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Journal articles on the topic 'Multivariate time series forecasting'

Author: Grafiati

Published: 10 May 2022

Last updated: 12 June 2025

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1

Athanasopoulos, George, and Farshid Vahid. "Forecasting multivariate time series." International Journal of Forecasting 31, no. 3 (2015): 680–81. http://dx.doi.org/10.1016/j.ijforecast.2015.03.003.

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2

Wang, Miss Lei. "Advanced Multivariate Time Series Forecasting Models." Journal of Mathematics and Statistics 14, no. 1 (2018): 253–60. http://dx.doi.org/10.3844/jmssp.2018.253.260.

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3

Şişman-Yılmaz, N. Arzu, Ferda N. Alpaslan, and Lakhmi Jain. "ANFISunfoldedintime for multivariate time series forecasting." Neurocomputing 61 (October 2004): 139–68. http://dx.doi.org/10.1016/j.neucom.2004.03.009.

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4

Duan, Ziheng, Haoyan Xu, Yida Huang, Jie Feng, and Yueyang Wang. "Multivariate Time Series Forecasting with Transfer Entropy Graph." Tsinghua Science and Technology 28, no. 1 (2023): 141–49. http://dx.doi.org/10.26599/tst.2021.9010081.

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Shapovalova, Yuliya, Nalan Baştürk, and Michael Eichler. "Multivariate Count Data Models for Time Series Forecasting." Entropy 23, no. 6 (2021): 718. http://dx.doi.org/10.3390/e23060718.

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Count data appears in many research fields and exhibits certain features that make modeling difficult. Most popular approaches to modeling count data can be classified into observation and parameter-driven models. In this paper, we review two models from these classes: the log-linear multivariate conditional intensity model (also referred to as an integer-valued generalized autoregressive conditional heteroskedastic model) and the non-linear state-space model for count data. We compare these models in terms of forecasting performance on simulated data and two real datasets. In simulations, we consider the case of model misspecification. We find that both models have advantages in different situations, and we discuss the pros and cons of inference for both models in detail.

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Yin, Yi, and Pengjian Shang. "Forecasting traffic time series with multivariate predicting method." Applied Mathematics and Computation 291 (December 2016): 266–78. http://dx.doi.org/10.1016/j.amc.2016.07.017.

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7

Thomakos, Dimitrios D., and Konstantinos Nikolopoulos. "Forecasting Multivariate Time Series with the Theta Method." Journal of Forecasting 34, no. 3 (2015): 220–29. http://dx.doi.org/10.1002/for.2334.

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Shih, Shun-Yao, Fan-Keng Sun, and Hung-yi Lee. "Temporal pattern attention for multivariate time series forecasting." Machine Learning 108, no. 8-9 (2019): 1421–41. http://dx.doi.org/10.1007/s10994-019-05815-0.

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9

Van Der Knoop, H. S. "Conditional forecasting with a multivariate time series model." Economics Letters 22, no. 2-3 (1986): 233–36. http://dx.doi.org/10.1016/0165-1765(86)90238-7.

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10

Ji, Xin, Haifeng Zhang, Jianfang Li, Xiaolong Zhao, Shouchao Li, and Rundong Chen. "Multivariate time series prediction of high dimensional data based on deep reinforcement learning." E3S Web of Conferences 256 (2021): 02038. http://dx.doi.org/10.1051/e3sconf/202125602038.

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In order to improve the prediction accuracy of high-dimensional data time series, a high-dimensional data multivariate time series prediction method based on deep reinforcement learning is proposed. The deep reinforcement learning method is used to solve the time delay of each variable and mine the data characteristics. According to the principle of maximum conditional entropy, the embedding dimension of the phase space is expanded, and a multivariate time series model of high-dimensional data is constructed. Thus, the conversion of reconstructed coordinates from low-dimensional to high-dimensional can be kept relatively stable. The strong independence and low redundancy of the final reconstructed phase space construct an effective model input vector for multivariate time series forecasting. Numerical experiments of classical multivariable chaotic time series show that the method proposed in this paper has better forecasting effect, which shows the forecasting effectiveness of this method.

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Ahmadi, Ahmadi, and R. Adisetiawan. "Multivariate Time Series in Macroeconomics." Eksis: Jurnal Ilmiah Ekonomi dan Bisnis 11, no. 2 (2020): 151. http://dx.doi.org/10.33087/eksis.v11i2.209.

