come on the fact this year jan 31st is a sunday does not invalidate the model. whenever jan 31st falls within the working days of week, it is hi-prob up day for the world indexes, based on all historical data points available.
i havent modeled that but i can assure you the most negative bias weeks for the markets are the last two before expiration. MMs are aware of this when when they tweak option pricing to accommodate fat tails.
I'm trying to get a handle on this problem. If anyone can add to or correct my thinking that would be greatly appreciated. 1. As a process to understand I first calculated the number of trading days for 100 years. So 250trading days per yr(100 yrs)= 25,000 observed occurrences. 2. 100 observations for each trading day in a year. 3. 2 possible outcomes, either up or down for each 100 occurrences. .5- Given the asumption that each occurrence is independent and evenly distributed as in a coin toss. 4. 1 SE Sqr. root of 100= 10 10(.5)= 5 5. So is 80% up days for a calendar day significant with an expected average of 50? 80-50=30 and 30/5= 6SE. 6. Now, law of large numbers would suggest that given enough occurrences we should expect 6SE, but how rare is this? I couldn't get the online binomial calculators to show enough sig figures so... 7. I found the following (How Unlucky is 25-Sigma? -Kevin Dowd, John Cotter, Chris Humphrey and Margaret Woods Banking & Finance Subject Area UCD Business Schools Corresponding author: Kevin.Dowd@nottingham.ac.uk WP 08 /13 ⢠a 3-sigma event is to be expected about every 741 days or about 1 trading day in every three years; ⢠a 4-sigma event is to be expected about every 31,560 days or about 1 trading day in 126 years (!); ⢠a 5-sigma event is to be expected every 3,483,046 days or about 1 day every 13,932 years(!!) ⢠a 6-sigma event is to be expected every 1,009,976,678 days or about 1 day every 4,039,906 years Seems quite significant, but then now please suggest how I might think of this related to a time series. Thanks.
One hundred years of relative daily historical performance distilled into a daily "probability" distribution with accuracy to the second decimal point? I would guess the table's value approaches zero. An unnuanced, broad-brush frequency distribution may have some potentially entertaining descriptive value, but it is a far cry from a probability distribution with predictive value. (And to the second decimal point!)
We live in an ever changing world with major events happens randomly, and with various length of economic cycles, it would not be scientific to use the performance of the past 100 years to predict the performance of the future. However, the table does reflect the upward trend of the market in the past years, which is a no-brainer. Still, I appreciate the table as much as I appreciate a coin toss. It's useful, but it's not scientific. PA PS: It's good marketing material for funds tho.
Save your time, give it up, you will never figure out the markets unless of course your fancy calculator can compute the following: (Daily Fear - Daily Greed)/Professional money manipulating price + rookies trading on their first day - people (money) with a gambling approach trading their life savings + people (money) with gambling approach but with some money to blow * (Amount news put out there to distract Sunday Joe - Amount of professionals that read between the lines) = Daily trend
You bring up an interesting concept. What other than the past do we have to make forecasts? I should think most actions we take by virtue of choice is dictated by the regularity of observed patterns. So I think that so long as the frequency of regularity pasterns remain intact, and significant, what reason do we have to dismiss them? My question is really an attempt to understand modeling time series. Although I believe the numbers do seem rather impressive, I know from experience that events can hog up a great portion of of the data and essentially cluster the impressive occurrences for that period. I think of it like a coin in a coin toss game that at some point gets replaced by a biased coin for a portion of time. Seeing the final results many iterations later perhaps might show a distribution of heads that are at the 5 sigma level, but without seeing the tosses during the portion of time with the biased coin, one might presume a constant process, which of if the coin were switched back to the fair coin would be the wrong conclusion.