Package smile.timeseries
Methods for time series analysis may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and wavelet analysis; the latter include auto-correlation and cross-correlation analysis. In the time domain, correlation and analysis can be made in a filter-like 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_t-l 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.
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ClassDescriptionAutoregressive model.The fitting method.Autoregressive moving-average model.Portmanteau test jointly that several autocorrelations of time series are zero.The type of test.Time series utility functions.