### Trend since 1998—significant??

I had a question sent to me about the trend since 1998. As many of you know, my last post included an analysis which showed that the linear regression trend since 1998 was statistically significant.

My questioner asked if I had accounted for autocorrelation in my analysis. The short answer is "No, I did not." The reason? According to my analysis, it wasn't necessary.

Here are my methods and R code.

#Get coverage-corrected HadCRUT4 data and rename the first two columns

CW<-read.table("http://www-users.york.ac.uk/~kdc3/papers/coverage2013/had4_krig_annual_v2_0_0.txt", header=F)

names(CW)[1]<-"Year"

names(CW)[2]<-"Temp"

#Analysis for autocorrelation—I check manually as well but so far the auto.arima function has performed admirably.

library(forecast)

auto.arima(resid(lm(Temp~Year, data=CW, subset=Year>=1998)), ic=c("bic"))

The surprising result?

trend.98<-lm(Temp~Year, data=CW, subset=Year>=1998)

summary(trend.98)

Trends versus start year. Error bars are the 95% confidence intervals. |

Here are my methods and R code.

#Get coverage-corrected HadCRUT4 data and rename the first two columns

CW<-read.table("http://www-users.york.ac.uk/~kdc3/papers/coverage2013/had4_krig_annual_v2_0_0.txt", header=F)

names(CW)[1]<-"Year"

names(CW)[2]<-"Temp"

#Analysis for autocorrelation—I check manually as well but so far the auto.arima function has performed admirably.

library(forecast)

auto.arima(resid(lm(Temp~Year, data=CW, subset=Year>=1998)), ic=c("bic"))

The surprising result?

Series: resid(lm(Temp ~ Year, data = CW, subset = Year >= 1998))I was expecting something on the order of ARIMA(1,0,1), which is the autocorrelation model for the monthly averages. Taking the yearly average rather than the monthly average effectively removed autocorrelation from the temperature data, allowing the use of a white-noise regression model.

ARIMA(0,0,0) with zero mean

sigma^2 estimated as 0.005996: log likelihood=18.23

AIC=-34.46 AICc=-34.18 BIC=-33.69

trend.98<-lm(Temp~Year, data=CW, subset=Year>=1998)

summary(trend.98)

Call:The other surprise? That the trend since 1998 was significant even with a white-noise model. Sixteen data points is not normally enough to reach statistical significance unless a trend is very strong.

lm(formula = Temp ~ Year, data = CW, subset = Year >= 1998)

Residuals:

Min 1Q Median 3Q Max

-0.14007 -0.05058 0.01590 0.05696 0.11085

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -19.405126 9.003395 -2.155 0.0490 *

Year 0.009922 0.004489 2.210 0.0443 *

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.08278 on 14 degrees of freedom

Multiple R-squared: 0.2587, Adjusted R-squared: 0.2057

F-statistic: 4.885 on 1 and 14 DF, p-value: 0.04425

Temperature trend since 1998 |

Thanks for the additional analysis!

ReplyDeleteThis gives me an excellent idea for a parody post.

ReplyDeletePost the link of the parody when you have write it. I'd love to read it.

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