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Gold is one of the most popular commodities and investment alternatives. Gold prices are thought to be influenced by several other factors such as the US Dollar, oil price, inflation rate, and stock exchange so that gold price modeling is not only influenced by its own value. This research was conducted to determine the best forecasting model and to find out what factors influence the price of gold. This research modeled the price of gold in a multivariate and reviewed the univariate modeling that will be used as a comparison model of multivariate modeling. Univariate modeling is done using ARIMA model where the modeling results state that gold price fluctuations as white noise. Multivariate gold price modeling is done using Vector Error Correction Model with gold, oil, US Dollar and Dow Jones indices, and inflation rate as predictors. The results showed that the VECM model has been able to model the gold price well and all the factors studied influenced the gold price. The US dollar and oil prices are negatively correlated with gold prices, while the inflation rate is positively correlated with gold prices. The Dow Jones index was positively correlated with gold prices in just two periods.

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12

Wan, Renzhuo, Chengde Tian, Wei Zhang, Wendi Deng, and Fan Yang. "A Multivariate Temporal Convolutional Attention Network for Time-Series Forecasting." Electronics 11, no. 10 (2022): 1516. http://dx.doi.org/10.3390/electronics11101516.

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Multivariate time-series forecasting is one of the crucial and persistent challenges in time-series forecasting tasks. As a kind of data with multivariate correlation and volatility, multivariate time series impose highly nonlinear time characteristics on the forecasting model. In this paper, a new multivariate time-series forecasting model, multivariate temporal convolutional attention network (MTCAN), based on a self-attentive mechanism is proposed. MTCAN is based on the Convolution Neural Network (CNN) model, using 1D dilated convolution as the basic unit to construct asymmetric blocks, and then, the feature extraction is performed by the self-attention mechanism to finally obtain the prediction results. The input and output lengths of this network can be determined flexibly. The validation of the method is carried out with three different multivariate time-series datasets. The reliability and accuracy of the prediction results are compared with Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Convolutional Long Short-Term Memory (ConvLSTM), and Temporal Convolutional Network (TCN). The prediction results show that the model proposed in this paper has significantly improved prediction accuracy and generalization.

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He, Zichao, Chunna Zhao, and Yaqun Huang. "Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network." Applied Sciences 12, no. 11 (2022): 5731. http://dx.doi.org/10.3390/app12115731.

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Multivariate time series forecasting has long been a subject of great concern. For example, there are many valuable applications in forecasting electricity consumption, solar power generation, traffic congestion, finance, and so on. Accurately forecasting periodic data such as electricity can greatly improve the reliability of forecasting tasks in engineering applications. Time series forecasting problems are often modeled using deep learning methods. However, the deep information of sequences and dependencies among multiple variables are not fully utilized in existing methods. Therefore, a multivariate time series deep spatiotemporal forecasting model with a graph neural network (MDST-GNN) is proposed to solve the existing shortcomings and improve the accuracy of periodic data prediction in this paper. This model integrates a graph neural network and deep spatiotemporal information. It comprises four modules: graph learning, temporal convolution, graph convolution, and down-sampling convolution. The graph learning module extracts dependencies between variables. The temporal convolution module abstracts the time information of each variable sequence. The graph convolution is used for the fusion of the graph structure and the information of the temporal convolution module. An attention mechanism is presented to filter information in the graph convolution module. The down-sampling convolution module extracts deep spatiotemporal information with different sparsities. To verify the effectiveness of the model, experiments are carried out on four datasets. Experimental results show that the proposed model outperforms the current state-of-the-art baseline methods. The effectiveness of the module for solving the problem of dependencies and deep information is verified by ablation experiments.

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14

Lee, Won Kyung. "Partial Correlation-Based Attention for Multivariate Time Series Forecasting." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 10 (2020): 13720–21. http://dx.doi.org/10.1609/aaai.v34i10.7132.

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A multivariate time-series forecasting has great potentials in various domains. However, it is challenging to find dependency structure among the time-series variables and appropriate time-lags for each variable, which change dynamically over time. In this study, I suggest partial correlation-based attention mechanism which overcomes the shortcomings of existing pair-wise comparisons-based attention mechanisms. Moreover, I propose data-driven series-wise multi-resolution convolutional layers to represent the input time-series data for domain agnostic learning.

