Time Series

Time series are collections of values that are ordered in time. Preserving this ordering helps identify trends, detect seasonal patterns, and predict future values. Such series show up in many fields, from econometrics (unemployment rates, ), finance (stock prices, ), and demography (birth rates, ) to meteorology (rainfall, ), physiology (heart rates, ), and information technology (network traffic, ). Time series are tightly integrated into the Wolfram Language, allowing for seamless workflows with absolute or calendar time, regular or irregular sampling, scalar or vector values, single or multiple series, and in the presence of missing data. The Wolfram Language offers an extensive collection of tools for processing time series. These tools range from descriptive statistics, filters, and visualization to forecasts, simulation, and highly automated modeling frameworks.

ReferenceReference

Construction

TimeSeries series of time-value pairs

EventSeries special time series with no interpolation between samples

TemporalData a collection of time series

ResamplingMethod  ▪  MissingDataMethod  ▪  TemporalRegularity

RandomFunction  ▪  FinancialData  ▪  FinancialIndicator  ▪  CountryData

Visualization »

ListLinePlot visualize a time series

DateListPlot  ▪  Histogram  ▪  SmoothHistogram  ▪  QuantilePlot  ▪  ...

Basic Operations

TimeSeriesWindow give the time series in the specified time window

TimeSeriesInsert insert time-value pairs into a time series

TimeSeriesRescale  ▪  TimeSeriesResample  ▪  TimeSeriesShift  ▪  TimeSeriesThread  ▪  TimeSeriesMap  ▪  TimeSeriesMapThread  ▪  RegularlySampledQ  ▪  MinimumTimeIncrement

Basic Statistics »

Mean find the mean of the values

StandardDeviation  ▪  Variance  ▪  Median  ▪  Quantile  ▪  ...

EmpiricalDistribution find the empirical distribution of the values

HistogramDistribution  ▪  KernelMixtureDistribution  ▪  EstimatedDistribution

Filtering & Aggregating Time Series

MovingMap apply a function to a moving overlapping window

TimeSeriesAggregate apply a function to a moving non-overlapping window

Differences  ▪  Accumulate  ▪  MovingAverage  ▪  MovingMedian  ▪  ...

LowpassFilter  ▪  HighpassFilter  ▪  MeanFilter  ▪  ...

Fitting and Interpolation

FindFit fit a function of time to the time series

Interpolation  ▪  LinearModelFit  ▪  NonlinearModelFit  ▪  ...

Time Series Process Modeling »

TimeSeriesModelFit automatically fit a time series model

TimeSeriesForecast  ▪  CorrelationFunction  ▪  PowerSpectralDensity  ▪  ...

Time Specifications »

DateObject, TimeObject date, time specifications

Now  ▪  DatePlus  ▪  LocalTime  ▪  TimeZoneConvert  ▪  UnitConvert  ▪  ...

Wolfram Data Drop

Databin representation of a databin accumulated in the Wolfram Data Drop