Base R ships with a lot of functionality useful for time series, in particular in the stats package. This is complemented by many packages on CRAN, which are briefly summarized below. There is also a considerable overlap between the tools for time series and those in the
Econometrics
and
Finance
task views. The packages in this view can be roughly structured into the following topics. If you think that some package is missing from the list, please let us know.
Basics
-
Infrastructure
:
Base R contains substantial infrastructure for representing and analyzing time series data. The fundamental class is
"ts"
that can represent regularly spaced time series (using numeric time stamps). Hence, it is particularly well-suited for annual, monthly, quarterly data, etc.
-
Rolling statistics
:
Moving averages are computed by
ma
from
forecast, and
rollmean
from
zoo. The latter also provides a general function
rollapply, along with other specific rolling statistics functions.
roll
provides parallel functions for computing rolling statistics.
-
Graphics
:
Time series plots are obtained with
plot()
applied to
ts
objects.
(Partial) autocorrelation functions plots are implemented in
acf()
and
pacf(). Alternative versions are provided by
Acf()
and
Pacf()
in
forecast, along with a combination display using
tsdisplay().
SDD
provides more general serial dependence diagrams, while
dCovTS
computes and plots the distance covariance and correlation functions of time series.
Seasonal displays are obtained using
monthplot()
in stats and
seasonplot
in
forecast.
Wats
implements wrap-around time series graphics.
ggseas
provides ggplot2 graphics for seasonally adjusted series and rolling statistics.
dygraphs
provides an interface to the Dygraphs interactive time series charting library.
ZRA
plots forecast objects from the
forecast
package using dygraphs.
Basic fan plots of forecast distributions are provided by
forecast
and
vars. More flexible fan plots of any sequential distributions are implemented in
fanplot.
Times and Dates
-
Class
"ts"
can only deal with numeric time stamps, but many more classes are available for storing time/date information and computing with it.
For an overview see
R Help Desk: Date and Time Classes in R
by Gabor Grothendieck and Thomas Petzoldt in
R News 4(1)
, 29-32.
-
Classes
"yearmon"
and
"yearqtr"
from
zoo
allow for more convenient computation with monthly and quarterly observations, respectively.
-
Class
"Date"
from the base package is the basic class for dealing with dates in daily data. The dates are internally stored as the number of days since 1970-01-01.
-
The
chron
package
provides classes for
dates(),
hours()
and date/time (intra-day) in
chron().
There is no support for time zones and daylight savings time.
Internally,
"chron"
objects are (fractional) days since 1970-01-01.
-
Classes
"POSIXct"
and
"POSIXlt"
implement the POSIX standard for date/time (intra-day) information and also support time zones and daylight savings time.
However, the time zone computations require some care and might be system-dependent.
Internally,
"POSIXct"
objects are the number of seconds since 1970-01-01 00:00:00 GMT.
Package
lubridate
provides functions that facilitate certain POSIX-based computations.
-
Class
"timeDate"
is provided in the
timeDate
package (previously: fCalendar).
It is aimed at financial time/date information and deals with time zones and daylight savings times via a new concept of "financial centers".
Internally, it stores all information in
"POSIXct"
and does all computations in GMT only.
Calendar functionality, e.g., including information about weekends and holidays for various stock exchanges, is also included.
-
The
tis
package
provides the
"ti"
class for time/date information.
-
The
"mondate"
class
from the
mondate
package facilitates computing with dates in terms of months.
-
The
tempdisagg
package
includes methods for temporal disaggregation and interpolation of a low frequency time series to a higher frequency series.
-
TimeProjection
extracts useful time components of a date object, such as day of week, weekend, holiday, day of month, etc, and put it in a data frame.
Time Series Classes
-
As mentioned above,
"ts"
is the basic class for regularly spaced time series using numeric time stamps.
-
The
zoo
package
provides infrastructure for regularly and irregularly spaced time series using arbitrary classes for the time stamps (i.e., allowing all classes from the previous section).
It is designed to be as consistent as possible with
"ts".
Coercion from and to
"zoo"
is available for all other classes mentioned in this section.
-
The package
xts
is based on
zoo
and provides uniform handling of R's different time-based data classes.
-
Various packages implement irregular time series
based on
"POSIXct"
time stamps, intended especially for financial applications. These include
"its"
from
its,
"irts"
from
tseries,
and
"fts"
from
fts.
-
The class
"timeSeries"
in
timeSeries
(previously: fSeries) implements time series with
"timeDate"
time stamps.
-
The class
"tis"
in
tis
implements time series with
"ti"
time stamps.
-
The package
tframe
contains infrastructure for setting time frames in different formats.