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Sobanapuram Muruganandam, Narendran, and Umamakeswari Arumugam. "Dynamic Ensemble Multivariate Time Series Forecasting Model for PM2.5." Computer Systems Science and Engineering 44, no. 2 (2023): 979–89. http://dx.doi.org/10.32604/csse.2023.024943.

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Yazdanbakhsh, Omolbanin, and Scott Dick. "Forecasting of Multivariate Time Series via Complex Fuzzy Logic." IEEE Transactions on Systems, Man, and Cybernetics: Systems 47, no. 8 (2017): 2160–71. http://dx.doi.org/10.1109/tsmc.2016.2630668.

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Kun-Huang Huarng, Tiffany Hui-Kuang Yu, and Yu Wei Hsu. "A Multivariate Heuristic Model for Fuzzy Time-Series Forecasting." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 37, no. 4 (2007): 836–46. http://dx.doi.org/10.1109/tsmcb.2006.890303.

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18

Ng, C. N., P. C. Young, and C. Wang. "Recursive Identification. Estimation and Forecasting of Multivariate Time-series." IFAC Proceedings Volumes 21, no. 9 (1988): 593–96. http://dx.doi.org/10.1016/s1474-6670(17)54792-8.

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19

Calderon, Sergio, and Fabio H. Nieto. "Forecasting with Multivariate Threshold Autoregressive Models." Revista Colombiana de Estadística 44, no. 2 (2021): 369–83. http://dx.doi.org/10.15446/rce.v44n2.91356.

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   An important stage in the analysis of time series is the forecasting. How- ever, the forecasting in non-linear time series models is not straightforward as in linear time series models because an exact analytical of the conditional expectation is not easy to obtain. Therefore, a strategy of forecasting with multivariate threshold autoregressive(MTAR) models is proposed via predictive distributions through Bayesian approach. This strategy gives us the forecast for the response and exogenous vectors. The coverage percentages of the forecast intervals and the variability of the predictive distributions are analysed in this work. An application to Hydrology is presented.         

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20

Rasheed, Abdul, Muhammad Asad Ullah, and Imam Uddin. "PKR Exchange Rate Forecasting Through Univariate and Multivariate Time Series Techniques." NICE Research Journal 13, no. 4 (2020): 49–67. http://dx.doi.org/10.51239/nrjss.v13i4.226.

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This study aims to examine and compare the accuracy of time series and econometric forecasting models in the context of the exchange rate as we know that fluctuation in the exchange rate may affect the economic activities at the macro – level. For this purpose, the author has chosen the Pakistani Rupee exchange rate against United States Dollars with the annual data from 1980 to 2018. The results revealed that the exponential model provides the most effective accuracy in forecasting rather than the Naive, ARIMA and ARDL Co-integration model. This paper has also covered the gap of unavailability of literature regarding the application of ARDL and Exponential Smoothing model for the forecasting of the exchange rate in Pakistan. It is also anticipated that historical data do not play a vital role in the forecasting of the future trend of time series i.e. Pakistani Rupees against US Dollars. However, all three-time series anticipated that the recent observations play a significant role in the speculation of the upcoming future trend. Keywords: Forecasting, Exchange Rate, Naïve Model, ARDL Co-Integration model, Econometrics

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21

Huang, Lei, Feng Mao, Kai Zhang, and Zhiheng Li. "Spatial-Temporal Convolutional Transformer Network for Multivariate Time Series Forecasting." Sensors 22, no. 3 (2022): 841. http://dx.doi.org/10.3390/s22030841.

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Multivariate time series forecasting has long been a research hotspot because of its wide range of application scenarios. However, the dynamics and multiple patterns of spatiotemporal dependencies make this problem challenging. Most existing methods suffer from two major shortcomings: (1) They ignore the local context semantics when modeling temporal dependencies. (2) They lack the ability to capture the spatial dependencies of multiple patterns. To tackle such issues, we propose a novel Transformer-based model for multivariate time series forecasting, called the spatial–temporal convolutional Transformer network (STCTN). STCTN mainly consists of two novel attention mechanisms to respectively model temporal and spatial dependencies. Local-range convolutional attention mechanism is proposed in STCTN to simultaneously focus on both global and local context temporal dependencies at the sequence level, which addresses the first shortcoming. Group-range convolutional attention mechanism is designed to model multiple spatial dependency patterns at graph level, as well as reduce the computation and memory complexity, which addresses the second shortcoming. Continuous positional encoding is proposed to link the historical observations and predicted future values in positional encoding, which also improves the forecasting performance. Extensive experiments on six real-world datasets show that the proposed STCTN outperforms the start-of-the-art methods and is more robust to nonsmooth time series data.

