I’ve been pondering since this morning, what’s up with this heat?

Near-gratuitous One Piece reference (watch every episode here!). One Piece is awesome. Make a note. Awesome.

So. Today’s weather:

Walking around with the missus (we went to Grant’s tomb – boring, but, in their defence, closed for the holiday. Still), she commented on the heat, its unseasonality, how freezing cold it had been in her youth, etc. Honestly, she should have known better – a statistician and a contrarian for a husband? Crazy idea.

My counter-arguments: (1) that the temperature on the day of Thanksgiving is a variable, like any other. The week of Thanksgiving, maybe. But the day? Temperature and time both are continuous variables. A single day is just way too precise to pin something like that on; (2) my wife was probably remembering particularly cold days from her youth, which was affecting her memory of the true average temperatures for this period.

So, being the manner of econometrician that I am. After dinner, I jumped on the web and started looking. I found my way to Almanac.com, and started pulling out the temperature for all of the November 22nds since the birth of my wife (1981; a fine year for pretty girls).

I had to jump from Central Park to JFK in 1994 (no Central Park data past then, but I checked a handful of the dates since, and there’s no apparent measurement problem). Descriptive statistics:

So, what do I do? I start looking for 60 degrees (today’s) in the 95% Confidence Interval for the mean temperature on Thanksgiving Day.

$ latex begin{eqnarray*}
95\%CI_{\mu } &=&\overline{x}\pm t_{.025,26}\times \sigma _{\overline{x}} \\
&=&\overline{x}\pm t_{.025,26}\times \frac{\sigma }{\sqrt{n}} \\
&=&45.4\pm 2.056\times 1.76 \\
&=&41.78\text{ to }49
\end{eqnarray*} $

WordPress’ latex plug-in is ass. It was supposed to look like this:

So today’s 60 degrees just (just) misses out. Like fun it does.

The conclusion: Confidence Interval conclusions can vary, but we can say that, for example, 95% of Thanksgivings will not have a mean temperature of 60 degrees (97.5% of them will be less than 60 degrees – by a long way). We are 95% certain that the population mean (the true mean for Thanksgiving Day) is not 60 degrees.

Is today’s temperature therefore extreme? We can visit the 99% confidence interval:

$ latex begin{eqnarray*}
99\%CI_{\mu } &=&\overline{x}\pm t_{.005,26}\times \sigma _{\overline{x}} \\
&=&\overline{x}\pm t_{.005,26}\times \frac{\sigma }{\sqrt{n}} \\
&=&45.4\pm 2.779\times 1.76 \\
&=&40.51\text{ to }50.29
\end{eqnarray*} $

Or, again,

Again, um, just? Barely. There is less than a 1% chance that, on any given Thanksgiving Day, the mean temperature will be this far from the average (and less than half of one percent that it will be this high). Statistically, it was an extreme event.

There is far less than a 1% chance: the p-value for an average temperature of 60 degrees is, in fact, basically 0 (the t-statistic being 8.3)

I managed a partial victory. The two lowest days – and the only two below 30 degrees – occurred in my wife’s youth, and the lowest occurred the year she was freezing cold out in the parade itself. So I scored a minor point.

A caveat is the mean. I used the entire series. This is to say, a caveat to the numbers – that result isn’t going anywhere.

Suppose I used only the Thanksgivings up until this one? Today’s was the maximum for the series: the next highest was 59 degrees. Cutting out today’s 60 degrees lowers the average to 44.8, and the standard deviation to 8.84. It also lowers the sample size, increasing the “critical value” t-statistic slightly (due to the lower degrees of freedom) as well as the standard error. The new 99% Confidence interval narrows, slightly, but also shifts downwards: 40 degrees to 49.6. Either way, 60 degrees (new t-statistic 8.77) is still nowhere near likely to be another average temperature in a hurry.

“The subprime crisis is the baby of Alan Greenspan: excess global liquidity,”

That’s not the story (I brought you here under false pretenses). What a great quote, though.

A huge spike in global inflation generated by China and India could lead to 1970s-style hyper-inflation in Australia, one of Australia’s largest asset managers, Queensland Investment Corporation, has warned.

The analysis of QIC’s chief executive, Doug McTaggart, charts a path to spiralling inflation, huge economic consequences and plummeting stockmarkets – with precious little central banks will be able to do about it.

…

Mr McTaggart’s argument is built on growing evidence that China and India are at the point of skills shortages that are driving up wage costs, with potentially dire consequences for inflation.

Deutsche Bank South Asia regional economist Sanjeev Sanyal, in Singapore, says: “It’s already the case that both these countries are seeing huge increases in salaries.

“The question is: can they they get productivity gains large enough in other areas to offset these increases?”

In a private briefing to heads of global fund manager associations in Sydney this month, Mr McTaggart outlined his bleak view that as a result of the skills shortages China and India are poised to become exporters of inflation.

“[Then] we get inflation in Australia and the US, and probably at quite high levels, and it is outside the control of the central banks,” Mr McTaggart says.

“They will be forced to raise interest rates savagely to extract the liquidity from the market in order to try to bring it under control, and I think they will fail.

“You can imagine the 1970s’ double-digit inflation, double-digit unemployment and recessionary circumstances for a long period.”

The quote came from the key to this conclusion: that central banks don’t much control the money supply any longer – hardly unexpected, given the transition to debt-backed money supplies in so many of our economies.

In Mr McTaggart’s analysis, central banks have lost the ability to respond to the consequences of hyper-inflation because their control over the money supply has been decoupled.

He said the US Federal Reserve, in particular, had responded to crises by pumping up global liquidity.

But excess liquidity had found expression in asset bubbles including the 2000 dotcom boom and the most recent subprime problems in the US.

I’ve thought, for a long time, that the US, certainly, faced this threat – not the global economy, though.

Writing exams

I’ve managed to pull questions from NBA/WNBA data and this paper on hedge funds. I’m making an effort, this time. I’m quite pleased with the exam so far (this is Stats: Economics is still to be written).

For now, then, Penny Arcade:

Also, this counts as a post about Hannah Montana. That’s 4, now. One more and I shall buy her CD just to freak out my wife. Ooh! Or my students. Yeah…