scholarly journals Time series forecasting: problem of heavy-tailed distributed noise

2021 ◽  
Author(s):  
Marta Markiewicz ◽  
Agnieszka Wyłomańska
Keyword(s):  
Time Series ◽  
Regression Tree ◽  
Time Series Forecasting ◽  
Statistical Machine Learning ◽  
Practical Applications ◽  
Challenging Tasks ◽  
Heavy Tailed Distribution ◽  
Likelihood Approach ◽  
Heavy Tailed ◽  
Student’S T

AbstractTime series forecasting has been the area of intensive research for years. Statistical, machine learning or mixed approaches have been proposed to handle this one of the most challenging tasks. However, little research has been devoted to tackle the frequently appearing assumption of normality of given data. In our research, we aim to extend the time series forecasting models for heavy-tailed distribution of noise. In this paper, we focused on normal and Student’s t distributed time series. The SARIMAX model (with maximum likelihood approach) is compared with the regression tree-based method—random forest. The research covers not only forecasts but also prediction intervals, which often have hugely informative value as far as practical applications are concerned. Although our study is focused on the selected models, the presented problem is universal and the proposed approach can be discussed in the context of other systems.

Recursive Estimation for Some Nonstationary Processes

1996 ◽  
Vol 46 (3-4) ◽  
pp. 159-168
Author(s):  
N. Ordoukhani ◽  
A. Thavaneswaran ◽  
M. Samanta
Keyword(s):  
Time Series ◽  
Missing Values ◽  
Nonlinear Models ◽  
Nonstationary Time Series ◽  
Recursive Estimation ◽  
Time Series Models ◽  
Nonstationary Processes ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

Recently a criterion for recursive estimation for some nonlinear models has been studied in Thavaneswaran and Abraham (1988). In this paper the problem of recursive estimation of signals for some linear nonstationary time series models having heavy tailed distribution as errors is discussed. It is noted that the situation treated in Thavaneswaran and Abraham (1994) is a special ease for some nonstationary models. Estimation of missing values is also discussed in some detail.

HEAVY-TAILED DISTRIBUTION AND LOCAL LONG MEMORY IN TIME SERIES OF MOLECULAR MOTION ON THE CELL MEMBRANE

2011 ◽  
Vol 10 (01) ◽  
pp. 93-119 ◽  
Author(s):  
HU SHENG ◽  
YANG QUAN CHEN ◽  
TIANSHUANG QIU
Keyword(s):  
Time Series ◽  
Cell Membrane ◽  
Long Memory ◽  
Molecular Motion ◽  
Statistical Characteristics ◽  
Jump Time ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed ◽  
Memory Characteristics

The joint presence of heavy-tailed distribution and long memory in time series always leads to certain trouble in correctly obtaining the statistical characteristics for time series modeling. These two properties i.e., heavy-tailed distribution and long memory, cannot be neglected in time series analysis, because the tail thickness of the distribution and long memory property of the time series are critical in characterizing the essence of the resulting natural or man-made phenomenon of the time series. Meanwhile, the fluctuation of the varying local long memory parameter may be used to capture the internal changes which underlie the externally observed phenomenon. Therefore, in this paper, we proposed to use the variance trend, heavy-tailed distribution, long memory, and local long memory characteristics to analyze a time series recorded as in [1] from tracking the jumps of individual molecules on cell membranes. The tracked molecules are Class I major histocompatibility complex (MHCI) expressed on rat hepatoma cells. The analysis results show that the jump time series of molecular motion on the cell membrane obviously has both heavy-tailed distribution and local long memory characteristics. The tail heaviness parameters, long memory parameters, and the local long memory parameters of ten MHCI molecular jump time series are all summarized with tables and figures in the paper. These reported tables and figures are not only interesting but also important in terms of additional novel insights and characterization of the time series under investigation.

scholarly journals Compression-Based Methods of Time Series Forecasting

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 284
Author(s):  
Konstantin Chirikhin ◽  
Boris Ryabko
Keyword(s):  
Time Series ◽  
Real World ◽  
Social Indicators ◽  
Computation Time ◽  
Time Series Forecasting ◽  
Real World Data ◽  
World Data ◽  
Practical Applications ◽  
Multiple Data ◽  
Universal Codes

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.

Deep Learning for text in limted data settings

2020 ◽  
Author(s):  
Pathikkumar Patel ◽  
Bhargav Lad ◽  
Jinan Fiaidhi
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Deep Learning ◽  
Sentiment Analysis ◽  
Transfer Learning ◽  
Text Classification ◽  
State Of The Art ◽  
Time Series Forecasting ◽  
Text Data ◽  
Performance Levels

During the last few years, RNN models have been extensively used and they have proven to be better for sequence and text data. RNNs have achieved state-of-the-art performance levels in several applications such as text classification, sequence to sequence modelling and time series forecasting. In this article we will review different Machine Learning and Deep Learning based approaches for text data and look at the results obtained from these methods. This work also explores the use of transfer learning in NLP and how it affects the performance of models on a specific application of sentiment analysis.

scholarly journals A Neutrosophic Forecasting Model for Time Series Based on First-Order State and Information Entropy of High-Order Fluctuation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 455 ◽  
Author(s):  
Hongjun Guan ◽  
Zongli Dai ◽  
Shuang Guan ◽  
Aiwu Zhao
Keyword(s):  
Time Series ◽  
Information Entropy ◽  
Stock Exchange ◽  
Time Series Forecasting ◽  
High Order ◽  
Stock Index ◽  
Neutrosophic Set ◽  
Forecasting Model ◽  
Forecasting Models ◽  
Proposed Model

In time series forecasting, information presentation directly affects prediction efficiency. Most existing time series forecasting models follow logical rules according to the relationships between neighboring states, without considering the inconsistency of fluctuations for a related period. In this paper, we propose a new perspective to study the problem of prediction, in which inconsistency is quantified and regarded as a key characteristic of prediction rules. First, a time series is converted to a fluctuation time series by comparing each of the current data with corresponding previous data. Then, the upward trend of each of fluctuation data is mapped to the truth-membership of a neutrosophic set, while a falsity-membership is used for the downward trend. Information entropy of high-order fluctuation time series is introduced to describe the inconsistency of historical fluctuations and is mapped to the indeterminacy-membership of the neutrosophic set. Finally, an existing similarity measurement method for the neutrosophic set is introduced to find similar states during the forecasting stage. Then, a weighted arithmetic averaging (WAA) aggregation operator is introduced to obtain the forecasting result according to the corresponding similarity. Compared to existing forecasting models, the neutrosophic forecasting model based on information entropy (NFM-IE) can represent both fluctuation trend and fluctuation consistency information. In order to test its performance, we used the proposed model to forecast some realistic time series, such as the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), the Shanghai Stock Exchange Composite Index (SHSECI), and the Hang Seng Index (HSI). The experimental results show that the proposed model can stably predict for different datasets. Simultaneously, comparing the prediction error to other approaches proves that the model has outstanding prediction accuracy and universality.

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