Econometrics: why co-integration is needed - page 3
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OK, more on that point, please. Where are the false correlations?
In trading, cointegration is needed to build portfolios of financial instruments - such that their value is a stationary process. Stationarity in this case is constancy of expected payoff and dispersion. The constructed portfolio is sold, if its value is significantly greater than expected payoff, and bought, if it is significantly less. Bollinger bands can be used to define thresholds. In the general case, several processes of the same order of integration (not necessarily the first one) are considered. These processes are called cointegrated if there is a linear combination of them such that its order of integration is lower than that of the original processes. By the way, it already follows from the definition that the processes in question must be expressed in the same currency. Moreover, for cointegration there must be economic preconditions - exchange rates have no reason to be cointegrated, but share prices, for example, can be. Co-integration of the two processes is checked elementary - we build a pairwise linear regression on the first half of the data, check stationarity of the regression residues on the first half of the sample (Dickey-Fuller test or any other unit root test), then calculate errors of the same regression on the second half of the data and also check these errors for unit root. If both tests show no unit root - you have probably found a pair of cointegrated processes (no one guarantees that this cointegration relationship will hold in the future). For stocks, the best known example is Chevron vs Exxon Mobil (CVX-XOM). The case of many variables is more complicated. I'm writing from my phone, so I won't go into it. Let me just say that we are going to discuss vector autoregressive models, vector error correction models and Johansen test (VAR, VEC, Johansen test). Again - the test is done on the first half of the data, and tested on the second half. For stocks, a possible prerequisite for cointegration is, for example, that the companies belong to the same sector of the economy. All this works, if not done through the ass. The processes must be tradable (if you have found cointegration with an index, but it is not traded anywhere - your cointegration is useless). Including a trend in the model is also an example of what not to do until you understand the method.
If you look at the last picture at the beginning of the topic, it is a DF to check for cointegration.
For portfolios it is more or less clear, but now I have and can prove that I have cointegration. So what?
I can't agree that there can't be cointegration in forex. To be specific with me, the dollar index was taken and compared to the eurodollar pair. This speaks to the economic basis for the existence of cointegration between these series.
More broadly, the foreign exchange market is one, as the currency serves the trade exchange between different countries and is linked within a global system.
The presence of a trend. It didn't just appear, it appeared as a result of poking around. If you read about cointegration, the issue of trend is fundamental.
I asked a specific question, not a general one.
In my post I wrote in general terms.
The presence of cointegration proves the presence of correlation in an extended form, taking into account long-run variance.
I don't understand anything. I will read what false correlations are.
The cointegration of the two processes can be checked elementary - build a pairwise linear regression on the first half of the data, check the stationarity of the regression residuals on the first half of the sample (Dickey-Fuller test or any other unit root test), then calculate errors of the same regression on the second half of the data and also check these errors for unit root. If both tests show no unit root - you have probably found a pair of cointegrated processes (no one guarantees that this cointegration relationship will hold in the future).
So the local econometrician is very small-minded, as he prefers to fit and test everything on the same data and not retest anything outside the sample, i.e. on the forwards, as for him such testing is an unnecessary bliss. He believes that traders invented out-of-sample tests on purpose in order to mislead brainless econometricians.
The local econometrician is very small-minded, as he prefers to fit and check everything on the same data and not to double-check anything outside the sample, i.e. on forwards, as for him such a check is an unnecessary nonsense. He believes that traders invented out-of-sample tests on purpose in order to mislead brainless econometricians.