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22

Li, Shaowei, He Huang, and Wei Lu. "A Neural Networks Based Method for Multivariate Time-Series Forecasting." IEEE Access 9 (2021): 63915–24. http://dx.doi.org/10.1109/access.2021.3075063.

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23

Zhang, Huihui, Shicheng Li, Yu Chen, Jiangyan Dai, and Yugen Yi. "A Novel Encoder-Decoder Model for Multivariate Time Series Forecasting." Computational Intelligence and Neuroscience 2022 (April 14, 2022): 1–17. http://dx.doi.org/10.1155/2022/5596676.

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The time series is a kind of complex structure data, which contains some special characteristics such as high dimension, dynamic, and high noise. Moreover, multivariate time series (MTS) has become a crucial study in data mining. The MTS utilizes the historical data to forecast its variation trend and has turned into one of the hotspots. In the era of rapid information development and big data, accurate prediction of MTS has attracted much attention. In this paper, a novel deep learning architecture based on the encoder-decoder framework is proposed for MTS forecasting. In this architecture, firstly, the gated recurrent unit (GRU) is taken as the main unit structure of both the procedures in encoding and decoding to extract the useful successive feature information. Then, different from the existing models, the attention mechanism (AM) is introduced to exploit the importance of different historical data for reconstruction at the decoding stage. Meanwhile, feature reuse is realized by skip connections based on the residual network for alleviating the influence of previous features on data reconstruction. Finally, in order to enhance the performance and the discriminative ability of the new MTS, the convolutional structure and fully connected module are established. Furthermore, to better validate the effectiveness of MTS forecasting, extensive experiments are executed on two different types of MTS such as stock data and shared bicycle data, respectively. The experimental results adequately demonstrate the effectiveness and the feasibility of the proposed method.

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Chiu, Yi Chia, and Joseph Z. Shyu. "Applying multivariate time series models to technological product sales forecasting." International Journal of Technology Management 27, no. 2/3 (2004): 306. http://dx.doi.org/10.1504/ijtm.2004.003957.

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25

Ghosh, B., B. Basu, and M. O'Mahony. "Multivariate Short-Term Traffic Flow Forecasting Using Time-Series Analysis." IEEE Transactions on Intelligent Transportation Systems 10, no. 2 (2009): 246–54. http://dx.doi.org/10.1109/tits.2009.2021448.

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26

Kling, John L., and David A. Bessler. "A comparison of multivariate forecasting procedures for economic time series." International Journal of Forecasting 1, no. 1 (1985): 5–24. http://dx.doi.org/10.1016/s0169-2070(85)80067-4.

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27

Du, Shengdong, Tianrui Li, Yan Yang, and Shi-Jinn Horng. "Multivariate time series forecasting via attention-based encoder–decoder framework." Neurocomputing 388 (May 2020): 269–79. http://dx.doi.org/10.1016/j.neucom.2019.12.118.

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28

Chakraborty, Kanad, Kishan Mehrotra, Chilukuri K. Mohan, and Sanjay Ranka. "Forecasting the behavior of multivariate time series using neural networks." Neural Networks 5, no. 6 (1992): 961–70. http://dx.doi.org/10.1016/s0893-6080(05)80092-9.

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29

Turner, Lindsay W., and Stephen F. Witt. "Forecasting Tourism Using Univariate and Multivariate Structural Time Series Models." Tourism Economics 7, no. 2 (2001): 135–47. http://dx.doi.org/10.5367/000000001101297775.

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30

Myklebust, Jogeir, Asgeir Tomasgard, and Sjur Westgaard. "Forecasting gas component prices with multivariate structural time series models." OPEC Energy Review 34, no. 2 (2010): 82–106. http://dx.doi.org/10.1111/j.1753-0237.2010.00176.x.

