smile.timeseries.package-info Maven / Gradle / Ivy
/*
* Copyright (c) 2010-2021 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Smile is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Smile. If not, see
* 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.
*
* @author Haifeng Li
*/
package smile.timeseries;