Forecasting and Univariate Modeling
-
The
forecast
package
provides a class and methods for univariate time series forecasts, and provides many functions implementing different forecasting models including all those in the stats package.
-
Exponential smoothing
:
HoltWinters()
in stats provides some basic models with partial optimization,
ets()
from the
forecast
package provides a larger set of models and facilities with full optimization.
The
MAPA
package combines exponential smoothing models at different levels of temporal aggregation to improve forecast accuracy.
smooth
implements some generalizations of exponential smoothing.
-
The theta method
is implemented in the
thetaf
function from the
forecast
package.
An alternative and extended implementation is provided in
forecTheta.
-
Autoregressive models
:
ar()
in stats (with model selection) and
FitAR
for subset AR models.
-
ARIMA models
:
arima()
in stats is the basic function for ARIMA, SARIMA, ARIMAX, and subset ARIMA models.
It is enhanced in the
forecast
package via the function
Arima()
along with
auto.arima()
for automatic order selection.
arma()
in the
tseries
package provides different algorithms for ARMA and subset ARMA models.
FitARMA
implements a fast MLE algorithm for ARMA models.
Package
gsarima
contains functionality for Generalized SARIMA time series simulation.
The
mar1s
package handles multiplicative AR(1) with seasonal processes.
TSTutorial
provides an interactive tutorial for Box-Jenkins modelling.
Improved prediction intervals for ARIMA and structural time series models are provided by
tsPI.
-
Periodic ARMA models
:
pear
and
partsm
for periodic autoregressive time series models, and
perARMA
for periodic ARMA modelling and other procedures for periodic time series analysis.
-
ARFIMA models
:
Some facilities for fractional differenced ARFIMA models are provided in the
fracdiff
package.
The
arfima
package has more advanced and general facilities for ARFIMA and ARIMA models, including dynamic regression (transfer function) models.
armaFit()
from the
fArma
package is an interface for ARIMA and ARFIMA models.
Fractional Gaussian noise and simple models for hyperbolic decay time series are handled in the
FGN
package.
-
Transfer function
models
are provided by the
arimax
function in the
TSA
package, and the
arfima
function in the
arfima
package.
-
Outlier detection
following the Chen-Liu approach is provided by
tsoutliers.
-
Structural models
are implemented in
StructTS()
in stats, and in
stsm
and
stsm.class.
KFKSDS
provides a naive implementation of the Kalman filter and smoothers for univariate state space models.
Bayesian structural time series models are implemented in
bsts
-
Non-Gaussian time series
can be handled with GLARMA state space models via
glarma, and using Generalized Autoregressive Score models in the
GAS
package.
Conditional Auto-Regression models using Monte Carlo Likelihood methods are implemented in
mclcar.
-
GARCH models
:
garch()
from
tseries
fits basic GARCH models.
Many variations on GARCH models are provided by
rugarch.
Other univariate GARCH packages include
fGarch
which implements ARIMA models with a wide class of GARCH innovations.
There are many more GARCH packages described in the
Finance
task view.
-
Stochastic volatility
models
are handled by
stochvol
in a Bayesian framework.
-
Count time series
models
are handled in the
tscount
and
acp
packages.
ZIM
provides for Zero-Inflated Models for count time series.
tsintermittent
implements various models for analysing and forecasting intermittent demand time series.
-
Censored time series
can be modelled using
cents
and
carx.
-
Portmanteau tests
are provided via
Box.test()
in the stats package.
Additional tests are given by
portes
and
WeightedPortTest.
-
Change point detection
is provided in
strucchange
(using linear regression models),
in
trend
(using nonparametric tests),
and in
wbsts
(using wild binary segmentation).
The
changepoint
package provides many popular changepoint methods,
and
ecp
does nonparametric changepoint detection for univariate and multivariate series.
Online change point detection for univariate and multivariate time series is provided by
onlineCPD.
-
Time series imputation
is provided by the
imputeTS
package.
Some more limited facilities are available using
na.interp()
from the
forecast
package.
-
Forecasts can be combined
using
ForecastCombinations
which supports the most frequently used methods to combine forecasts.
forecastHybrid
provides functions for ensemble forecasts, combining approaches from the
forecast
package.
opera
has facilities for online predictions based on combinations of forecasts provided by the user.
-
Forecast evaluation
is provided in the
accuracy()
function from
forecast.
Distributional forecast evaluation using scoring rules is available in
scoringRules
-
Miscellaneous
:
ltsa
contains methods for linear time series analysis,
timsac
for time series analysis and control,
and
tsbugs
for time series BUGS models.
