help for whittle

Estimate long memory in a timeseries via Whittle's method

whittle
varname
[if exp]
[in range]
[,
powers(numlist)
detrend
exact
]

whittle is for use with time-series data.
You must tsset your data before using whittle; see help tsset. varname
may not contain gaps. varname may contain time series operators.
whittle supports the by prefix, which may be used to operate on each
time series in a panel. Alternatively, the if qualifier may be used to specify
a single time series in a panel.

Description

whittle
computes two forms of the Whittle (1962)
estimate of the long memory (fractional integration) parameter, d, of a
timeseries. If a series
exhibits long memory, it is neither stationary (I[0]) nor is it a unit
root (I[1]) process; it is an I(d) process, with d a real number.

The local Whittle estimator applies a log-likelihood approach to compute an estimate of d.
Alternatively, an exact local Whittle estimator, derived by Shimotsu and Phillips (2005) can be computed.
A linear trend can be extracted from the series.

A choice must be made of the number of harmonic ordinates to be included
in the estimator. The local Whittle estimate is an estimate of
the slope of the series' power spectrum in the vicinity of the zero
frequency; if too few ordinates are included, the slope is calculated from
a small sample. If too many are included, medium and high-frequency components
of the spectrum will contaminate the estimate.
whittle uses the default value of T^0.65 where T is the sample size.

The command displays the d estimate, number of lags, conventional
standard error, and asymptotic standard error.

Options

powers(numlist) specifies a list of one or more fractional values for the power of sample size T to be
included in computing the local Whittle estimate. This overrides the default value of T^0.65, chosen from
sample size.

trend specifies that a linear trend should be removed from the series before
the local Whittle estimate is computed.

exact specifies that the exact local Whittle estimator should be computed.

Examples

. use http://fmwww.bc.edu/ec-p/data/wooldridge/nile.dta, clear

. whittle nile

. whittle nile, detrend

. whittle nile, exact

. whittle nile, powers(0.5 0.6 0.7)

. whittle nile, powers(0.5 0.6 0.7) exact

. webuse pennxrate,clear

. keep if id<10

. by id: whittle realxrate, exact

Authors

Christopher F. Baum, Boston College, USA

baum@bc.edu

Stan Hurn, Queensland University of Technology, Australia

s.hurn@qut.edu.au

Kenneth Lindsay, Glasgow University, UK

kenneth.lindsay@glasgow.ac.uk

References

Shimotsu, K., and P. Phillips. 2005. Exact local Whittle estimation of fractional
integration. Annals of Statistics 33: 1890–1933.

Whittle, P. 1962. Gaussian estimation in stationary time series.
Bulletin of the International Statistical Institute 39: 105–129.

Also see

On-line: tsset, arfima,
gphudak (if installed), roblpr (if installed), modlpr (if installed)