# The Effect of Data Transformation on Singular Spectrum Analysis for Forecasting
## 1 Introduction  
Amidst the emergence of Big Data and Data Mining techniques, forecasting continues to remain an important tool for planning and resource allocation in all industries. Accordingly, researchers, academics, and forecasters alike invest time and resources into methods for improving the accuracy of forecasts from both parametric and nonparametric forecasting models. One approach to improving the accuracy of forecasts is via data transformations prior to fitting time series models. For example, it is noted in [1] that data transformations can simplify the forecasting task, whilst evidence from other research indicates that, in economic analysis, taking logarithms can provide forecast improvements if it results in stabilising the variance of a series [2]. However, studies also indicate that data transformations will not always improve forecasts [3] and that they could complicate time series analysis models [4, 5]. In fact, a key challenge for forecasting under data transformation is to transform the data back to its original scale, a process which could result in a forecasting bias [6, 7]. Historically, most studies have focused on the impact of data transformations on parametric models such as Regression and Autoregressive Integrated Moving Average (ARIMA) models [8, 9]. More recently, authors have resorted to evaluating the impact of data transformations on several other forecasting models [10, 11], further highlighting the relevance and importance of the topic. Our interest is focused on the evaluation of the impact of data transformations on a time series analysis and forecasting technique called Singular Spectrum Analysis (SSA). In brief, the SSA technique is a popular denoising, forecasting, and missing value prediction technique with both univariate and multivariate capabilities [12, 13]. Recently, its diverse applications have focused on forecasting solutions for varied industries and fields, from tourism [14, 15] and economics [16, 17, 18] to fashion [19], climate [20, 21], and several other sectors [22, 23, 24]. Regardless of its wide and varied applications, researchers have yet to explore the effect of data transformations on the forecasting performance of this nonparametric forecasting technique. Previously, in [25], the authors evaluated the forecasting performance of the two basic SSA algorithms under different data structures. However, their work did not extend to evaluating the impact of data transformations to provide empirical evidence for future research. Accordingly, through this paper, we aim to contribute to the existing research gap by studying the effects of different data transformation options on the forecasting behaviour of SSA. Logarithmic transformation is the most commonly used transformation in time series analysis. It has been used to convert multiplicative time series structures to additive structures or to reduce the time series skewness volatility and increase stability [2, 26]. The autocorrelation structure in the time series may change under different transformations that may affect the model, and different transformations may result in different specifications for ARIMA models [6, 27]. Like ARIMA models, SSA too can be greatly influenced by transformations. For instance, if data transformation makes noise uncorrelated or reduces the complexity of the time series, it can improve SSA performance [21, 26]. As data standardisation and logarithmic transformations are the easiest in terms of interpretability and back-transformation to the original scale, we explore the effect of these data transformations on the forecasting performance of SSA. The remainder of this paper is organised as follows. In Section 2, we provide a detailed exposition of SSA and its recurrent and vector forecasting algorithms. In Section 3, we present data transformation techniques and their effect on forecasting accuracy. Procedures for examining the effect of transformation based on different characteristics of time series are presented in Section 4.