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».
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).
None of these profiles can be predicted with any certainty but
the stochastic trends are there.
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.
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.
Thus, I am distinguishing between a deterministic trend (which includes both linear and non-linear trends) and
a stochastic trend.
«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.
This representation is flawed both statistically, because time series that contain
a stochastic trend can not be approximated by a deterministic trend (13), and historically, because the time trend overstates gains in radiative forcing during the 1950's and overstates gains during the last 10 y (Fig. 1).
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.
Note also, that the Augmented Dickey Fuller test is designed to test exactly what you posted above, namely, whether it is likely that the underlying DGP is deterministic (trend) or if the series contains
a stochastic trend.
===================== 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.
With the above in mind, I will proceed to show you what you have actually simulated using my simple 4 parameter (i.e. ARIMA (3,1,0)-RRB-
stochastic trend estimate.
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).
Forecasting confidence intervals for trend stationary and
stochastic trend specification over 1885 - 2008, with parameter estimates based on 1881 - 1935 sample, here, with accompanying figures here.
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.
Future winter SST forecasts are projected linear
trends with an added
stochastic component derived from the empirical noise.
Although the technical explanation for
stochastics is a bit complicated, the general theory is that a market
trending higher may see closes near the highs, while a market that is
trending lower may see closes near the lows.
I looked at the
Stochastic Oscillator and price action to decipher the
trend to avoid adding indicators.
For simplicity, you can use price action and the
Stochastic Oscillator to judge the market
trend.
We have adapted it for swing trading by observing the weekly chart for
trends and the daily chart for
stochastic entries.
The ADX helps identify whether the market is in a
trend or rangebound, while
Stochastic indicates potential overbought and oversold conditions that tend to precede a reversal.
If the
Stochastic cross alert custom indicator red arrow appears above price bars, then a bearish
trend is in the horizon and you should be gathering your profits for an exit.
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.
You are referring to a
trend over half a century but we are talking about tests using stationary
stochastic simulations.
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.
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.
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»).
I want to understand better how it is you decide that GHGs are responsible for a deterministic forced
trend when you have this powerful but poorly understood
stochastic noise rocess operating in the background.
The record shows large annual variation but no long term
trend, which suggests a
stochastic process with low autocorrelation.
In your earlier reply to me you hinted that your examples of
stochastic vs deterministic
trends were only for illustrative purposes.
However, if the information in that sample period is statistically consistent only with a
stochastic I (1) process then there is no valid reason provided by the data alone to have any confidence that «
trend» can be projected to other periods.
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.
In other words, global temperature contains a
stochastic rather than deterministic
trend, and is statistically speaking, a random walk.
Allow me to pick up where you left off and provide some more illustrations, because I still don't have the feeling that people understand the fundamental difference between
stochastic and deterministic
trends.
Stochastic and RSI
trend lines reveal similar overbought conditions ahead.
On the other hand, the Slow
Stochastic momentum indicator is steadily pulling from the oversold territory to show that, the bulls could find an entry and continue with the upside
trend.