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Wan, Renzhuo, Shuping Mei, Jun Wang, Min Liu, and Fan Yang. "Multivariate Temporal Convolutional Network: A Deep Neural Networks Approach for Multivariate Time Series Forecasting." Electronics 8, no. 8 (2019): 876. http://dx.doi.org/10.3390/electronics8080876.

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Multivariable time series prediction has been widely studied in power energy, aerology, meteorology, finance, transportation, etc. Traditional modeling methods have complex patterns and are inefficient to capture long-term multivariate dependencies of data for desired forecasting accuracy. To address such concerns, various deep learning models based on Recurrent Neural Network (RNN) and Convolutional Neural Network (CNN) methods are proposed. To improve the prediction accuracy and minimize the multivariate time series data dependence for aperiodic data, in this article, Beijing PM2.5 and ISO-NE Dataset are analyzed by a novel Multivariate Temporal Convolution Network (M-TCN) model. In this model, multi-variable time series prediction is constructed as a sequence-to-sequence scenario for non-periodic datasets. The multichannel residual blocks in parallel with asymmetric structure based on deep convolution neural network is proposed. The results are compared with rich competitive algorithms of long short term memory (LSTM), convolutional LSTM (ConvLSTM), Temporal Convolution Network (TCN) and Multivariate Attention LSTM-FCN (MALSTM-FCN), which indicate significant improvement of prediction accuracy, robust and generalization of our model.

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Vlasenko, Alexander, Nataliia Vlasenko, Olena Vynokurova, and Dmytro Peleshko. "A Novel Neuro-Fuzzy Model for Multivariate Time-Series Prediction." Data 3, no. 4 (2018): 62. http://dx.doi.org/10.3390/data3040062.

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Time series forecasting can be a complicated problem when the underlying process shows high degree of complex nonlinear behavior. In some domains, such as financial data, processing related time-series jointly can have significant benefits. This paper proposes a novel multivariate hybrid neuro-fuzzy model for forecasting tasks, which is based on and generalizes the neuro-fuzzy model with consequent layer multi-variable Gaussian units and its learning algorithm. The model is distinguished by a separate consequent block for each output, which is tuned with respect to the its output error only, but benefits from extracting additional information by processing the whole input vector including lag values of other variables. Numerical experiments show better accuracy and computational performance results than competing models and separate neuro-fuzzy models for each output, and thus an ability to implicitly handle complex cross correlation dependencies between variables.

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Chen, Jason Li, Gang Li, Doris Chenguang Wu, and Shujie Shen. "Forecasting Seasonal Tourism Demand Using a Multiseries Structural Time Series Method." Journal of Travel Research 58, no. 1 (2017): 92–103. http://dx.doi.org/10.1177/0047287517737191.

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Multivariate forecasting methods are intuitively appealing since they are able to capture the interseries dependencies, and therefore may forecast more accurately. This study proposes a multiseries structural time series method based on a novel data restacking technique as an alternative approach to seasonal tourism demand forecasting. The proposed approach is analogous to the multivariate method but only requires one variable. In this study, a quarterly tourism demand series is split into four component series, each component representing the demand in a particular quarter of each year; the component series are then restacked to build a multiseries structural time series model. Empirical evidence from Hong Kong inbound tourism demand forecasting shows that the newly proposed approach improves the forecast accuracy, compared with traditional univariate models.

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Nguyen, Nam, and Brian Quanz. "Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (2021): 9117–25. http://dx.doi.org/10.1609/aaai.v35i10.17101.

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Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or abandons modeling cross-series correlations. A promising line of work exploits scalable matrix factorization for latent-space forecasting, but is limited to linear embeddings, unable to model distributions, and not trainable end-to-end when using deep learning forecasting. We introduce a novel temporal latent auto-encoder method which enables nonlinear factorization of multivariate time series, learned end-to-end with a temporal deep learning latent space forecast model. By imposing a probabilistic latent space model, complex distributions of the input series are modeled via the decoder. Extensive experiments demonstrate that our model achieves state-of-the-art performance on many popular multivariate datasets, with gains sometimes as high as 50% for several standard metrics.

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Saputra, Anggie Wahyu, Aji Prasetya Wibawa, Utomo Pujianto, Agung Bella Putra Utama, and Andrew Nafalski. "LSTM-based Multivariate Time-Series Analysis: A Case of Journal Visitors Forecasting." ILKOM Jurnal Ilmiah 14, no. 1 (2022): 57–62. http://dx.doi.org/10.33096/ilkom.v14i1.1106.57-62.

