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bchadwick

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Joey has a lot of good points. I'm not as good on the pure math side, but I come from a causal modeling background in the social sciences which uses a lot of statistics.

I didn't fully understand the problem you posed. It sounds like you have an account or portfolio that increases or decreases in value on a daily basis and trends upwards on average, and you have depositors that make random withdrawals on a daily basis, and you want to find out how much of the account needs to be in cash so that, 95% of the time, the guys making withdrawals have enough money. The only data you have is the daily size of the account, so that daily changes reflect both increases/decreases due to the investment portion and decreases/increases due to withdrawals/deposits. Is that it?


Of what's been said above, I don't have much to add, but if you do analyze just the down-residuals, you really should have some explicit reason for doing so - something that suggests that the there are special processes that affect the down side differently than the up side. This reason should include some expectation that the distribution of residuals would not be normal (or at least not be symmetric). Otherwise, just go ahead and use simple regression residuals on detrended data. If you do analyze down-residuals separately, you should also analyze the up-residuals separately and compare the results to see if they are symmetrical. There is presumably some kind of test to do this, though I'm sure someone has figured the test out long ago and I don't know it off hand. I suppose if symmetrical, up residuals and down residuals should have equal variances and equal, but opposite signed, means. You could use a t-test for equivalence of means for the means and a test for equivalence of variances for the variances, I guess, but that may be overkill. Really you just want to see if the upside residuals look substantially different from the downside ones.

The more I think about it, the more this seems like a complicated problem; more likely, there are additional constraints that haven't been mentioned in this thread that would simplify it.
 
There's no simple reason that (B1 - B0)/B0 ought to be affected by growth of B.

The skewness can be handled usually by Box-Cox transformation (look up on Internet for full description).

The consecutive thing is only important if there are dependencies among the residuals. If so then the GARCH approach mentioned above would probably be better (but I am not a believer in that here, but I could be convinced).
 
Hey bchadwick -

Thanks for the insights - I agree with your point about analyzing the upside residuals as well. You need to be a little careful with comparing the two distributions to see if they are the same because the residual distributions depend on each other because the sum of the residuals must equal 0.

It's better to fix the residuals in the modelling, say by Box-Cox transformation mentioned above or some other method. At any rate, to compare two distributions to see if they are the same use Kolmogorov-Smirnoff test (or similar) instead of separate tests on different moments.
 
JoeyDVivre Wrote:
-------------------------------------------------------
> There's no simple reason that (B1 - B0)/B0 ought
> to be affected by growth of B.
>
> The skewness can be handled usually by Box-Cox
> transformation (look up on Internet for full
> description).
>
> The consecutive thing is only important if there
> are dependencies among the residuals. If so then
> the GARCH approach mentioned above would probably
> be better (but I am not a believer in that here,
> but I could be convinced).

Thnx for reply! I will certainly check the Box-cox;

Of course Growth of B is affected by many things, like Business activity in the country, Income levels of populations, Economy growth etc. Peoples Preferences in terms of saving and expenses

As here in GEORGIA (the country not the state) the financial market isn't developed, very tiny stock exchange, Statistical Data not available like in US etc... No Benchmarkes, e.g. to calculate Market Prices ... For example the T-Bills (notes) here cannot be used as Benchmarks I didn't want to make complex correlation model... because mainly of data insufficiency and these reasons

To sum you I'd like to veryfy this:

so you suggest that I should calculate (B1 - B0)/B0 % daily changes... Skim off B INCREASES data... and usin only Decreases as A SAMPLE from Population and do Standart Statistical Analysis.... (Of course the type of distribution had to be determined)

BUT AGAIN, I am afraid not to UNDERESTIMATE the Volatility.... Because of consequtive decreases....

Or Maybe I should calculate the Consequtive changes separately, and treat them also individualy as Samples from Populations??? Actually THIS IS ACTUALLY WHAT I DID;


P.S. Actually the situation is connected with Financial Risk at the Bank- Particularly LIquidity Risk...

You know Banks Have Liabilities (Deman Deposits, CDs,... Equity) and Uses them to Finance Assets; So When Bank gets Demand Deposits for example it has to put part of them in reserves at Fed and The rest into lets say loans;

This Deposits have flow ins and Flow Outs - So A Bank has to Maintain Also Liquidity RAtio of these Libilities As Cash Equivalents as to meet the Depositors Flow Out Needs (And Also the Need for Loans but thats not the case now)

WHAT WE NEED TO DETERMINE IS "REASONABLE" LIQUIDITY RATIO FOR BANK, CONSIDERING LIABILITY STRUCTURE (Because Different LIabilities Have different behaviour in termas of Flow INs and OUTs); And this Ratio should follow the change of Libility Structure;

Thanks for your Time; Looking forwardto your replies;

Best Wishes,
 
JoeyDVivre,

If you have time, could you reply to my post?

