Carbon trading and COVID-19: a hybrid machine learning approach for international carbon price forecasting.

Accurate carbon price forecasting can better allocate carbon emissions and thus ensure a balance between economic development and potential climate impacts. In this paper, we propose a new two-stage framework based on processes of decomposition and re-estimation to forecast prices across international carbon markets. We focus on the Emissions Trading System (ETS) in the EU, as well as the five main pilot schemes in China, spanning the period from May 2014 to January 2022. In this way, the raw carbon prices are first separated into multiple sub-factors and then reconstructed into factors of 'trend' and 'period' with the use of Singular Spectrum Analysis (SSA). Once the subsequences have been thus decomposed, we further apply six machine learning and deep learning methods, allowing the data to be assembled and thus facilitating the prediction of the final carbon price values. We find that from amongst these machine learning models, the Support vector regression (SSA-SVR) and Least squares support vector regression (SSA-LSSVR) stand out in terms of performance for the prediction of carbon prices in both the European ETS and equivalent models in China. Another interesting finding to come out of our experiments is that the sophisticated algorithms are far from being the best performing models in the prediction of carbon prices. Even after accounting for the impacts of the COVID-19 pandemic and other macro-economic variables, as well as the prices of other energy sources, our framework still works effectively.

Singular Spectrum Analysis of Tremorograms for Human Neuromotor Reaction Estimation

Singular spectrum analysis (SSA) is a method of time series analysis and is used in various fields, including medicine. A tremorogram is a biological signal that allows evaluation of a person’s neuromotor reactions in order to infer the state of the motor parts of the central nervous system (CNS). A tremorogram has a complex structure, and its analysis requires the use of advanced methods of signal processing and intelligent analysis. The paper’s novelty lies in the application of the SSA method to extract diagnostically significant features from tremorograms with subsequent evaluation of the state of the motor parts of the CNS. The article presents the application of a method of singular spectrum decomposition, comparison of known variants of classification, and grouping of principal components for determining the components of the tremorogram corresponding to the trend, periodic components, and noise. After analyzing the results of the SSA of tremorograms, we proposed a new algorithm of grouping based on the analysis of singular values of the trajectory matrix. An example of applying the SSA method to the analysis of tremorograms is shown. Comparison of known clustering methods and the proposed algorithm showed that there is a reasonable correspondence between the proposed algorithm and the traditional methods of classification and pairing in the set of periodic components.

Analysing Trends and Forecasting of COVID-19 Pandemic in Malaysia using Singular Spectrum Analysis

The Singular Spectrum Analysis (SSA) is a powerful non-parametric time series analysis that has demonstrated its capability in forecasting different time series in various disciplines. SSA falls in the framework of data-driven modelling of dynamical system which does not rely on any underlying assumption except the inherent dynamics which are captured over time. The capabilities of SSA are mainly aff orded by its direct connection to the singular value decomposition (SVD). It is generally accepted that SVDbased methods are very affective for the noise reduction in deterministic time series and consequently for forecasting, as well as for extracting trends and structures. Despite its strength, several shortcomings of SSA in the analysis of COVID-19 time series have been reported in the literature. The aim of this paper is to determine the scope of this limitation and we confine our investigation in the analysis and forecasting of COVID-19 Pandemic in Malaysia. We scrutinize the results fromthe SSA analysis of the number of daily confirmed cases to gain further insight into the intrinsic trends of the pandemic. Groupings of the singular spectra that contributes to different features of the pandemic time series are identified using analysis of the singular value spectrum, periodogram analysis and analysis of the weighted correlation matrix. It was revealed that under stationary conditions, the principal eigentriple is sufficient to produce reliable forecast. However, in non-stationary conditions, for example during a movement control order, it is useful to also study the minor eigentriples which could contain transient dynamics that may persist.

Modelling COVID-19 Scenarios for the States and Federal Territories of Malaysia.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causes COVID-19 disease, which has become pandemic since December 2019. In the recent months, among five countries in the Southeast Asia, Malaysia has the highest per-capita daily new cases and daily new deaths. A mathematical modelling approach using a Singular Spectrum Analysis (SSA) technique was used to generate data-driven 30-days ahead forecasts for the number of daily cases in the states and federal territories in Malaysia at four consecutive time points between 27 July 2021 and 26 August 2021. Each forecast was produced using SSA prediction model of the current major trend at each time point. The objective is to understand the transition dynamics of COVID-19 in each state by analysing the direction of change of the major trends during the period of study. The states and federal territories in Malaysia were grouped in four categories based on the nature of the transition. Overall, it was found that the COVID-19 spread has progressed unevenly across states and federal territories. Major regions like Selangor, Kuala Lumpur, Putrajaya and Negeri Sembilan were in Group 3 (fast decrease in infectivity) and Labuan was in Group 4 (possible eradication of infectivity). Other states e.g. Pulau Pinang, Sabah, Sarawak, Kelantan and Johor were categorised in Group 1 (very high infectivity levels) with Perak, Kedah, Pahang, Terengganu and Melaka were classified in Group 2 (high infectivity levels). It is also cautioned that SSA provides a promising avenue for forecasting the transition dynamics of COVID-19; however, the reliability of this technique depends on the availability of good quality data.

