UAH v6.1 Global Temperature Update for January, 2025: +0.46 deg. C

Here’s the Tokyo station, as frequently featured on this site.

1979 was the warmest year up to that point, by almost 1°C.

BTW, do you have a source for that data? And is there a reason why you’ve split it into two sections and missed out 8 years in between?

Here’s the BEST figures, which only go up to 2020.

Could you provide a link for the JMA data? It might just be looking in the wrong place, but all I can find on their website is individual stations or global data.

“There was some sort of step change in 1990”

So you tried to pretend the warming hadn’t happened. And still dodging the fact that 1979 was not one of the coldest years in Japan.

Here’s the full data for Hachijojima, with a black dotted line indicating 1979, and a red line indicating where, according to JMA, there is “data inhomogeneity caused by changes in instrumentation, observation methods and/or site location”.

And here’s the full data for Naze, which definitely shows a rise since 1930.

“Show us a function of ‘t’ in years as a predictor that accurately gives a value of the dependent variable.”

The function doesn’t predict the variables. It describes the mean value at any point in time. The variable will be f(t) + e_t, where e_t is a random value.

“You either didn’t read the article closely or didn’t understand it.”

Stop with this patronizing nonsense – it just makes you look like the idiot. Your quote is just describing the formal definition I gave.

“You do realize that a stochastic process is a random process, right?”

You do realize how big an idiot you sound like, right? What else would you think a stochastic process meant?

“If you remove the underlying trend that is a function of time, you just removed the temperature data.”

No.

“You are trying to show that a linear regression line is a stationary process.”

Idiot. You keep claiming to understand this, but keep demonstrating you don’t.

“It IS a straight line”

The function does not have to be a straight line. It told you that in the first thing you pasted

The trend does not have to be linear.

“It is a “line of best fit.”

Yes, and?

“Linear regression was originally used to verify that a proposed functional relationship was in fact linear.”

Citation required.

“Time and temperature have no functional relationship.”

You still don’t know what functional relationship means, and this is a deflection from stationarity, which is what we were discussing.

“If f(t) is not a constant, i.e. the value of the mean is shifting over time, then it fails the stationarity test”

and

“If f(t) is the MEAN value then not only does it have to be a straight line in order to have stationarity, it has to be a horizontal straight line.”

Yes. That’s why it’s trend-stationary, not stationary.

“Tell us the functional relationship between time and temperature that will allow you to tell me what the temperature will be.”

You quote the definition of a functional relationship, but still don;t understand what it means.

“The increase in temperature typically described is a random walk with drift.”

That’s your claim. It makes no sense that temperature, let alone global temperature, follows a random walk. The implication would be that last years record temperature is the new normal. There would be a greater 50% chance that 2025 will be warmer than 2024. In the real world temperatures tend towards an equilibrium. That equilibrium is the trend.

“This results in a steadily increasing trend line, i.e. a linear regression best-fit line.”

With a unit root, there’s no guarantee of that. It depends on the size of your ɑ and e.

Here are 20 runs using your model with ɑ = 0.01, and e coming from a normal distribution with σ = 0.2. Over 100 time units, the trend given by ɑ, would mean an increase of 1. In these graphs the blue line shows the starting point and the red line the expected end point.

It’s quite possible that a positive deterministic trend combined with a random walk results in a negative trend. That’s the problem with unit roots.

“The problem is that unless ɑ is a constant you still won’t get stationarity.”

Once again, we are talking about trend-stationarity, not stationarity.

“A hockey stick is not trend-stationary.”

If by “hockey stick” you mean it’s warming faster now than it was in the past – yes, that absolutely can be trend-stationary. You keep demonstrating you just don’t understand what these words mean. So I’ll just repeat the Wiki page on it in the vain hope you will try to educate yourself.

In the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process.[1] The trend does not have to be linear.

https://en.wikipedia.org/wiki/Trend-stationary_process

“You apparently can’t answer my question about what the temperature will be on March 1, 2026 so how do you justify claiming that there is a functional relationship between temperature and time?”

You still seem to think that a function has to be known to exist. A function is simply the mapping of one value to another.

“No, that’s what it *is*.”

You assert that a temperature time series has a unit root. That’s just your claim, and one that is demonstrably false. Show me the statistical test you used to demonstrate what ever actual time series you are talking about has a unit root, then we can discuss it. Otherwise it’s just you making wild nonphysical claims, or more likely you just don;t understand what the maths means.

“Of course it makes sense. A random walk, i.e. natural variation, coupled with a drift up or down. ”

And here you demonstrate the lack of understanding. A random walk is not natural variation around a trend. It’s the cumulative sum of all natural variation.

“Then where does the hockey stick come into play?”

What “hockey stick”. You still haven’t explained what time series you are talking about. If you mean something that has an accelerated warming rate, that’s where the non-linear trend comes into play.

“You are describing “reversion to the mean”, i.e. a variable with a constant mean.”

It’s reversion to the trend. The mean changes over time.

“You have now devolved to repeating what I just told you as if it were your idea.”

What you told me was:

This results in a steadily increasing trend line, i.e. a linear regression best-fit line.

What I said, and demonstrated, was that with a unit root that wasn’t necessarily true.

“The problem is that you can’t get a hockey stick with a constant ɑ.”

You can with a unit root. I’m not sure why you are even arguing this as I assume that was the point you were trying to make in the first place. Once again you demonstrate you don;t actually understand what you are arguing.

“If the trend is not stationary over time, i.e. the drift is ɑ^d, then you can’t use a *linear* regression to project the trend.”

That should be “e.g.” not “i.e.”. I’ve still no idea what “linear regression” you are arguing about. The graph Jim was objecting to had no linear regression, I’ve pointed out the problems with trying to use a simple linear regression for non-linear data. Monkton keeps making that mistake.

But you are still wrong. You can easily use linear regression on a polynomial.

“You keep circling back to assuming that the drift is constant while refusing to actually state that assumption. ”

Please quote the specific example where I’ve done that. What I’ll say is that a straight line is often the best starting point. But you always have to look for the possibility that the line is changing.

“What “unit root”?”

Y_t = Y_(t – 1) + ɑ + e_t

I’ve highlighted it for you.

Rest of you comment is just a load of strawmen. If you disagree with something you need to point tot he actual thing I’ve said or done.

“Unit root series are not always trend stationary.”

They are never trend stationary. That’s the point.

“If ɑ is also a function of t, which it is for a hockey stick, then you probably can’t have a unit root.”

You can. See all those graphs I produced using your model.

“You keep trying to justify your linear regression trends of temperature but keep failing.”

Again, Which particular linear equation are you talking about?

“My other points are not strawmen”

They are when you keep attacking me for things I have not done. I’ll ask again without a hope of you responding – point to any specific time you think I’ve tried to use a linear equation to predict more than a year into the future.

That’s why it’s a tricky subject.

I’m still not sure what the issue is here though. I am just saying one particular data set shows warming, when Jim said it didn’t. I’m not saying anything about the cause or trying to predict the future trend from it.