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Forecasting is the process of predicting something in the future based on previous patterns. Forecasting will never be 100% accurate because the future has a problem of uncertainty. However, using the right method can make forecasting have a low error rate value to provide a good forecast for the future. This study aims to determine the effect of increasing the number of hidden layers and neurons on the performance of the long short-term memory (LSTM) forecasting method. LSTM performance measurement is done by root mean square error (RMSE) in various architectural scenarios. The LSTM algorithm is considered capable of handling long-term dependencies on its input and can predict data for a relatively long time. Based on research conducted from all models, the best results were obtained with an RMSE value of 0.699 obtained in model 1 with the number of hidden layers 2 and 64 neurons. Adding the number of hidden layers can significantly affect the RMSE results using neurons 16 and 32 in Model 1.

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Chirikhin, Konstantin, and Boris Ryabko. "Compression-Based Methods of Time Series Forecasting." Mathematics 9, no. 3 (2021): 284. http://dx.doi.org/10.3390/math9030284.

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Time series forecasting is an important research topic with many practical applications. As shown earlier, the problems of lossless data compression and prediction are very similar mathematically. In this article, we propose several forecasting methods based on real-world data compressors. We consider predicting univariate and multivariate data, describe how multiple data compressors can be combined into one forecasting method with automatic selection of the best algorithm for the input data. The developed forecasting techniques are not inferior to the known ones. We also propose a way to reduce the computation time of the combined method by using the so-called time-universal codes. To test the proposed techniques, we make predictions for real-world data such as sunspot numbers and some social indicators of Novosibirsk region, Russia. The results of our computations show that the described methods find non-trivial regularities in data, and time universal codes can reduce the computation time without losing accuracy.

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Thomakos, Dimitrios, Johannes Klepsch, and Dimitris N. Politis. "Model Free Inference on Multivariate Time Series with Conditional Correlations." Stats 3, no. 4 (2020): 484–509. http://dx.doi.org/10.3390/stats3040031.

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New results on volatility modeling and forecasting are presented based on the NoVaS transformation approach. Our main contribution is that we extend the NoVaS methodology to modeling and forecasting conditional correlation, thus allowing NoVaS to work in a multivariate setting as well. We present exact results on the use of univariate transformations and on their combination for joint modeling of the conditional correlations: we show how the NoVaS transformed series can be combined and the likelihood function of the product can be expressed explicitly, thus allowing for optimization and correlation modeling. While this keeps the original “model-free” spirit of NoVaS it also makes the new multivariate NoVaS approach for correlations “semi-parametric”, which is why we introduce an alternative using cross validation. We also present a number of auxiliary results regarding the empirical implementation of NoVaS based on different criteria for distributional matching. We illustrate our findings using simulated and real-world data, and evaluate our methodology in the context of portfolio management.

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Sako, Kady, Berthine Nyunga Mpinda, and Paulo Canas Rodrigues. "Neural Networks for Financial Time Series Forecasting." Entropy 24, no. 5 (2022): 657. http://dx.doi.org/10.3390/e24050657.

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Financial and economic time series forecasting has never been an easy task due to its sensibility to political, economic and social factors. For this reason, people who invest in financial markets and currency exchange are usually looking for robust models that can ensure them to maximize their profile and minimize their losses as much as possible. Fortunately, recently, various studies have speculated that a special type of Artificial Neural Networks (ANNs) called Recurrent Neural Networks (RNNs) could improve the predictive accuracy of the behavior of the financial data over time. This paper aims to forecast: (i) the closing price of eight stock market indexes; and (ii) the closing price of six currency exchange rates related to the USD, using the RNNs model and its variants: the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The results show that the GRU gives the overall best results, especially for the univariate out-of-sample forecasting for the currency exchange rates and multivariate out-of-sample forecasting for the stock market indexes.

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39

Amalou, Ibtissam, Naoual Mouhni, and Abdelmounaim Abdali. "Multivariate time series prediction by RNN architectures for energy consumption forecasting." Energy Reports 8 (November 2022): 1084–91. http://dx.doi.org/10.1016/j.egyr.2022.07.139.