Best Regards,

koSTARica
 
My son, be admonished of making many books there is no end.

This seems to have morphed into a statistical consulting project and that's pretty tough to do in a forum like this. There are several issues that you need to solve here:
1) Data - I like % change as above, but I almost never throw out data without really compelling reasons. I would not throw away increases.
2) Serial Correlation - You need to see if the data has some serial correlation if you are worried about consecutive declines. If the data is Markov there is no need o worry about this.
3) What sort of answer you want from the analysis - For a bank liquidity analysis, I would probably be doing an extreme value analysis. This fixes lots of your problems with the distribution because you have the extremal types theorem helping you in the same way a CLT would help you in estimating the distribution of a mean. You aren't really interested in estimating a distribution but are interested in estimating the worst event that can happen and controlling the probability of a liquidity crisis. EVT was invented for such problems.

GL
 
Good Lord....I need to take some statistics classes. CFA doesn't even scratch the surface.
 
Thanks man, for your reply; Sorry to trouble you with my posts;

I've heard 'bout EVT, but have no practical 'relationship' with; I will consider your advice and do some reasearch about that;

I do not want to consider Increases, because I don't want to rely on them as I want results to be more pesimistic; (Is it better to write 0 (zeros) instead of Increases or completely remove them?)

Do you advice using daily percentage change data for EVT?

Because maybe the consequtive decreases indicate some kind of crisis at that time (Because I do not know what happened at that time, so I thought it would be logical to incorporate such data and consider consequtive decreases, as It may indicate e.g.the Maximum Decrease in Periods of Crisis)

Anyway I think, you get irritated with my posts:) So whenever you are in good mood, please respond:)

Best Wishes,

koSTARica
 
P.S. Could you give me a reference on EVT? Maybe link, with practical example and easily written material? Would be very helpful;
 
koSTARica Wrote:
-------------------------------------------------------
> Thanks man, for your reply; Sorry to trouble you
> with my posts;
>
> I've heard 'bout EVT, but have no practical
> 'relationship' with; I will consider your advice
> and do some reasearch about that;
>
Stuart Coles' book called something like An introduction to Statistical modelling of extremes (or something similar) is a good place to start.

> I do not want to consider Increases, because I
> don't want to rely on them as I want results to be
> more pesimistic; (Is it better to write 0 (zeros)
> instead of Increases or completely remove them?)

Not what I would do.
>
> Do you advice using daily percentage change data
> for EVT?

Yep.
>
> Because maybe the consequtive decreases indicate
> some kind of crisis at that time (Because I do not
> know what happened at that time, so I thought it
> would be logical to incorporate such data and
> consider consequtive decreases, as It may indicate
> e.g.the Maximum Decrease in Periods of Crisis)
>
By all means, look at the time structure of the data, but whether this effect happens is an empirical question.

> Anyway I think, you get irritated with my posts:)
> So whenever you are in good mood, please
> respond:)
>
I am not irritated by AF. If I was, I wouldn't respond.
> Best Wishes,
>
> koSTARica
 
Joey, while you're at it, if you have time, can you draft a letter to his boss asking him for a raise.
 
koSTAR, you need Joey a case of the finest lager. He went above and beyond the call...
 
JoeyDVivre>>

Thanks! I really appreciate your comments;

Actually nobody asks me to do such things at works, Georgias FInancial and Capital markets are hardly developed are lagging 20 year or more from e.g. US; At work they managemant doesn't give a sh%t what an internal Liquidity Ratio might be because they want to just be in line with Central Banks 30% Covenant;

Actually the need for liquidity might be 40%!

This is one of my initiative projects:) (Of course there is a proverb "Initiative F%$s the Initiator" But I don't care!:)

------------------------------------------------------

As to the subject: I will ignore consequtive decreases, because that only empirical result, and may not nessesarily be some distinct event; Also It's a bit "early" for me to go with Markov Pocess;

About EVT - everywhere I checkedso far it is explained on pure mathematical language which is a bit hard to connect with my case:(

I would really appreciate some link 'understandable' article on the net;

Anyway, Best wishes from Georgia; Come over once, other then financial markets its an unique country; When you have time check it on Wikepeia or I can tell some :)
 
Please guys, could you give link to EVT (Extreme Value Theory/Paradigm) examples - for begginers?:(

Examples like e.g. ocean levels over past century, and then picking out extreme values and do analysis- something like this-

Most resouces I checked uses pure mathematical language to explain theory:((
 
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