Minnesota’s weather is “normal”

The bulk of my math-brain today was focused on finishing a write-up of an analysis of Minneapolis-St. Paul daily temperatures. It’s a nice time series that I found at the University of Dayton’s temperature archive, conveniently available as a csv file. Minnesota temperatures look like this:

Daily temperatures at MSP

Daily temperatures at MSP

Mildly sinusoidal. Turns out there’s not much linear trend over this time period, even though in many cities there has been a significant warming trend over the last 15-20 years. (I wonder if this needs more analysis for MSP — I just did some basic trend analysis.) And remarkably, you can do a pretty good Fourier series fit for this data!

Data with Fourier series forecast at the end

Data with Fourier series forecast at the end

The blue part at the end is a forecast of temperatures from the Fourier series I fit (using the “forecast” package in R).

Obviously the temperature data is much fuzzier than the Fourier series: what’s the noise? We can look at what the noise looks like by plotting the residuals:

ResidualsPlot

 

Hm. Looks like sometimes our weather is much colder than predicted — what a surprise. How much? Let’s look at a density plot of those residuals:

Density plot of residuals

Density plot of residuals

Dang — that almost looks normal! And hence the title.

 

 

 

Of course it’s not quite normal: this is the land of Lake Wobegon. If all the children are above average, it’s because

QQ plot of standardized residuals from rugarch

QQ plot of standardized residuals from rugarch

we’re close to normal, but a little bit skewed…. (Read about QQ plots at Wikipedia or NIST.)

One thought on “Minnesota’s weather is “normal”

Leave a Reply

Your email address will not be published.