# The Effect of Data Transformation on Singular Spectrum Analysis for Forecasting
## 6 Concluding Remarks  
This paper focused on evaluating the impact of data transformations on the forecasting performance of SSA, a nonparametric filtering and forecasting technique. Following a concise introduction, the paper introduces the SSA forecasting approaches followed by the transformation techniques considered here. Regardless of its popularity (and in contrast to other methods such as ARIMA and neural networks), there has been no empirical attempt to quantify the impact of data transformations on the forecasting capabilities of SSA. Accordingly, we consider the impact of standardisation and logarithmic transformations on the forecasting performance of both vector and recurrent forecasting in SSA. In order to ensure robustness within the analysis, we not only compare the forecasts using the RMSFE but also rely on a nonparametric repeated measure factorial test. The forecast evaluation is based on 100 time series with varying characteristics in terms of frequencies, skewness, normality, and stationarity. Following the application of SSA to three versions of the same dataset, i.e. the original data, standardised data, and log transformed data, we generate out-of-sample forecasts at horizons of 1, 3, 6, and 12 steps ahead. Our findings indicate that, in general, data transformations do not affect SSA forecasts. However, the interaction between sampling frequency and transformations are found to be significant, indicating that data transformations are significant at certain sampling frequencies. According to the results of this study, in time series with a higher sampling frequency (i.e. daily or hourly data), standardisation can improve SSA forecasting accuracy in the very long term at daily frequencies only. On the other hand, in time series with low sampling frequencies (i.e. quarterly and annual), neither logarithmic transformation nor standardisation is suitable across all horizons. In other time series' sampling frequencies (weekly and monthly), data transformation with standardisation can affect all forecasting horizons (except \(h=12\)) when faced with monthly data and at \(h=1\) step ahead when faced with weekly data. The results also show improvement in forecasting accuracy in weekly data with logarithmic transformations at \(h=6\) and \(h=12\) steps ahead. These findings provide additional guidance to forecasters, researchers, and practitioners alike in terms of improving the accuracy of forecasts when modelling data with SSA. Future research should consider the relative gains of suggested data transformations at different sampling frequencies in relation to other benchmark forecasting models as well as theories explaining the mechanism of these effects in detail. Moreover, the development of automated SSA forecasting algorithms could be informed by the findings of this paper to ensure that data transformations are conducted prior to forecasting at selected sample frequencies. **Author Contributions:** Conceptualisation, H.H. ; methodology, H.H. and M.R.Y. ; software, A.K. and M.R.Y. ; validation, A.K. and M.R.Y. ; formal analysis, M.R.Y. and E.S.S. ; investigation, H.H. ; data curation, E.S.S. ; writing--original draft preparation, all authors contributed equally; writing--review and editing, all authors contributed equally; visualisation, M.R.Y. and A.K. ; supervision, H.H. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Conflicts of Interest:** The authors declare that there is no conflict of interest.