Frequency analysis
-
Spectral density estimation
is provided by
spectrum()
in the stats package, including the periodogram, smoothed periodogram and AR estimates.
Bayesian spectral inference is provided by
bspec.
quantspec
includes methods to compute and plot Laplace periodograms for univariate time series.
The Lomb-Scargle periodogram for unevenly sampled time series is computed by
lomb.
spectral
uses Fourier and Hilbert transforms for spectral filtering.
psd
produces adaptive, sine-multitaper spectral density estimates.
kza
provides Kolmogorov-Zurbenko Adaptive Filters including break detection, spectral analysis, wavelets and KZ Fourier Transforms.
multitaper
also provides some multitaper spectral analysis tools.
-
Wavelet methods
:
The
wavelets
package includes computing wavelet filters, wavelet transforms and multiresolution analyses.
Wavelet methods for time series analysis based on Percival and Walden (2000) are given in
wmtsa.
WaveletComp
provides some tools for wavelet-based analysis of univariate and bivariate time series including cross-wavelets, phase-difference and significanc tests.
biwavelet
can be used to plot and compute the wavelet spectra, cross-wavelet spectra, and wavelet coherence of non-stationary time series. It also includes functions to cluster time series based on the (dis)similarities in their spectrum.
Tests of white noise using wavelets are provided by
hwwntest.
Further wavelet methods can be found in the packages
brainwaver,
rwt,
waveslim,
wavethresh
and
mvcwt.
-
Harmonic regression
using Fourier terms is implemented in
HarmonicRegression.
The
forecast
package also provides some simple harmonic regression facilities via the
fourier
function.
Decomposition and Filtering
-
Filters and smoothing
:
filter()
in stats provides autoregressive and moving average linear filtering of multiple univariate time series.
The
robfilter
package provides several robust time series filters,
while
mFilter
includes miscellaneous time series filters useful for smoothing and extracting trend and cyclical components.
smooth()
from the stats package computes Tukey's running median smoothers, 3RS3R, 3RSS, 3R, etc.
sleekts
computes the 4253H twice smoothing method.
-
Decomposition
:
Seasonal decomposition is discussed below.
Autoregressive-based decomposition is provided by
ArDec.
rmaf
uses a refined moving average filter for decomposition.
-
Singular Spectrum Analysis
is implemented in
Rssa
and
spectral.methods.
-
Empirical Mode Decomposition
(EMD)
and Hilbert spectral analysis is provided by
EMD.
Additional tools, including ensemble EMD, are available in
hht.
An alternative implementation of ensemble EMD and its complete variant are available in
Rlibeemd.
Seasonality
-
Seasonal decomposition
:
the stats package provides classical decomposition in
decompose(), and STL decomposition in
stl().
Enhanced STL decomposition is available in
stlplus.
stR
provides Seasonal-Trend decomposition based on Regression.
-
x12
provides a wrapper for the
X12 binaries
which must be installed first.
x12GUI
provides a graphical user interface for
x12.
X-13-ARIMA-SEATS binaries are provided in the
x13binary
package,
with
seasonal
providing an R interface.
-
Analysis of seasonality
:
the
bfast
package provides methods for detecting and characterizing abrupt changes within the trend and seasonal components obtained from a decomposition.
npst
provides a generalization of Hewitt's seasonality test.
-
season:
Seasonal analysis of health data including regression models, time-stratified case-crossover, plotting functions and residual checks.
-
seas:
Seasonal analysis and graphics, especially for climatology.
-
deseasonalize:
Optimal deseasonalization for geophysical time series using AR fitting.
Stationarity, Unit Roots, and Cointegration
-
Stationarity and unit roots
:
tseries
provides various stationarity and unit root tests including Augmented Dickey-Fuller, Phillips-Perron, and KPSS.
Alternative implementations of the ADF and KPSS tests are in the
urca
package, which also includes further methods such as Elliott-Rothenberg-Stock, Schmidt-Phillips and Zivot-Andrews tests.
The
fUnitRoots
package also provides the MacKinnon test,
while
uroot
provides seasonal unit root tests.
CADFtest
provides implementations of both the standard ADF and a covariate-augmented ADF (CADF) test.
-
Local stationarity
:
locits
provides a test of local stationarity and computes the localized autocovariance.
Time series costationarity determination is provided by
costat.
LSTS
has functions for locally stationary time series analysis.
Locally stationary wavelet models for nonstationary time series are implemented in
wavethresh
(including estimation, plotting, and simulation functionality for time-varying spectrums).
