Timeseries Dataset

A timeseries dataset is an ordered labeled dataset (with temporal data records) whose label contains temporal values.

• Context:
  • It can range from being a Simple Temporal Dataset to being a Structured Temporal Dataset.
  • It can range from being a Continuous Time-Series Dataset to being a Discrete Time-Series Dataset.
  • It can range from being a Numeric Time-Series Dataset to being a Non-Numeric Time-Series Dataset to being a Mixed-Data Time-Series Dataset.
  • It can range from being a Real Timeseries Dataset to being a Synthetic Timeseries Dataset.
  • It can range from being a Stable Timeseries Dataset to being a Dynamic Timeseries Dataset.
  • It can range from being a Timeseries Snapshot to being a Timeseries Datalog.
  • It can be visualized by a Time-Series Infographic.
  • It can be represented by a Temporal Data Structure.
  • It can be the Input to a Temporal Data Analysis Task (such as timeseries outlier detection).
  • It can be the Input to a Temporal Forecasting Task.
• Example(s):
  • a Univariate Timeseries Dataset, such as the M3 Dataset.
  • an Event Data Set.
  • an Online Dataset.
  • a Sequential Corpus.
  • a Transaction Dataset (with a Timestamp).
  • a Daily Revenue Dataset.
  • a Panel Dataset.
  • a Time-to-Event Dataset.
  • Real US GNP Timeseries (Billions of real dollars, seasonally adjusted) Vintages 1965:Q4 to present Excel spreadsheet.
  • …
• Counter-Example(s):
  • a Text Dataset.
  • a DNA Dataset.
• See: Temporal Expression, Censored Dataset.

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/time_series Retrieved:2017-10-29.
  • A time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.

    Time series are very frequently plotted via line charts. Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, intelligent transport and trajectory forecasting , container shipping freight rate forecasting ,earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. While regression analysis is often employed in such a way as to test theories that the current values of one or more independent time series affect the current value of another time series, this type of analysis of time series is not called "time series analysis", which focuses on comparing values of a single time series or multiple dependent time series at different points in time. Interrupted time series analysis is the analysis of interventions on a single time series Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility.) Time series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language ).

2013

• http://en.wikipedia.org/wiki/Time_series
  • … Additionally time series analysis techniques may be divided into parametric and non-parametric methods. The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving average model). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure.

    Additionally methods of time series analysis may be divided into linear and non-linear, univariate and multivariate.

    Time series analysis can be applied to:

    • real-valued, continuous data
    • discrete numeric data
    • discrete symbolic data (i.e. sequences of characters, such as letters and words in English language).

2011

• (Keogh, 2011c) ⇒ Eamonn Keogh. (2011). “Time Series.” In: (Sammut & Webb, 2011) p.987

2005

• http://www.stats.gla.ac.uk/steps/glossary/time_series.html
  • QUOTE: A time series is a sequence of observations which are ordered in time (or space). If observations are made on some phenomenon throughout time, it is most sensible to display the data in the order in which they arose, particularly since successive observations will probably be dependent. Time series are best displayed in a scatter plot. The series value X is plotted on the vertical axis and time t on the horizontal axis. Time is called the independent variable (in this case however, something over which you have little control). There are two kinds of time series data:
    1. Continuous, where we have an observation at every instant of time, e.g. lie detectors, electrocardiograms. We denote this using observation X at time t, X(t).
    2. Discrete, where we have an observation at (usually regularly) spaced intervals. We denote this as Xt.
  • Examples
    • Economics - weekly share prices, monthly profits
    • Meteorology - daily rainfall, wind speed, temperature
    • Sociology - crime figures (number of arrests, etc), employment figures

2001

• (Brillinger, 2001) ⇒ David R. Brillinger. (2001). “Time Series: Data analysis and theory." SIAM. ISBN:0898715016
  • BOOK OVERVIEW: Intended for students and researchers, this text employs basic techniques of univariate and multivariate statistics for the analysis of time series and signals. It provides a broad collection of theorems, placing the techniques on firm theoretical ground. The techniques, which are illustrated by data analyses, are discussed in both a heuristic and a formal manner, making the book useful for both the applied and the theoretical worker. An extensive set of original exercises is included. Time Series: Data Analysis and Theory takes the Fourier transform of a stretch of time series data as the basic quantity to work with and shows the power of that approach. It considers second- and higher-order parameters and estimates them equally, thereby handling non-Gaussian series and nonlinear systems directly. The included proofs, which are generally short, are based on cumulants.

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