Imputing monthly values for quarterly time series. An application performed with Swiss business cycle data

Abstract

This paper compares algorithms to deal with the problem of missing values in higher frequency data. We refer to Swiss business tendency survey data at monthly and quarterly frequency. There is a wide range of imputation algorithms. To evaluate the different approaches, we apply them to series that are de facto monthly, from which we create quarterly data by deleting two out of three data points from each quarter. At the same time, the monthly series are ideal to deliver higher frequency information for multivariate imputation algorithms. With this set of indicators, we conduct imputations of monthly values, resorting to two univariate and four multivariate algorithms. We then run tests of forecasting accuracy by comparing the imputed monthly data with the actual values. Finally, we take a look at the congruence of an imputed monthly series from the quarterly survey question on firms’ capacity utilisation with other monthly data reflecting the Swiss business cycle. The results show that an algorithm based on the Chow and Lin approach, amended with a variable pre-selection procedure, delivers the most precise imputations, closely followed by the standard Chow-Lin algorithm and then multiple regression. The cubic spline and the EM algorithm do not prove useful.