Imputing monthly values for quarterly time series : an application performed with Swiss business cycle data

This paper documents a comparative application of algorithms to deal with the problem of missing values in higher frequency data sets. We refer to Swiss business tendency survey (BTS) data, in particular the KOF manufacturing surveys, which are conducted in both monthly and quarterly frequency, where an information sub-set is collected at quarterly frequency only. This occurs in many countries, for example, the harmonised survey programme of the European Union also has this frequency pattern. There is a wide range of ways to address this problem, comprising univariate and multivariate approaches. To evaluate the suitability of the different approaches, we apply them to series that are artificially quarterly, i.e., de facto monthly, from which we create quarterly data by deleting two out of three data points from each quarter. The target series for imputation of missing (deleted) observations comprise the set of time series from the monthly KOF manufacturing BTS survey. At the same time, these series are ideal to deliver higher frequency information for multivariate imputation algorithms, as they share a common theme, the Swiss business cycle. With this set of indicators, we conduct the different imputations. On this basis, we then run standard tests of forecasting accuracy by comparing the imputed monthly series to the original monthly series. Finally, we take a look at the congruence of the imputed monthly series from the quarterly survey question on firms' technical capacities with existing monthly data on the Swiss economy. Due to the massive shock from the Covid-19 pandemic, we restrict the in-sample analyses to data from 1967m2 to 2019m12 and at the end take a look at how well our imputations would have fared in real-time during the pandemic in 2020 and 2021. The results show that for our data corpus, algorithms based on the approach suggested by Chow and Lin deliver the most precise imputations, followed by multiple OLS regressions. Of the multivariate methods that we consider, the EM algorithm's performance is disappointing, and amongst the univariate methods, simply carrying the last observation forward procedure proved superior to cubic spline imputations, and this in particular at the end of the time series.