Traditional Time Series Analysis Methods Research Articles

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After the declaration of the ‘Endemic,’ it is crucial to understand the cyclical fluctuations and turning points in the overall economic status of the nation. To promptly and accurately grasp the magnitude and speed of these economic changes, a short-term forecasting analysis was conducted using the composite index of business indicators data from January 2003 to April 2023. In this study, a two-step analysis was performed to propose a standardized forecasting process.
 Firstly, for short-term forecasting of the composite index of business indicators, the results of time series analyses considering only endogenous variables were compared with those incorporating exogenous variables. Subsequently, the study explored machine learning methods, which have been actively discussed recently, and compared and analyzed their prediction performance with traditional time series analysis methods. The analysis revealed that the addition of exogenous variables in time series analysis resulted in higher prediction accuracy compared to analyses considering only endogenous variables. Furthermore, machine learning models exhibited superior prediction performance compared to traditional time series models. As a result of the analysis with the Time-GAN model, which has the best predictive performance, it was found that there would be a rise for 1-2 months due to the growth of private consumption caused by the endemic, but it would decrease again in the 3rd month.

Stochastic Volatility Modeling of Daily Streamflow Time Series

AbstractUnder the changing climate, the natural characteristics of hydrological processes are assumed to have been intensified, and the volatility of these processes to have increased significantly. However, the applicability of traditional time series analysis methods and the commonly used Gaussian GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) to streamflow modeling has been limited. Although SV‐type (stochastic volatility) models have appeared as competitive alternatives to GARCH‐type models owing to their flexibility in modeling volatilities, they have not been applied in hydrological studies. Therefore, this study assesses the applicability of SV models to streamflow modeling using daily streamflow series from 21 hydrological stations in the Yellow River basin. Considering the influence of different types of GARCH and residual distributions, 7 hybrid models with variance fluctuation (fractional autoregressive integrated moving average‐GARCH) based on 9 distributions are compared to determine the optimal model for each station. Then 4 SV‐type models are introduced and compared with the results of the optimal GARCH‐type model to verify their applicability. The results show that: (a) the Gaussian distribution is not applicable in both GARCH‐type and SV‐type models for modeling daily streamflow; (b) although the GARCH‐type models are shown to describe the volatility of streamflow processes and improve the modeling performance, large residuals have been observed in the results of the analysis during the peak flow period; and (c) SV‐type models can better describe the streamflow series with time‐varying variance and accurately capture the occurrence of peak streamflow. The findings of this study offer practical and promising time series analysis methods for daily streamflow modeling.

Iteration empirical mode decomposition method for filling the missing data of GNSS position time series

The Global Navigation Satellite System (GNSS) can provide the daily position time series for the geodesy and geophysical studies. However, due to various unpredictable factors, such as receiver failure or bad observation conditions, missing data inevitably exist in GNSS position time series. Most traditional time series analysis methods require the time series should be completed. Therefore, filling the missing data is a valuable step before analyzing the GNSS time series. In this study, a new method named Iteration Empirical Mode Decomposition (Iteration EMD) is proposed to fill the missing data in GNSS position time series. The simulation experiments are performed by randomly removing different missing percentages of the synthetic time series, with the added different types noise. The results show that Iteration EMD approach performs well regardless of high or low missing percentage. When the missing percentage increases from 5 % to 30 % with a step of 5 %, all the Root Mean Square Errors (RMSE) and Mean Absolute Errors (MAE) of Iteration EMD are smaller than Interpolation EMD. The relative improvements at different percentages of Iteration EMD relative to Interpolation EMD are significant, especially for the high missing percentage. The real GNSS position time series of eight stations were selected to further evaluate the performance of Iteration EMD with an average missing percentage 8.15 %. Principal Component Analysis (PCA) was performed on the filled time series, which is used to assess the interpolation performance of Iteration EMD and Interpolation EMD. The results show that Iteration EMD can preserve variance 75.9 % with the first three Principal Components (PC), more than 66.5% of interpolation EMD. Therefore, we can conclude that Iteration EMD is an efficient interpolation method for GNSS position time series, which can make full use of available information in existing time series to fill the missing data.