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He, Hui, Qi Zhang, Simeng Bai, Kun Yi, and Zhendong Niu. "CATN: Cross Attentive Tree-Aware Network for Multivariate Time Series Forecasting." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (2022): 4030–38. http://dx.doi.org/10.1609/aaai.v36i4.20320.

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Modeling complex hierarchical and grouped feature interaction in the multivariate time series data is indispensable to comprehend the data dynamics and predicting the future condition. The implicit feature interaction and high-dimensional data make multivariate forecasting very challenging. Many existing works did not put more emphasis on exploring explicit correlation among multiple time series data, and complicated models are designed to capture long- and short-range pattern with the aid of attention mechanism. In this work, we think that pre-defined graph or general learning method is difficult due to their irregular structure. Hence, we present CATN, an end-to-end model of Cross Attentive Tree-aware Network to jointly capture the inter-series correlation and intra-series temporal pattern. We first construct a tree structure to learn hierarchical and grouped correlation and design an embedding approach that can pass dynamic message to generalize implicit but interpretable cross features among multiple time series. Next in temporal aspect, we propose a multi-level dependency learning mechanism including global&local learning and cross attention mechanism, which can combine long-range dependencies, short-range dependencies as well as cross dependencies at different time steps. The extensive experiments on different datasets from real world show the effectiveness and robustness of the method we proposed when compared with existing state-of-the-art methods.

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Wang, Yueyang, Ziheng Duan, Yida Huang, Haoyan Xu, Jie Feng, and Anni Ren. "MTHetGNN: A heterogeneous graph embedding framework for multivariate time series forecasting." Pattern Recognition Letters 153 (January 2022): 151–58. http://dx.doi.org/10.1016/j.patrec.2021.12.008.

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Gao, Yuan, and Han Shang. "Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates." Risks 5, no. 2 (2017): 21. http://dx.doi.org/10.3390/risks5020021.

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Vanhoenshoven, Frank, Gonzalo Nápoles, Wojciech Froelich, Jose L. Salmeron, and Koen Vanhoof. "Pseudoinverse learning of Fuzzy Cognitive Maps for multivariate time series forecasting." Applied Soft Computing 95 (October 2020): 106461. http://dx.doi.org/10.1016/j.asoc.2020.106461.

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Seong, Byeong-Chan. "Comparison of Forecasting Performance in Multivariate Nonstationary Seasonal Time Series Models." Communications for Statistical Applications and Methods 18, no. 1 (2011): 13–21. http://dx.doi.org/10.5351/ckss.2011.18.1.013.

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Hur, Nam-Kyun, Jae-Yoon Jung, and Sahm Kim. "A Study on Air Demand Forecasting Using Multivariate Time Series Models." Korean Journal of Applied Statistics 22, no. 5 (2009): 1007–17. http://dx.doi.org/10.5351/kjas.2009.22.5.1007.

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West, Mike. "Bayesian forecasting of multivariate time series: scalability, structure uncertainty and decisions." Annals of the Institute of Statistical Mathematics 72, no. 1 (2019): 1–31. http://dx.doi.org/10.1007/s10463-019-00741-3.

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J. F. Braga, Dieinison, Ticiana L. Coelho da Silva, Atslands Rocha, et al. "Time Series Forecasting to Support Irrigation Management." Journal of Information and Data Management 10, no. 2 (2019): 66–80. http://dx.doi.org/10.5753/jidm.2019.2037.

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Abstract:

Irrigated agriculture is the most water-consuming sector in Brazil, representing one of the main challenges for the sustainable use of water. This study has investigated and evaluated popular machine learning techniques like Gradient Boosting and Random Forest, deep learning models and univariate time series models to predict the value of reference evapotranspiration, a metric of water loss from the crop to the environment. The reference evapotranspiration ET0, plays an essential role in irrigation management since it can be used to reduce the amount of water that will not be absorbed by the crop. We performed the experiments with two real datasets generated by weather stations. The results show that the deep learning models are data-hungry, even when we increased the training set it was not enough to outperform multivariate models like Random Forest, Gradient Boosting and M5’ which indeed execute faster than the deep learning models during the training phase. However, the univariate time series model as the evaluated deep learning models (stacked LSTM and BLSTM) is a viable and lower-cost solution for predicting ET0, since we need to monitor only one variable.

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Zahara, Soffa, and Sugianto. "Peramalan Data Indeks Harga Konsumen Berbasis Time Series Multivariate Menggunakan Deep Learning." Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) 5, no. 1 (2021): 24–30. http://dx.doi.org/10.29207/resti.v5i1.2562.

