Interface  Description 

TimeSeries 
Time series utility functions.

Class  Description 

AR 
Autoregressive model.

ARMA 
Autoregressive movingaverage model.

BoxTest 
Portmanteau test jointly that several autocorrelations of time series
are zero.

Enum  Description 

AR.Method 
The fitting method.

BoxTest.Type 
The type of test.

Methods for time series analysis may be divided into two classes: frequencydomain methods and timedomain methods. The former include spectral analysis and wavelet analysis; the latter include autocorrelation and crosscorrelation analysis. In the time domain, correlation and analysis can be made in a filterlike manner using scaled correlation, thereby mitigating the need to operate in the frequency domain.
The foundation of time series analysis is stationarity. A time series
{r_t}
is said to be strictly stationary if the joint
distribution of (r_t1,...,r_tk)
is identical to that of
(r_t1+t,...,r_tk+t)
for all t, where k is an arbitrary
positive integer and (t1,...,tk)
is a collection of
k positive integers. In other word, strict stationarity requires
that the joint distribution of (r_t1,...,r_tk)
is
invariant under time shift. This is a very strong condition that
is hard to verify empirically. A time series {r_t}
is weakly stationary if both the mean of r_t and the covariance
between r_t and r_tl are tim invariant, where l is an arbitrary
integer.
Intuitively, a stationary time series is one whose properties do not depend on the time at which the series is observed. Thus, time series with trends, or with seasonality, are not stationary — the trend and seasonality will affect the value of the time series at different times. On the other hand, a white noise series is stationary — it does not matter when you observe it, it should look much the same at any point in time. Note that a time series with cyclic behaviour (but with no trend or seasonality) is stationary.
Differencing is a widely used data transform for making time series stationary. Differencing can help stabilize the mean of the time series by removing changes in the level of a time series, and so eliminating (or reducing) trend and seasonality. In addition, transformations such as logarithms can help to stabilise the variance of a time series.