This claim isn't derived from his research *, but is his judgement, based on the same kind of assessment
of stochastic trends that economists do, and very similar to the judgements involved in relating smoking and cancer.
We focus on the presence or absence
of stochastic trends.
The ambiguity on the unit root question in paper discussed, stems from the use of the PP test, which I believe my simulations disqualifies it in light
of my stochastic trend specification (see previous comment).
Note that the whole purpose
of that stochastic trend analysis (with plot) was to juxtapose your analysis (which assumes stationarity under the H0) with my analysis (which doesn't assume stationarity under the H0).
Not exact matches
The methodology developed in Lovejoy's two recent papers could also be used by researchers to help analyze precipitation
trends and regional climate variability and to develop new
stochastic methods
of climate forecasting, he adds.
In essence, technical indicators incorporated into your live charts like volume indicators,
trend lines, Fibonacci levels,
stochastic oscillators etc., can block out the market noise, forming a better picture
of the markets and
trends that lie ahead.
I have a nice little swing trade strategy
of late that buys stong stocks on the dip, and sells them after a week or two when they revert to their
trend following some basic RSI,
stochastics and vol.
This is why we decomposed the temperature data into a slow, non-linear
trend line (shown here) and a
stochastic component — a standard procedure that even makes it onto the cover picture
of a data analysis textbook, as well as being described in a climate time series analysis textbook.
That requires a model
of the
stochastic variations in the data and a precise definition
of, what the
trend means in the particular consideration.
«The seasonal unit root test makes it possible to determine the
stochastic trend of monthly temperatures using an autoregressive model,» says Prof. Wai Ming To.
What you are looking at, David, is more function
of stochastic noise than underlying
trend.
Nevertheless, the salutary aspect
of the GISP 2 data is the clear indication it provides
of a gentle, truly secular cooling
trend since the Holocene optimum, overlain by weakly stationary, strongly structured, quasi-Gaussian
stochastic variations whose ordinate distribution and power - spectrum both diverge from anything resembling a Poisson process
of abrupt jumps.
This inability has little effect on the results — statistical estimates are based on the notion
of cointegration, which uses
stochastic trends as fingerprints to match temporal changes in temperature and radiative forcing.
Cointegration indicates that internal climate variability and / or the omission
of some components
of radiative forcing (e.g., stratospheric water vapor, black or organic carbon, nitrite aerosols, etc.) do not impart a
stochastic or deterministic
trend that would interfere with the interpretation
of temperature changes at the subdecadal scale (SI Appendix).
Obtain future
stochastic projections by extending the
trend (e.g. by extrapolation) and adding back random «realisations»
of the noise model («Monte Carlo simulation»).
None
of these profiles can be predicted with any certainty but the
stochastic trends are there.
With proxy data that has a high auto correlation or long term persistence one can obtain extended lengths
of time where a
stochastic trend can appear.
In your earlier reply to me you hinted that your examples
of stochastic vs deterministic
trends were only for illustrative purposes.
===================== Note that this is a DIFFERENT discussion than the discussion about the PRESENCE
OF A UNIT ROOT, as the ARIMA (0,1,2) specification also describes a
stochastic trend.
My dig about things being inconvenient was more intended for the humour than anything else, but I note you still refer to «unphysical conclusions» rather than «unphysical observations» i.e. the
stochastic nature
of this
trend.
If the goal is to see whether the temperature is forced (deterministic) as opposed to random (
stochastic), than the best
trend estimate is to take the estimate
of the net radiative forcing.
However, and more to the point, both
of these structures in fact represent
stochastic trends, so I have no clue what all the huffing and puffing is about (well, I do have a clue, but it has nothing to do with science).
For fun i browsed some
of his papers, that you could find online, and i found a lot
of «statistical significant temperature
trends» and very little «unit root» and «
stochastic trends».