Single-variable method for predicting trends in chlorophyll a concentration based on the similarity of time series

Algal blooms are increasing in global water bodies, which threatens social development. Predicting the chlorophyll a (Chla) concentration is useful for water environmental management. Most previous studies of Chla prediction required multiple variables and considerable computation. Therefore, a similarity-based prediction algorithm (SPA) was developed for this prediction. The mean relative error (MRE) and dynamic time warping (DTW) algorithms are similarity measures used to create SPAs (SPA-MRE, SPA-DTW and SPA-MRE&DTW).Model validation was performed at the Yuqiao Reservoir north of Tianjin, China. The Chla concentration dataset of the Yuqiao Reservoir contains hourly data for 745 days from 2017 to 2020. According to the model validation results, SPA methods performed better than traditional time-series analysis methods (ARIMA (−9.7%) and Holt-Winters (−21.2%)). The MRE predicted by the SPA method at 24 h was 0.187.These three SPA methods showed different characteristics and applicability. SPA-MRE was suitable for predicting low Chla concentrations. SPA-DTW was suitable for predicting high Chla concentrations with obvious fluctuations. SPA-MRE combined with DTW exhibited the best comprehensive performance. Moreover, the SPA maintained high robustness and reliability even in the absence of 9% of the data.SPA is a single-variable prediction method that is more cost-effective than traditional regression-based and mechanism-based methods. SPA can be used with adjacent data for forecasting as in traditional time-series analysis models, and time series similar to the current series can be retrieved from historical data and used for predictions based on similarity. This study provides a robust and reliable prediction method for algal bloom management. SPA can be used to deeply mine characteristic information from historical data.

Visibility-graphlet approach to the output series of a Hodgkin–Huxley neuron

The output signals of neurons that are exposed to external stimuli are of great importance for brain functionality. Traditional time-series analysis methods have provided encouraging results; however, the associated patterns and their correlations in the output signals of neurons are masked by statistical procedures. Here, graphlets are employed to extract the local temporal patterns and the transitions between them from the output signals when neurons are exposed to external stimuli with selected stimulating periods. A transition network is defined where the node is the graphlet and the direct link is the transition between two successive graphlets. The transition-network structure is affected by the simulating periods. When the stimulating period moves close to an integer multiple of the neuronal intrinsic period, only the backbone or core survives, while the other linkages disappear. Interestingly, the size of the backbone (number of nodes) equals the multiple. The transition-network structure is conservative within each stimulating region, which is defined as the range between two successive integer multiples. Nevertheless, the backbone or detailed structure is significantly altered between different stimulating regions. This alternation is induced primarily from a total of 12 active linkages. Hence, the transition network shows the structure of cross correlations in the output time-series for a single neuron.

Market concentration and market power of the Swedish mortgage Sector – a wavelet panel efficiency analysis

Abstract Based on a panel wavelet efficiency analysis, we conclude that there is a systematic pattern of positive asymmetric price transmission inefficiencies in the interest rates of the largest Swedish mortgage lenders. Thus, there seems to be a higher propensity for mortgage lenders to swiftly increase their customers’ mortgage interest rates subsequent to an increase in its borrowing costs, than to decrease their customers’ mortgage rates subsequent to a corresponding decrease in the cost of borrowing. A unique contribution is our proposed wavelet method which enables a robust detection of positive asymmetric price transmission effects at various time-frequency scales, while simultaneously controlling for non-stationary trends, autocorrelation, and structural breaks. Since traditional time-series analysis methods essentially implies that several wavelet time scales are aggregated into one single time series, the blunt traditional error correction analysis totally failed to discover APT effects for this data set. In summary, using the wavelet method we show that even though the customers in the end finally will benefit from decreases in the mortgage lenders’ financing costs, the lenders wait disproportionally long before the customers’ mortgage rates are decreased.

An Efficient Time Series Subsequence Pattern Mining and Prediction Framework with an Application to Respiratory Motion Prediction

Traditional time series analysis methods are limited on some complex real-world time series data. Respiratory motion prediction is one of such challenging problems. The memory-based nearest neighbor approaches haveshown potentials in predicting complex nonlinear time series compared to many traditional parametric prediction models. However, the massive time series subsequences representation, the similarity distance measures, the number of nearest neighbors, and the ensemble functions create challenges as well as limit the performance of nearest neighbor approaches in complex time series prediction. To address these problems, we propose a flexible time series pattern representation and selection framework, called the orthogonalpolynomial-based variant-nearest-neighbor (OPVNN) approach. For the respiratory motion prediction problem, the proposed approach achieved the highest and most robust prediction performance compared to the state-of-the-art time series prediction methods. With a solid mathematical and theoretical foundation in orthogonal polynomials, the proposed time series representation, subsequence pattern mining and prediction framework has a great potential to benefit those industry and medical applications that need to handle highly nonlinear and complex time series data streams, such as quasi-periodic ones.