-
Cointegration
:
The Engle-Granger two-step method with the Phillips-Ouliaris cointegration test is implemented in
tseries
and
urca. The latter additionally contains functionality for the Johansen trace and lambda-max tests.
tsDyn
provides Johansen's test and AIC/BIC simultaneous rank-lag selection.
CommonTrend
provides tools to extract and plot common trends from a cointegration system.
Parameter estimation and inference in a cointegrating regression are implemented in
cointReg.
Nonlinear Time Series Analysis
-
Nonlinear autoregression
:
Various forms of nonlinear autoregression are available in
tsDyn
including additive AR, neural nets, SETAR and LSTAR models, threshold VAR and VECM. Neural network autoregression is also provided in
GMDH.
bentcableAR
implements Bent-Cable autoregression.
BAYSTAR
provides Bayesian analysis of threshold autoregressive models.
-
tseriesChaos
provides an R implementation of the algorithms from the
TISEAN
project
.
-
Autoregression Markov switching models
are provided in
MSwM,
while dependent mixtures of latent Markov models are given in
depmix
and
depmixS4
for categorical and continuous time series.
-
Tests
:
Various tests for nonlinearity are provided in
fNonlinear.
tseriesEntropy
tests for nonlinear serial dependence based on entropy metrics.
-
Additional functions for nonlinear time series
are available in
nlts
and
nonlinearTseries.
-
Fractal time series modeling and analysis
is provided by
fractal.
fractalrock
generates fractal time series with non-normal returns distributions.
Dynamic Regression Models
-
Dynamic linear models
:
A convenient interface for fitting dynamic regression models via OLS is available in
dynlm;
an enhanced approach that also works with other regression functions and more time series classes is implemented in
dyn.
More advanced dynamic system equations can be fitted using
dse.
Gaussian linear state space models can be fitted using
dlm
(via maximum likelihood, Kalman filtering/smoothing and Bayesian methods),
or using
bsts
which uses MCMC.
Functions for distributed lag non-linear modelling are provided in
dlnm.
-
Time-varying parameter
models
can be fitted using the
tpr
package.
-
orderedLasso
fits a sparse linear model with an order constraint on the coefficients in order to handle lagged regressors where the coefficients decay as the lag increases.
-
Dynamic modeling
of various kinds is available in
dynr
including discrete and continuous time, linear and nonlinear models, and different types of latent variables.
Multivariate Time Series Models
-
Vector autoregressive (VAR) models
are provided via
ar()
in the basic stats package including order selection via the AIC. These models are restricted to be stationary.
MTS
is an all-purpose toolkit for analyzing multivariate time series including VAR, VARMA, seasonal VARMA, VAR models with exogenous variables, multivariate regression with time series errors, and much more.
Possibly non-stationary VAR models are fitted in the
mAr
package, which also allows VAR models in principal component space.
sparsevar
allows estimation of sparse VAR and VECM models,
while
BigVAR
estimates VAR and VARX models with structured lasso penalties.
Automated VAR models and networks are available in
autovarCore.
More elaborate models are provided in package
vars,
tsDyn,
estVARXls()
in
dse, and a Bayesian approach is available in
MSBVAR.
Another implementation with bootstrapped prediction intervals is given in
VAR.etp.
mlVAR
provides multi-level vector autoregression.
VARsignR
provides routines for identifying structural shocks in VAR models using sign restrictions.
-
VARIMA models
and
state space models
are provided in the
dse
package.
EvalEst
facilitates Monte Carlo experiments to evaluate the associated estimation methods.
-
Vector error correction models
are available via the
urca,
vars
and
tsDyn
packages, including versions with structural constraints and thresholding.
-
Time series component analysis
:
Time series factor analysis is provided in
tsfa.
ForeCA
implements forecatable component analysis by searching for the best linear transformations that make a multivariate time series as forecastable as possible.
PCA4TS
finds a linear transformation of a multivariate time series giving lower-dimensional subseries that are uncorrelated with each other.
-
Multivariate state space models
are implemented in the
FKF
(Fast Kalman Filter) package. This provides relatively flexible state space models via the
fkf()
function: state-space parameters are allowed to be time-varying and intercepts are included in both equations.
An alternative implementation is provided by the
KFAS
package which provides a fast multivariate Kalman filter, smoother, simulation smoother and forecasting.
Yet another implementation is given in the
dlm
package which also contains tools for converting other multivariate models into state space form.
dlmodeler
provides a unified interface for
dlm,
KFAS
and
FKF.
MARSS
fits constrained and unconstrained multivariate autoregressive state-space models using an EM algorithm.
All of these packages assume the observational and state error terms are uncorrelated.
