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Time-Series Graph

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...

Basic Continuous Time Signals

Basic Continuous Time Signals

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Sampling Continuous Time Signal

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...

Linear time-invariant Systems

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...

Discrete-Time Fourier Series

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...

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PyDTS: A Python Toolkit for Deep Learning Time Series Modelling.

Pascal A Schirmer¹, Iosif Mporas¹

¹School of Physics, Engineering, and Computer Science, University of Hertfordshire, Hatfield AL10 9AB, UK.

Entropy (Basel, Switzerland)

|April 26, 2024

Summary

This summary is machine-generated.

This article explores time series modelling for analyzing and forecasting data. It introduces a Python toolkit (PyDTS) for practical applications like denoising and anomaly detection.

Keywords:

anomaly detection deep learning degradation modelling denoising forecasting machine learning nonlinear modelling time series modelling

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Area of Science:

Data Science
Applied Mathematics

Background:

Time series data is critical across sectors for analysis and forecasting.
Key applications include denoising, forecasting, nonlinear transient modeling, anomaly detection, and degradation modeling.
Existing mathematical frameworks involve statistical, linear algebra, and machine/deep learning approaches.

Purpose of the Study:

To provide a comprehensive overview of time series modelling techniques.
To introduce a novel Python-based toolkit (PyDTS) for practical time series analysis.
To demonstrate the toolkit's utility through examples and benchmarking.

Main Methods:

Review of statistical, linear algebra, and machine/deep learning methodologies for time series.
Development and integration of popular time series modeling techniques into the PyDTS toolkit.
Empirical evaluation of PyDTS using diverse datasets.

Main Results:

The article categorizes time series modeling approaches based on mathematical frameworks.
A Python toolkit (PyDTS) is presented, integrating various modeling methodologies.
Benchmarking across diverse datasets demonstrates the toolkit's practical utility and performance.

Conclusions:

Time series modeling is essential for data analysis and forecasting in numerous fields.
The PyDTS toolkit offers a practical, integrated solution for diverse time series challenges.
This work facilitates the application and advancement of time series modeling through accessible tools.