Lambda the Ultimate

From Stephen Wolfram's announcement:

But today I am thrilled to be able to announce that after only five months the prize is won--and we have answer: the Turing machine is in fact universal!

...

We plan an official prize ceremony in a few weeks--fittingly enough, at Bletchley Park, where Alan Turing did his wartime work.

But for now I'm just thrilled to see such a nice piece of science come out.

It's a very satisfying way to spend $25,000.

The universal Turing machine in question is a cellular automaton with two states and three colors.

Situation:
I had tired a 1000-data generated by random error(i.i.d.), then I sub it into different unit root tests. I got different results among the tests. The following are the test statistics I got:

For R project:
adf.test @ tseries ~ -10.2214 (lag = 9)
ur.df @ urca ~ -21.8978
ur.sp @ urca ~ -27.68
pp.test @ tseries ~ -972.3343 (truncation lag =7)
ur.pp @ urca ~ -973.2409
ur.kpss @ urca ~ 0.1867
kpss.test @ tseries ~ 0.1867 (truncation lag =7)

For MATLAB:
(adf test) ~ -0.43979

Questions:
1. Tests under same test name, say Phillips-perron test (pp.test & ur.pp), they have different test statistics. Why?
2. Don't the Phillips-perron test based on the Dickey-Fuller distribution table? How the value being so negative (-9xx)?
3. What is truncation lag? Is it the same with lag terms?

I've learned a lot from LTU over the past few years, and I'm very grateful for all the discussions and the patience. LTU has inspired me to create my own language, of which I only have an interpreter so far. To help organize my thoughts, and to spread the word about advanced programming languages to a wider audience, I've written a post explaining some poorly understood features (outside of academia or LTU at least) which I think will become increasingly important in the coming years.

On the Importance of Purity:

The benefits of advanced programmings languages are sometimes difficult to grasp for every day programmers. It's sometimes hard to understand the features of such languages and how they relate to industrial software development, especially since the arguments are couched in terms such as "referential transparency", "totality", "side-effect-free", "monads", "non-determinism", "strong static typing", "algebraic data types", "higher-order functions", "laziness/call-by-need", and so on.

Many of these features are attributed to "pure" languages, but purity can be hard to understand in the context of everyday programming. I will explain the importance of a number of these features and how they impact the everyday programmer's life.

The explanations aren't rigourous, and perhaps even the distinctions I draw overlap somewhat in the real world, but I'm hoping it's an accessible intro to newbies; I'm still one myself after all! I won't post anymore on the subject here unless others think it's sufficiently on-topic, but I welcome any corrections or suggestions to my post! Post there if it's off-topic for LTU. This concludes my self-promotional message. :-)