We use the data from CRU, and input it into R using the code in the post R Code to Read CRU Data. The initial approach to testing whether global temperatures from CRU is to run a Dickey-Fuller Test for Unit Root.
The augmented Dickey-Fuller test checks whether a series has a unit root. The default null hypothesis is that the series does have a unit root.
A unit root refers to the coefficeint b in the sequence being greater than one and leads to series with a tendency to wander infinitely far from the starting point, and display ‘trendiness’ or the appearence of trends with no specific driving variable.
Xt = bXt-1 + e
The adf.test() command needs the tseries library for this test.
R automates the process of finding, downloading and installing libraries. In Windows, you are presented with a list of packages after selecting a CRAN mirror site (if you are connected to the internet). Then, on selecting xseries all the required packages are loaded. In this case:
package 'scatterplot3d' successfully unpacked and MD5 sums checked package 'mlbench' successfully unpacked and MD5 sums checked package 'randomForest' successfully unpacked and MD5 sums checked package 'SparseM' successfully unpacked and MD5 sums checked package 'xtable' successfully unpacked and MD5 sums checked package 'fBasics' successfully unpacked and MD5 sums checked package 'sandwich' successfully unpacked and MD5 sums checked package 'acepack' successfully unpacked and MD5 sums checked package 'lmtest' successfully unpacked and MD5 sums checked package 'car' successfully unpacked and MD5 sums checked package 'dynlm' successfully unpacked and MD5 sums checked package 'e1071' successfully unpacked and MD5 sums checked package 'leaps' successfully unpacked and MD5 sums checked package 'oz' successfully unpacked and MD5 sums checked package 'Hmisc' successfully unpacked and MD5 sums checked package 'chron' successfully unpacked and MD5 sums checked package 'fCalendar' successfully unpacked and MD5 sums checked package 'strucchange' successfully unpacked and MD5 sums checked package 'DAAG' successfully unpacked and MD5 sums checked package 'quadprog' successfully unpacked and MD5 sums checked package 'zoo' successfully unpacked and MD5 sums checked package 'its' successfully unpacked and MD5 sums checked package 'tseries' successfully unpacked and MD5 sums checked The downloaded packages are in C:Documents and SettingsDavid StockwellLocal SettingsTempRtmp11853downloaded_packages updating HTML package descriptions
The next steps are to load the library, get the CRU data into a variable and run the Dickey-Fuller Test for Unit Root.
> library(tseries) > d adf.test(d) Augmented Dickey-Fuller Test data: d Dickey-Fuller = -6.3935, Lag order = 12, p-value = 0.01 alternative hypothesis: stationary Warning message: p-value smaller than printed p-value in: adf.test(d)
We can try this again with annual values.
d adf.test(d) Augmented Dickey-Fuller Test data: d Dickey-Fuller = -2.0938, Lag order = 5, p-value = 0.5372 alternative hypothesis: stationary
For comparison we can apply the test to random numbers which don’t have a unit root, and the cumulative sum of random numbers that do. i.e.
adf.test(rnorm(1000)) adf.test(cumsum(rnorm(1000))
The results are similar to the results for monthly and annual temperature. Monthly temperatures don’t have a unit root and annual temperatures do have a unit root. This preliminary testing suggests annual temperatures are indistinguishable from a random walk. This doesn’t mean that they are, as more rigorous testing may succeed in rejecting the null hypothesis. The post Scale Invariance for Dummies suggests that temperatures are actually very close, but slightly less than the unit root.
Pingback: escort vienna,
Pingback: ta mere la chauve
Pingback: donna cerca uomo roma
Pingback: printable coupons
Pingback: comprar mexico
Pingback: kliknij tutaj
Pingback: warsztaty kulinarne
Pingback: Nue Design
Pingback: ifi it
Pingback: fmtrader scam
Pingback: fmtrader scam
Pingback: àìéøï òåáã äéîåøéí
Pingback: bforex ??????
Pingback: seo
Pingback: anunt
Pingback: page rank google
Pingback: Maui Wedding Photography
Pingback: ehpad
Pingback: Glenn Lyvers
Pingback: backlinks indexer is a scam
Pingback: sylwester 2015
Pingback: polecam
Pingback: The queen uses us to fix her toilet
Pingback: agenzia seo
Pingback: std testing
Pingback: blood testing
Pingback: Birmingham escorts,
Pingback: orjinal lida
Pingback: piese
Pingback: Pro plates
Pingback: fmtrader ???
Pingback: pinganillo
Pingback: calosc o depilacji
Pingback: novelty techpoint
Pingback: zobacz oferte
Pingback: Great Clips Prices
Pingback: fearless presentations
Pingback: Birmingham escorts
Pingback: business
Pingback: Birmingham escort agency.
Pingback: Komodo Liveaboard
Pingback: masaj
Pingback: best security site
Pingback: ????? ????
Pingback: meskieinfo.soup.io
Pingback: hard mouth
Pingback: oferta
Pingback: arganolie
Pingback: baby fair