Time Series: GARCH and ARMA

To model time series we look at GARCH models to estimate how volatility auto correlates over time and look at autoregressive patterns in the time series as well as exponentially declining moving average shocks that may change the measured variable. For instance the shocks of last period may be forgotten or the shocks of two or three periods ago may still be remembered but discounted. The key thing as with all modeling is to look to see if the error terms are well-behaved. If the measured variable in question is not well-behaved in its errors, then we have reason to suspect the model is incorrect and that everything is not what it appears to be. But to go beyond basic intuition, we have to consider whether the problematic behavior in error terms is conditional on a lurking variable. If error terms are very volatile initially and drop in volatility later then perhaps a lurking variable has turned on or off beyond the time series. For example, if someone asks you what does all this intellectual nonsense have to do with the price of oranges in Colombia, you answer that he is the connection as he is suggesting that one thing leads to another in the economy which does not follow in an efficient market because of anticipation effects yet he is the connection because if he wants to speculate on the prices of commodities internationally he has no business learning about the economy, all he needs is psychology as speculation is just about outsmarting the lawyer on the other end of the phone call. I personally don’t do psychology I do trading which is kind of the analogue to the military over phone calls while salesmen especially high pressure salesmen are like cops. If you ask a military guy why he isn’t tougher or talk tougher around cops why do you think? There is also the law which impacts how you function in every bit of society. Ditto if you ask a trader why he doesn’t fight back against high pressure salesmen provided he is in the wrong somehow in that he needs their help. Now I’m not saying psychology is not useful it just is often misused. If I want to answer that question properly: what does the price of oranges in Colombia have to do with intellectual work on the economy, I would argue in a land with rational actors, I am studying rational human behavior and can eventually imply a fair price for oranges in Colombia for which we can push prices to in some sort of microeconomic equilibrium. So I can answer that question fine. What he can’t answer though, is why he asked that question. He obviously asked it because global macro funds like Bridgewater in the United States specialize in reasoning and free brainstorming sessions about topics like how the price of coffee is affected by Federal Reserve interest rate movements. That fund is not like me as it is not quantitative but it is global macro and it is noted for managing a lot of money but not for exceptionally high returns or for exceptionally low volatility. If you go work for a fund like that and think you’ve mastered the USA hedge fund scene think again, as they may have some good computer programmers but they remind me a little of improv comedy classes at Second City: free group discussion! Build by saying “yes and”! You challenge me to perform research like Bridgewater and use that to prove whether my work is of any value to human society? Sure why not. What is a cult? It is a place where people do not speak to one another except with regards to credibility. Did I take your seat? I’m sorry. I guess it is no surprise to us that after 2008 when the most of us were rebuilding ourselves without bailout packages, the guys came in from the north and took over the easy places to take over and get interviewed at where you are just rounding errors in the management fee: great business model! But for them to now claim they hold the flag when we crawl out of the dead people’s heap and say this flag is still there, old regime America, ancient regime America? Well, I can only say, I try left and right to break off my connections with tough guys but they keep poking me, so I won’t use my American flag to fight the captured American flags. I’m just going to stand here with my American flag and you can try like Xerxes to get around it. I’m afraid this is real: we took down Xerxes finally. First we had to take down and isolate the Persian Greeks, and then the real Persians. And we did it all by trusting in the Second City which kind of emerged in the debris of the East Coast, saying we are still here. And then there was the tonguelashing of Theseus. Anyway, it is unfortunate what transpired but 1,000,000 under Emperor Xerxes lost to 300 under King Leonidas, and the 300 are USA southerners who don’t really fear the great north, because we have shown the world that man does not control money but money goes to whoever convinces money that it needs to go there. In that way, money is a lot like honor. If you have to throw away your honor to get money, I’d argue that is a lot like salting the earth. In the end the deformed Spartan led the formation. He wasn’t even really deformed he just couldn’t hold a shield so he clung to the law which is his spear instead of the shield which is mathematics. I ask Spartans to use mathematics as shields. We did a good job and we showed the world politics is no substitute for economics. Student council runs the dances so the students on it have to be popular and good at economics. Debate team is another issue in high school. If you want these politicians off of your back on the debate team you have to outdebate them and that’s another issue. And by the way commodities move on supply and demand balances so the price of oranges in Colombia will go up when there are frosts that affect supply, or when demand fluctuates based on disposable income changing the rate of food and drink consumption. But if I said that at the beginning, wouldn’t I prove myself wrong that all this intellectual work had any value? I am the connection: how much do you have to train to be ready for a sport? But I said he is the connection to be nice. He could imagine he was me. In Sparta, even Theseus can be king. Thank you Theseus who is some Chicago bouncer as he kept calling me through his American friends to get me to stop fighting and start trading. He thinks that we could have won using archery or if Delian League horsemen showed up. Instead we basically said: “GREEK FIRE!” Guess I spoke to the oracle after all she is in Philadelphia and is half human half elf and has seen it all before she saw me an elephant fly. This little story is a time series with well behaved errors so it doesn’t drift like an uncontained stochastic process that explodes into controversy or writer’s block after it goes on for a while. Now next we are doing Son of Sparta where the Asian Americans will show people that if Chicago is the second city, then what are we? Just because I say some things doesn’t change that I still look Asian in front of a mirror does it? Just like just because some guy says some things doesn’t change that he still looks like that….. there’s no place I’d rather be than this seat for which if I didn’t take it many other people would want it. Take care


No comments

Other posts

Complex visualization: Euler’s Identity
This is just a quick way to practice your ability to visualize in 3D, Euler’s Formula, which relates e^(ix) to the featured image, where basically the unit circle of trigonometric functions becomes a helix as the input into the function itself is mapped so f(x,y) as function of z, and we see how as we increase the Greek argument into the function, what e^(ix) is equal to remains fixed on...
Read more
Numerical Methods: Approximation
Numerical methods serve to approximate solutions to mathematical equations and solve mathematical problems using computational power after algorithms have been developed. Methods exist for finding roots of polynomial equations for example or factoring matrices. Generally a convergence process if stable leads to the right result much like Taylor polynomials approximating the values of various functions where the Taylor polynomials act as a series progressing towards infinite. Relevant concepts from calculus...
Read more
C++: Programming and Object Orientation
A computer programming language compared to a natural language lacks redundancy and is generally procedural while defining functions that take variables in scope and there is encapsulation which provides functions to work on the aspects of structures for example that can be worked on in that function. Data structures are conglomerates of pointers which reference locations in memory and what these locations hold, characters, integers and arrays and strings. Structures...
Read more
More posts