Time-Warping Invariants of Multidimensional Time Series

Abstract In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants. We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties.

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A Cumulative Sum Algorithm for Detecting Changes in the Covariance Matrix of Multidimensional Time Series

Vestnik MEI ◽

10.24160/1993-6982-2020-3-92-101 ◽

2020 ◽

Vol 3 (3) ◽

pp. 92-101

Author(s):

Gennadiy F. Filaretov ◽

◽

Pavel S. Simonenkov ◽

Keyword(s):

Time Series ◽

Covariance Matrix ◽

Cumulative Sum ◽

Multidimensional Time Series

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The Data Science of COVID-19 Spread: Some Troubling Current and Future Trends

Peace Economics Peace Science and Public Policy ◽

10.1515/peps-2020-0053 ◽

2020 ◽

Vol 26 (3) ◽

Author(s):

Rex W. Douglass ◽

Thomas Leo Scherer ◽

Erik Gartzke

Keyword(s):

Time Series ◽

Cross Section ◽

Observational Studies ◽

Data Science ◽

Future Trends ◽

Methodological Issues

AbstractOne of the main ways we try to understand the COVID-19 pandemic is through time series cross section counts of cases and deaths. Observational studies based on these kinds of data have concrete and well known methodological issues that suggest significant caution for both consumers and produces of COVID-19 knowledge. We briefly enumerate some of these issues in the areas of measurement, inference, and interpretation.

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New DTW Windows Type for Forward- and Backward-Lookingness Examination. Application for Inflation Expectation

Computational Economics ◽

10.1007/s10614-021-10103-y ◽

2021 ◽

Author(s):

Aleksandra Rutkowska ◽

Magdalena Szyszko

Keyword(s):

Time Series ◽

Information Content ◽

Dynamic Time Warping ◽

The Novel ◽

Time Warping ◽

Specific Question ◽

Inflation Expectation ◽

Standard Tool ◽

Dynamic Time ◽

Research Period

AbstractThis study provides an application of dynamic time warping algorithm with a new window constraint to assess consumer expectations’ information content regarding current and future inflation. Our study’s contribution is the novel application of DTW for testing expectations’ forward-lookingness. Additionally, we modify the algorithm to adjust it for a specific question on the information content of our data. The DTW overcomes constraints of the standard tool that examines forward-lookingness: DTW does not impose assumptions on time series properties. In empirical study we cover seven European counties and compare the DTW outcomes with the results of previous studies in these economies using a standard methodology. The research period covers 2001 to mid-2018. Application of DTW provides information on the degree of expectations’ forward-lookingness. The result, after standardization, are similar to the standard parameters of hybrid specification of expectations. Moreover, the rankings of most forward-looking consumers are replicated. Our results confirm the economic intuition, and they do not contradict previous studies.

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The Connections between COVID-19 and the Energy Commodities Prices: Evidence through the Dynamic Time Warping Method

Energies ◽

10.3390/en14134024 ◽

2021 ◽

Vol 14 (13) ◽

pp. 4024

Author(s):

Krzysztof Dmytrów ◽

Joanna Landmesser ◽

Beata Bieszk-Stolorz

Keyword(s):

Time Series ◽

Palm Oil ◽

Dynamic Time Warping ◽

Global Economy ◽

Price Change ◽

Commodity Prices ◽

The Other ◽

Time Warping ◽

Heating Oil ◽

Dynamic Time

The main objective of the study is to assess the similarity between the time series of energy commodity prices and the time series of daily COVID-19 cases. The COVID-19 pandemic affects all aspects of the global economy. Although this impact is multifaceted, we assess the connections between the number of COVID-19 cases and the energy commodities sector. We analyse these connections by using the Dynamic Time Warping (DTW) method. On this basis, we calculate the similarity measure—the DTW distance between the time series—and use it to group the energy commodities according to their price change. Our analysis also includes finding the time shifts between daily COVID-19 cases and commodity prices in subperiods according to the chronology of the COVID-19 pandemic. Our findings are that commodities such as ULSD, heating oil, crude oil, and gasoline are weakly associated with COVID-19. On the other hand, natural gas, palm oil, CO2 allowances, and ethanol are strongly associated with the development of the pandemic.

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