Apr

23

 Time Series Analysis with Applications in R, by Jonathan D. Cryer‏ and Kung-Sik Chan, was advertised to have the R code for its examples, but didn't. It has a few snippets for a few charts and an Introduction to R in the appendix. Kind of a rip off. I don't especially recommend it for those looking for some R code. There are the infuriating questions at the end of the chapter. I know you are supposed to work them out understand the material but I want a reference book. I'm not in college any more. I want the answers. It's more suited for entry-level college statistics.

There was an interesting chapter on trends in which they distinguish between stochastic and deterministic trends. Stochastic trends such as a random walk, have apparent "trends" merely as an artifact of the strong positive correlation between the series values at nearby time points and the increasing variance in the process as time goes by. This answers my question of why the time series charts line up. They distinguish deterministic trends, for example, the upward trend in temperature as summer approaches. There is a reason, a model for the trend, the tilt of the earth towards the sun causing higher temperatures.

Vince Fulco comments:

I've become partial to The R Book by Michael Crawley. A solid intermediate text with a walkthrough of various practical stats concepts. Best in electronic format at 950 pages.

James Sogi  writes:

Quick study of Spus shows historical variance increases in the afternoons which is in line with Cryes theory of appearance of trends in random walk and autocorrelation of near time series points in stochastic trend and increase in variance. This ties together with the thread on apparent trends in spu series. Interesting how there's always a fresh way of looking at the same old stuff.

On a different subject, Soros says in his update to his recent book Reflections on the Crash of 2008 that it is wrong to model equities on the same basis as natural models like we often do here, like Lotka-Volterra etc, as human reflexivity and self perception leads to bigger trends, panics, booms, etc than natural phenomenon which is not self aware. He's not sure how to model reflexivity and is afraid of locking in a model to a fixed algo.

A counter example in nature would be study of stampedes, lemmings, migrations, panics, temperature spikes clusters, hurricanes and extreme events, earthquakes, and other outlier type natural behavior or other discontinuous or extreme type data. We'll have the 2008-9 data in our series going forward, so the model might adjust itself, and if not the model, the data will be there. Question is will means revert. For self protection we must err on side of different lower kurtosis plus fatter tails described more as Pearson Type Vii or Student t or Cauchy type distribution. Got a bit of negative skew in there now too.

-9 | 96
-8 |
-7 | 0
-6 | 833
-5 | 74433
-4 | 98753300
-3 | 98443210
-2 | 998877666553322200
-1 | 99877777766655555444432222222111111000
-0 | 97777765432111110
0 | 0011122222334444455556666666667777888999
1 | 0001112233336667889999
2 | 012233446677
3 | 01112233344447
4 | 011139
5 | 4468
6 |
7 |
8 |
9 |
10 | 4
11 |
12 | 6

Like the expert distinguished prof, the Palindrome experienced systemic breakdown as a young man in Hungary. This must be a life changing experience. For everyone who lived through 2008 it also will be a life changing experience, though not on the same scale as Budapest 1943 or in Lebanon, or the Balkans, Malay, China, Russia, Africa.


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4 Comments so far

  1. Anton Johnson on April 25, 2009 10:55 am

    When modeling the S&P, working with the assumption of two price distributions taking place concurrently describes price action more accurately. The first level price distribution is most similar to an inverse-normal distribution with a positive skew, which describes the typical day to day price action. The second level distribution, which is modeling atypical price shocks, is most similar to an inverse-beta distribution (different alpha and beta values for positive or negative values, with positive being more leptokurtic and negative being negatively skewed). To approximate historic price shock frequency, this second level is generated to occur randomly three times in 1150 periods, with values being additive.

    Handling the outliers separately, along with daily range distribution calculation inputs derived from historic statistics, and accounting for the persistence of volatility, nicely approximates historic distribution characteristics.

  2. Curmudgeon 6321 on April 25, 2009 12:20 pm

    Mr. Johnson, I find your remarks very interesting. I am not sure what you mean when you refer to the "inverse normal"; is it the same as the Normal-inverse Gaussian distribution (NIG) ? Is there anything published about the approach you presented (i.e. mixture of NIG and inverse Beta)?

  3. Anonymous on April 25, 2009 2:22 pm

    one believes that Press in the JASA approx 2000 has an article on a similar mixture with empirical correspondences.. vic

  4. Anton Johnson on April 25, 2009 2:44 pm

    Response to Curmudgeon 6321:

    Inverse-normal distribution and NIG are one in the same, although NIG is more accurate. I am unaware of this approach having been published.

    While developing models, I found it futile force-fitting S&P prices into a single distribution type. Amongst other difficulties, attempting to adjusting equation inputs for outliers in an inverse-normal distribution, student-t, etc, will result in many model statistics varying unacceptably from historic statistical measurement.

    Although contrary to convention, my working hypothesis is that extreme outliers are event-driven and must be handled separately. To account for this and accurately model and describe a historic long-term S&P series, two (or more?) concurrent distribution types are needed. My work determined that inverse-normal distribution best describes typical historic daily price distributions, while inverse-beta distribution best describes the atypical historic outlier distribution.

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