The rescaled range – or range over standard deviation – analysis was first used by Harold Edwin Hurst when he analyzed the Nile River in the first half of the 20th century. Later on several modifications have been applied to make the analysis more robust and quantitative, especially as determination of the Hurst exponent and pertaining confidence intervals are concerned. We start the package with a collection of methods and options around Hurst analysis.
By now, long memory processes have made it into introductory textbooks on time series and the notion is known to a broad audience. However, only the very basic concepts are touched and as applies to all of statistics, a naive use of only the most common estimators and tests can entail misleading results.
For long memory processes, autocorrelations are not summable. Intermediate memory processes share some properties with the former but have summable autocorrelations. To name but a few challenges when dealing with intermediate and long memory processes, care has to be taken when
- applying asympotic thresholds to tests on series of finite size, as asympotics are sometimes reached only for very long time series, that are unrealistic, e.g. for financial time series;
- separating short memory effects, such as e.g. autoregressive processes with finite order, from long memory effects, as estimators may be heavily biased when short memory is present;
- applying some tests (e.g. the modified rescaled range test) to samples of finite size;
- discerning long memory from structural breaks;
- performing rolling or time varying analysis, as choosing window size is not straight forward.
The package includes a wide variety of time- and frequency domain estimators and tests. Special focus is given to finite size effects as key findings of research or financial analytics may be seriously affected. Accepted simulation techniques in literature are included in the package. Broadly used time series objects are accepted as input and output.