Research on the relationship between rainfall and reference crop evapotranspiration with multi-time scales

Limited by Fourier analysis and the selection of different wavelet base functions, the wavelet analysis method shows some deficiencies. For that reason, the empirical mode decomposition method is applied to analyze fluctuating periods and local features of annual rainfall and reference crop evapotranspiration (ET0) from 1959 to 2002. With respect to the correlation between variables, the traditional time series analysis methods often assume that data sequences are stationary which result in “spurious regression.” Therefore, the cointegration theory is introduced to describe the long-term equilibrium relationship of rainfall and ET0. At last, to understand the uncertainty between these two variables, the set pair analysis (SPA) method is used to present the identity, discrepancy, and contrary of rainfall and ET0 with multi-time scales. The results reveal that rainfall and ET0 have a complex relationship which may be related to El Nino, air–sea intersection, solar activity. Moreover, the fluctuation periods of rainfall and ET0 also have similar short and middle period level, and slightly different long period level. The changes of rainfall and ET0 present mainly the contrary and the discrepancy. This relationship will remain a long-term equilibrium.

Multivariate time series clustering on geophysical data recorded at Mt. Etna from 1996 to 2003

Time series clustering is an important task in data analysis issues in order to extract implicit, previously unknown, and potentially useful information from a large collection of data. Finding useful similar trends in multivariate time series represents a challenge in several areas including geophysics environment research. While traditional time series analysis methods deal only with univariate time series, multivariate time series analysis is a more suitable approach in the field of research where different kinds of data are available. Moreover, the conventional time series clustering techniques do not provide desired results for geophysical datasets due to the huge amount of data whose sampling rate is different according to the nature of signal. In this paper, a novel approach concerning geophysical multivariate time series clustering is proposed using dynamic time series segmentation and Self Organizing Maps techniques. This method allows finding coupling among trends of different geophysical data recorded from monitoring networks at Mt. Etna spanning from 1996 to 2003, when the transition from summit eruptions to flank eruptions occurred. This information can be used to carry out a more careful evaluation of the state of volcano and to define potential hazard assessment at Mt. Etna.

Charting the possible impact of national guidelines on the management of rheumatoid arthritis

Objective: To identify temporal trends in the prescription of disease‐modifying antirheumatic drugs (DMARDs) in patients with early rheumatoid arthritis (RA).Methods: Using data from the Swedish RA register (n = 2584), we analysed the proportion of RA patients prescribed DMARDs at their first consultation between 1997 and 2001. Statistical process control (SPC) was used to chart and analyse major changes in prescription behaviour, while more traditional time series analysis methods (i.e. regression) were used to corroborate the nature of any trend.Results: The SPC method identified an upward shift in the prescription of DMARDs in July 1998 and a change in the process by October 1998. Time series analysis confirmed an increasing trend in DMARD prescription over the period as a whole and the trend was statistically significant (p⩽0.0001). Further analysis showed that the trend was driven by a single shift in the data in July 1998 (p⩽0.0095), and once this shift was accounted for, no remaining trends within the periods (i.e. before and after the jump) could be detected (p = 0.5934 and 0.7497, respectively).Conclusion: The formulation and promulgation of Swedish guidelines in 1998 may have influenced the prescription of DMARDs for this patient group. Prospectively analysing data derived from clinical registers in real time using SPC shows promise as a means to evaluate interventions designed to have an impact on a national level.

A tool for analyzing information from data storage tags: the continuous wavelet transform (CWT)

Electronic Data Storage Tags (DSTs) have the potential of providing long term, high-resolution observation data of individual fish in the ecosystem. However, traditional time series analysis methods are limited in extracting the required information from DSTs. The continuous wavelet transform (CWT) is a tool for decomposing a time series into instantaneous frequency versus time characteristics. This allows data signals, which are restricted to specific frequencies (localized frequencies), or frequency components, which are restricted to specific time intervals (time localized) to be extracted and displayed in a highly intuitive way. The aim of this short communication is to present the CWT as a tool for extracting information from DST data. In the first case, synthetically generated data is used to demonstrate how the methodology captures different time–frequency dependent patterns in the time series data. The relevance of the methodology to real field data is demonstrated by an analysis of DST depth data from tagged Barents Sea coastal cod.