Econometrics: bibliography - page 9
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I came across a curious article on the hot-button topic of causality between quoters.
Usually, the connection is regarded in the forum as correlation.
The next step is cointegration, proposed by Granger in 1969. This is a more precise definition of the causal relationship between two quotes. What is meant is the following: two non-stationary quotients are taken, which have the following property: if we take the same number of differences of each quotient, i.e. both quotients have the same integration (usually one - I(1)), then the residual will be stationary. Then for these two non-stationary quotients we can find a vector by which by multiplying one of the quotients and adding it to the first one we get a new stationary series. That is, the sum of the two non-stationary series generates a stationary series.
This works for detecting synchronous movements on short intervals.
The article suggests identifying such synchronous movements of two quotes on long intervals.
That's how you get to the Definition of a Cross between major pairs, during its flux :-) and from there it's not far to pair trading :-)
If there is cointegration between three or more instruments, it will not be paired trading.
I'd like to find an algorithm somewhere for dumb people - say, for three instruments. I'm going to convert it to a five.
Can you suggest something easier, SunSunich?
I typed "cointegration" into the search box and immediately came across hrenfx's posts. There you go.
I'd like to find an algorithm somewhere for dumb people - say, for three instruments. I'm going to convert it to five.
The algorithm is elementary, as long as the cointegrated portfolio is found. To find the portfolio, use Johansen's method.
Let W=(W[1], ..., W[n]) be cointegrating vector, it is assumed constant. Some of its elements have positive signs, some have negative signs (this point should be obvious ;) ).
At time t, the vector miprices(t)=(M[1](t), ..., M[n](t))=0.5*(bid[1](t)+ask[1](t), ..., bid[n](t)+ask[n](t)) and spreads(t)=(S[1](t), ..., S[n](t))=(ask[1](t)-bid[1](t), ..., ask[n](t)-bid[n](t)). Square brackets contain instrument number (from 1 to n).
We need to calculate two prices: buy price of BasketAsk portfolio (long position for instruments for which W[i]>0; short position for the instruments for which W[i]<0) and sell price of BasketBid portfolio (short position for the instruments for which W[i]>0; long position for the instruments for which W[i]<0). The transaction costs (they increase the buy price and decrease the sell price, only the spread is further considered, as the rest depends on the market, instrument type, broker, etc.).
BasketBid(t) = sum(i = 1 ... n) { W[i] * (M[i](t) - 0.5 * S[i](t) * sign(W[i]) }
BasketAsk(t) = sum(i = 1 ... n) { W[i] * (M[i](t) + 0.5 * S[i](t) * sign(W[i]) }
Thus, for each point in time, we can calculate the buy and sell value of the portfolio.
The task is to buy cheap, sell expensive.
The portfolio is cointegrated, which means that during the analysis some residue series of the cointegration model has been built. Calculate the expected payoff (let it be V). We buy the portfolio when the BasketAsk price is less than V minus some threshold T. Sell the portfolio, when the BasketBid price is higher than V + T. T threshold is selected in such a way that two conditions are fulfilled:
1. repay transaction costs and make a profit.
2. The number of deals must be sufficiently large. If the threshold is too high - you will seldom make much profit. If the threshold is too low - you will often make a small profit. If the threshold is too small, you will often incur losses in the amount of transaction costs.
There are more ways, but they are more typical for HFT bots, that usually are not written in MQL.
p.s. It's very important to express absolutely all prices and spreads in the same unit. Always in the same currency. This applies to the construction phase of the portfolio as well as to the exploitation phase. If an instrument is traded in another currency - you need to consider the cost of hedging with a currency spot or futures on the corresponding exchange rate.
Mathemat, I hope, has explained in detail. If you have any questions, do not hesitate to contact me.
I'd like to find an algorithm somewhere for dumb people - say, for three instruments. I'm going to convert it to a five.
Can you suggest something easier, SunSunich?
I typed "cointegration" into the search and immediately came across hrenfx's posts. There you go.
Look here.
On time series econometrics and cointegration.
There's a book like this, see the table of contents in the attachment.
I'd like to find an algorithm somewhere for dumb people - say, for threeinstruments. I'm going to convert it to a five.
Can you suggest something easier, SunSunich?
I typed "cointegration" into the search - and immediately came acrosshrenfx'sposts . There you go.
or maybe you can use a tool from Leonid? here's a triple index spread (spread of threeinstruments)
the description of the indicator - see page 67 of the Leprechaun magazine (10th issue of 2010)...
The basic principle of spreads over 2 pairs - see Quasi Arbitrage in Short Term Trading
http:// www. procapital. ru/showthread.php?t=28081
Well, more legs can be inserted into the indicator according to the same principle...