Short-Term Forecasting of Daily Confirmed COVID-19 Cases in Malaysia Using RF-SSA Model.

Novel coronavirus (COVID-19) was discovered in Wuhan, China in December 2019, and has affected millions of lives worldwide. On 29th April 2020, Malaysia reported more than 5,000 COVID-19 cases; the second highest in the Southeast Asian region after Singapore. Recently, a forecasting model was developed to measure and predict COVID-19 cases in Malaysia on daily basis for the next 10 days using previously-confirmed cases. A Recurrent Forecasting-Singular Spectrum Analysis (RF-SSA) is proposed by establishing L and ET parameters via several tests. The advantage of using this forecasting model is it would discriminate noise in a time series trend and produce significant forecasting results. The RF-SSA model assessment was based on the official COVID-19 data released by the World Health Organization (WHO) to predict daily confirmed cases between 30th April and 31st May, 2020. These results revealed that parameter L = 5 (T/20) for the RF-SSA model was indeed suitable for short-time series outbreak data, while the appropriate number of eigentriples was integral as it influenced the forecasting results. Evidently, the RF-SSA had over-forecasted the cases by 0.36%. This signifies the competence of RF-SSA in predicting the impending number of COVID-19 cases. Nonetheless, an enhanced RF-SSA algorithm should be developed for higher effectivity of capturing any extreme data changes.

Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis.

BACKGROUND: Infectious disease is one of the main issues that threatens human health worldwide. The 2019 outbreak of the new coronavirus SARS-CoV-2, which causes the disease COVID-19, has become a serious global pandemic. Many attempts have been made to forecast the spread of the disease using various methods, including time series models. Among the attempts to model the pandemic, to the best of our knowledge, no studies have used the singular spectrum analysis (SSA) technique to forecast confirmed cases. OBJECTIVE: The primary objective of this paper is to construct a reliable, robust, and interpretable model for describing, decomposing, and forecasting the number of confirmed cases of COVID-19 and predicting the peak of the pandemic in Saudi Arabia. METHODS: A modified singular spectrum analysis (SSA) approach was applied for the analysis of the COVID-19 pandemic in Saudi Arabia. We proposed this approach and developed it in our previous studies regarding the separability and grouping steps in SSA, which play important roles in reconstruction and forecasting. The modified SSA approach mainly enables us to identify the number of interpretable components required for separability, signal extraction, and noise reduction. The approach was examined using different levels of simulated and real data with different structures and signal-to-noise ratios. In this study, we examined the capability of the approach to analyze COVID-19 data. We then used vector SSA to predict new data points and the peak of the pandemic in Saudi Arabia. RESULTS: In the first stage, the confirmed daily cases on the first 42 days (March 02 to April 12, 2020) were used and analyzed to identify the value of the number of required eigenvalues (r) for separability between noise and signal. After obtaining the value of r, which was 2, and extracting the signals, vector SSA was used to predict and determine the pandemic peak. In the second stage, we updated the data and included 81 daily case values. We used the same window length and number of eigenvalues for reconstruction and forecasting of the points 90 days ahead. The results of both forecasting scenarios indicated that the peak would occur around the end of May or June 2020 and that the crisis would end between the end of June and the middle of August 2020, with a total number of infected people of approximately 330,000. CONCLUSIONS: Our results confirm the impressive performance of modified SSA in analyzing COVID-19 data and selecting the value of r for identifying the signal subspace from a noisy time series and then making a reliable prediction of daily confirmed cases using the vector SSA method.

Forecasting COVID-19 pandemic using optimal singular spectrum analysis.

Coronavirus disease 2019 (COVID-19) is a pandemic that has affected all countries in the world. The aim of this study is to examine the potential advantages of Singular Spectrum Analysis (SSA) for forecasting the number of daily confirmed cases, deaths, and recoveries caused by COVID-19, which are the three main variables of interest. This paper contributes to the literature on forecasting COVID-19 pandemic in several ways. Firstly, an algorithm is proposed to calculate the optimal parameters of SSA including window length and the number of leading components. Secondly, the results of two forecasting approaches in the SSA, namely vector and recurrent forecasting, are compared to those from other commonly used time series forecasting techniques. These include Autoregressive Integrated Moving Average (ARIMA), Fractional ARIMA (ARFIMA), Exponential Smoothing, TBATS, and Neural Network Autoregression (NNAR). Thirdly, the best forecasting model is chosen based on the accuracy measure Root Mean Squared Error (RMSE), and it is applied to forecast 40 days ahead. These forecasts can help us to predict the future behaviour of this disease and make better decisions. The dataset of Center for Systems Science and Engineering (CSSE) at Johns Hopkins University is adopted to forecast the number of daily confirmed cases, deaths, and recoveries for top ten affected countries until October 29, 2020. The findings of this investigation show that no single model can provide the best model for any of the countries and forecasting horizons considered here. However, the SSA technique is found to be viable option for forecasting the number of daily confirmed cases, deaths, and recoveries caused by COVID-19 based on the number of times that it outperforms the competing models.