# The Effect of Data Transformation on Singular Spectrum Analysis for Forecasting
## 5 Data Analysis  
We used the same set of time series employed by [PERSON] et al. [25] to test the effect of data transformation on SSA forecasting accuracy, with different characteristics. The dataset contains 100 real time series with different sampling frequencies and stationarity, normality, and skewness characteristics, representing various fields and categories, obtained via the Data Market ([[http://datamarket.com](http://datamarket.com)]([http://datamarket.com](http://datamarket.com))). Table 1 presents the number of time series with each feature. It is evident that the real data includes data recorded at varying frequencies (annual, monthly, weekly, daily, and hourly) alongside varying distributions (normal distribution, skewed, stationary, and non-stationary). Interestingly, the majority of the data are non-stationary overtime, which resonates with expectations within real-life scenarios. The name and description of each time series and their codes assigned to improve presentation are presented in Table 11. Table 12 presents descriptive statistics for all time series to enable the reader to obtain a rich understanding of the nature of the real data. This also includes skewness statistics, and results from the normality (Shapiro-Wilk) and stationarity (Augmented Dickey-Fuller) tests. As visible in Table 11, the data comes from different fields such as energy, finance, health, tourism, housing market, crime, agriculture, economics, chemistry, ecology, and production. Figure 1 shows the time series for a selection of 9/100 series used in this study. This enables the reader to obtain a further understanding of the different structures underlying the data considered in the analysis. For example, A007 is representative of an asymmetric non-stationary time series for the labour market in a U.S. county. This monthly series shows seasonality with an increasing non-linear trend. In contrast, A022 is related to a meteorological variable that is asymmetric, yet stationary and highly seasonal in nature. An example of a time series that is both asymmetric and non-stationary is A038, which represents the production of silver. Here, structural breaks are visible throughout. A055 is an annual time series, which is stationary and asymmetric, and relates to the production of coloured fox fur. An example of a quarterly time series representing the energy sector is shown via A061. This time series is non-stationary and asymmetric with a non-linear trend and an increasing seasonality over time. Another example focuses on the airline industry (A075) and is also asymmetric and non-stationary in nature. It appears to showcase a linear and increasing trend along with seasonality. A skewed and non-stationary sales series is shown via A081, with the trend indicating increasing seasonality with \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Factor** & \multicolumn{5}{c}{**Levels**} \\ \hline Sampling Frequency & Annual & Monthly & Quarterly & Weekly & Daily & Hourly \\  & 5 & 83 & 4 & 4 & 2 & 2 \\ \hline Skewness & \multicolumn{2}{c}{Positive Skew} & Negative Skew & \multicolumn{2}{c}{Symmetric} \\  & 61 & & 21 & 18 \\ \hline Normality & \multicolumn{2}{c}{Normal} & \multicolumn{2}{c}{Non-normal} \\  & 18 & & 82 & \\ \hline Stationarity & \multicolumn{2}{c}{Stationary} & \multicolumn{2}{c}{Non-Stationary} \\  & 14 & & 86 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Number of time series with each feature. major drops in the time series between each season. A time series for house sales (A082) can be found to be normally distributed and non-stationary over time. It also shows a slightly curved non-linear trend and a sine wave that is disrupted by noise. Finally, the labour market is drawn on again via A094, but this is an example of a time series affected by several structural breaks leading to a non-stationary, asymmetric series, which also has seasonal periods and a clear non-linear trend.