series and the form of the aggregation did not lead to a significant difference on individual statistical properties of the series. However, the results of the normal distribution of the series changed after the temporal aggregation. Logarithmic conversion or not did not make much difference in terms of unit root tests at the levels of the series but led to some different findings in the first differences. Additionally, the results of the unit root test are affected by the aggregation forms. The results obtained from the aggregated series differ according to the original frequency in terms of seasonal unit root, deterministic seasonality, cointegration and causality analysis.