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Abstract:

Multivariate Time Series based forecasting is a type of forecasting that has more than one criterion changes from time to time that it can forecast based on historical patterns of data sequences. The Consumer Price Index (CPI) issued regularly every month by the Statistics Indonesia calculated based on data observations. This study is a development of previous research that only used on type of algorithm to predict CPI value resulting poor of accuracy due to lack of architecture variations testing. This study developed a CPI forecasting model with a new approach about using several types of deep learning algorithms, namely LSTM, Bidirectional LSTM, and Multilayer Perceptron with architectural variations of the number of neurons and epochs. Furthermore, this study adapt ADDIE model of Research and Development method. Based on the results, the best accuracy is obtained from the LSTM Bidirectional with 10 neurons and 2000 epoch resulting 3,519 of RMSE value. Meanwhile, based on the average RMSE value for the whole test, LSTM gets the smallest average of RMSE followed Bidirectional LSTM and Multilayer Perceptron with the RMSE value 4,334, 5,630, 6,304 respectively.

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FM, Mohammed Farooq Abdulla, Tamilselvan V, Harshini V S, and Deepthikka R S. "Purchase and Analytics for Grace Marketing." International Journal of Engineering Research in Computer Science and Engineering 9, no. 5 (2022): 21–24. http://dx.doi.org/10.36647/ijercse/09.05.art003.

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In recent years development of computer systems were able to learn and adapt without following explicit instructions, by using algorithms and statistical models to analyze and draw inferences from patterns in data is known as machine learning.In this phase sales of different lubricants were predicted using a multivariate time series forecasting algorithm.Previously it showed that the model was accurate in predicting the engine oil sales for a particular time.Using Regressions the accuracy of sales prediction was less (74%) and the models like SVM and Random forest were showing signs of over fitting.The accuracy obtained in the multivariate time series forecasting was good than other algorithms.Time series algorithms are used extensively for forecasting time-based data.In time series ARIMA,SARIMA and SARIMAX are the common methods to forecast time based data.SARIMAX are efficient in forecasting data which has seasonality trends than ARIMA which are good in forecasting data which is stationary in nature Time series methods are extensively used for forecasting time based data.In time series ARIMA,SARIMA and SARIMAX are the common methods to forecast tie based data.ARIMA is the abbreviation of Auto Regressive Integrated Moving Average a model which explains a given time series model based on its lags and other values.SARIMAX is the abbreviation of Seasonal Auto Regressive Integrated Moving Average with Xegeneous variables. ARIMA model is best for forecasting stationary time series data and SARIMAX is used for forecasting values which is seasonal in nature.

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FM, Mohammed Farooq Abdulla, Tamilselvan V, Harshini V S, and Deepthikka R S. "Purchase and Analytics for Grace Marketing." International Journal of Science, Engineering and Management 9, no. 4 (2022): 1–4. http://dx.doi.org/10.36647/ijsem/09.04.a001.

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Abstract:

In recent years development of computer systems were able to learn and adapt without following explicit instructions, by using algorithms and statistical models to analyze and draw inferences from patterns in data is known as machine learning.In this phase sales of different lubricants were predicted using a multivariate time series forecasting algorithm.Previously it showed that the model was accurate in predicting the engine oil sales for a particular time.Using Regressions the accuracy of sales prediction was less (74%) and the models like SVM and Random forest were showing signs of over fitting.The accuracy obtained in the multivariate time series forecasting was good than other algorithms.Time series algorithms are used extensively for forecasting time-based data.In time series ARIMA,SARIMA and SARIMAX are the common methods to forecast time based data.SARIMAX are efficient in forecasting data which has seasonality trends than ARIMA which are good in forecasting data which is stationary in nature Time series methods are extensively used for forecasting time based data.In time series ARIMA,SARIMA and SARIMAX are the common methods to forecast tie based data.ARIMA is the abbreviation of Auto Regressive Integrated Moving Average a model which explains a given time series model based on its lags and other values.SARIMAX is the abbreviation of Seasonal Auto Regressive Integrated Moving Average with Xegeneous variables. ARIMA model is best for forecasting stationary time series data and SARIMAX is used for forecasting values which is seasonal in nature.

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