-
Partially-observed Markov processes
are a generalization of the usual linear multivariate state space models, allowing non-Gaussian and nonlinear models. These are implemented in the
pomp
package.
-
Multivariate stochastic volatility models (using latent factors) are provided by
factorstochvol.
Analysis of large groups of time series
-
Time series clustering
is implemented in
TSclust,
dtwclust,
BNPTSclust
and
pdc.
-
TSdist
provides distance measures for time series data.
-
jmotif
implements tools based on time series symbolic discretization for finding motifs in time series and facilitates interpretable time series classification.
-
Methods for plotting and forecasting collections of hierarchical and grouped time series
are provided by
hts.
thief
uses hierarchical methods to reconcile forecasts of temporally aggregated time series.
An alternative approach to reconciling forecasts of hierarchical time series is provided by
gtop.
thief
Continuous time models
-
Continuous time autoregressive modelling
is provided in
cts.
-
Sim.DiffProc
simulates and models stochastic differential equations.
-
Simulation and inference for stochastic differential equations
is provided by
sde
and
yuima.
Resampling
-
Bootstrapping
:
The
boot
package provides function
tsboot()
for time series bootstrapping, including block bootstrap with several variants.
tsbootstrap()
from
tseries
provides fast stationary and block bootstrapping.
Maximum entropy bootstrap for time series is available in
meboot.
timesboot
computes the bootstrap CI for the sample ACF and periodogram.
BootPR
computes bias-corrected forecasting and boostrap prediction intervals for autoregressive time series.
Time Series Data
-
Data from Makridakis, Wheelwright and Hyndman (1998)
Forecasting: methods and applications
are provided in the
fma
package.
-
Data from Hyndman, Koehler, Ord and Snyder (2008)
Forecasting with exponential smoothing
are in the
expsmooth
package.
-
Data from Hyndman and Athanasopoulos (2013)
Forecasting: principles and practice
are in the
fpp
package.
-
Data from the M-competition and M3-competition
are provided in the
Mcomp
package. Data from the M4 competition are given in
M4comp.
-
pdfetch
provides facilities for downloading economic and financial time series from public sources.
-
Data from the Quandl online portal
to financial, economical and social datasets can be queried interactively using the
Quandl
package.
-
Data from the Datamarket online portal
can be fetched using the
rdatamarket
package.
-
Data from Cryer and Chan (2010)
are in the
TSA
package.
-
Data from Shumway and Stoffer (2011)
are in the
astsa
package.
-
Data from Tsay (2005)
Analysis of financial time series
are in the
FinTS
package, along with some functions and script files required to work some of the examples.
-
TSdbi
provides a common interface to time series databases.
-
fame
provides an interface for FAME time series databases
-
AER
and
Ecdat
both contain many data sets (including time series data) from many econometrics text books
Miscellaneous
-
dtw:
Dynamic time warping algorithms for computing and plotting pairwise alignments between time series.
-
ensembleBMA:
Bayesian Model Averaging to create probabilistic forecasts from ensemble forecasts and weather observations.
-
earlywarnings:
Early warnings signals toolbox for detecting critical transitions in time series
-
events:
turns machine-extracted event data into regular aggregated multivariate time series.
-
FeedbackTS:
Analysis of fragmented time directionality to investigate feedback in time series.
-
LPStimeSeries
aims to find "learned pattern similarity" for time series.
-
MAR1
provides tools for preparing ecological community time series data for multivariate AR modeling.
-
nets:
routines for the estimation of sparse long run partial correlation networks for time series data.
-
paleoTS:
Modeling evolution in paleontological time series.
-
pastecs:
Regulation, decomposition and analysis of space-time series.
-
ptw:
Parametric time warping.
-
RGENERATE
provides tools to generate vector time series.
-
RMAWGEN
is set of S3 and S4 functions for spatial multi-site stochastic generation of daily time-series of temperature and precipitation making use of VAR models. The package can be used in climatology and statistical hydrology.
-
RSEIS:
Seismic time series analysis tools.
-
rts:
Raster time series analysis (e.g., time series of satellite images).
-
sae2:
Time series models for small area estimation.
-
spTimer:
Spatio-temporal Bayesian modelling.
-
surveillance:
Temporal and spatio-temporal modeling and monitoring of epidemic phenomena.
-
TED:
Turbulence time series Event Detection and classification.
-
Tides:
Functions to calculate characteristics of quasi periodic time series, e.g. observed estuarine water levels.
-
tiger:
Temporally resolved groups of typical differences (errors) between two time series are determined and visualized.
-
TSMining:
Mining Univariate and Multivariate Motifs in Time-Series Data.
-
tsModel:
Time series modeling for air pollution and health.