Econometrics: why co-integration is needed - page 26
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(a) The t-statistic assumes that the data have a normal distribution and is only for such data, otherwise it distorts the result.
b) what is the new direction in the matstat to divide 100% by the value of the t-criterion, please enlighten
a) actually z-statistics
b) it's for seeds, to quickly estimate the error in percent.
But that's not the problem.
The problem is at the root. Everything I've read, built myself says that its predictability does not follow from the requirements for "correct". That's what I keep coming back to. Cointegration attracted by the fact that the inputs are in a stationary series. But the question of predictability remains.
a) is actually a z-statistic
So asymptotically normal instead of Student's is assumed, which is also far from certain.
b) it's for the seed to quickly estimate the error in percentages
But that's not the problem.
It's the root of the problem. Everything I've read, built myself says that its predictability does not follow from the requirements for "correct". That's what I keep coming back to. Cointegration attracted by the fact that the inputs are in a stationary series. But the question of predictability remains.
is assumed to be asymptotically normal instead of Student's, which is also far from certain.
And above all the question of predictability of cointegration itself. That's what I suggest we work on.That's what I'm suggesting we work on.
Here are the results. Took the H1 6736 bars. The pictures show the first 500 bars. The window of 118 bars (week). Shift by one bar.
Co-integration regression
EURUSD = C(1)*GBPUSD + C(2) + C(3)*@TREND
Difference between pairs
entry - crossing from bottom to top
exit - zero crossing
Entries from above are not considered - too complicated drawings are obtained.
At this sector we have got deals
deals in pips
I'm very curious about the behavior of coefficient с(i) in cointegration regression
I would like your opinion.
Cointegration regression
EURUSD = C(1)*GBPUSD + C(2) + C(3)*@TREND
You have cited many times the various equations you use to estimate cointegration. I seem to have missed the point when you justified why you include a deterministic trend component in the regression. Could you explain it again?
As far as I know, the deterministic component should only be included when the regressors contain such a component. In this case you can correctly use critical values of t-statistics, say, from MacKinnon's tables. I highly doubt that there is a deterministic linear trend in eurusd, gbpusd or some linear combination of them.
As we know, when cointegration really takes place - regression coefficient estimates (long-run models) have the property of superconstancy. Following your results, the cointegration of eurusd and gbpusd is present. Proceeding from these two propositions I suggest you to evaluate the regression ratios (necessarily with the same predictors) you have presented in two non-overlapping data areas, and then make sure by means of Chebyshev's inequality that the C(3) ratio estimations at these data areas differ statistically insignificantly. If this is the case, we should not try to trade the regression residuals mean, but the deterministic trend component. If the estimates of C(3) will differ significantly - I would advise to revise the structure of the regression to be estimated.
As far as I know, the deterministic component should only be included if the regressors contain such a component. In that case critical values of t-statistics can be correctly used, say, from MacKinnon's tables. I highly doubt that there is a deterministic linear trend in eurusd, gbpusd or some linear combination of them.
As we know, when cointegration really takes place - regression coefficient estimates (long-run models) have the property of superconstancy. Following your results, the cointegration of eurusd and gbpusd is present. Proceeding from these two propositions I suggest you to evaluate the regression ratios (necessarily with the same predictors) you have presented in two non-overlapping data areas, and then make sure by means of Chebyshev's inequality that the C(3) ratio estimations at these data areas differ statistically insignificantly. If this is the case, we should not try to trade the regression residuals mean, but the deterministic trend component. If the C(3) coefficient estimates are significantly different - I would suggest revising the structure of the regression being estimated.
You have cited many times the different equations you use to estimate cointegration. I seem to have missed the point when you justified why you include a deterministic trend component in the regression. Could you explain it again?
That's the thing, I can't claim anything.
As far as I'm concerned, comparing the different two plots in the past does nothing. Real trade - move one bar forward and this new plot differing by one bar will give new coefficients. The values of coefficients с(1) and с(2) are shown above - they change all the time and quite considerably. Here are the values of coefficient c(3)
Here is the estimation of the cointegration equation (not regression):
Dependent Variable: EURUSD
Method: Dynamic Least Squares (DOLS)
Date: 04/28/12 Time: 14:49
Sample: 118 6736
Included observations: 6619
Cointegrating equation deterministics: C @TREND
Automatic leads and lags specification (lead=34 and lag=34 based on AIC
criterion, max=34)
Long-run variance estimate (Bartlett kernel, Newey-West fixed bandwidth =
11.0000)
No d.f. adjustment for standard errors & covariance
Variable Coefficient Std. Error t-Statistic Prob.
GBPUSD 1.477877 0.039584 37.33545 0.0000
C -0.983188 0.064891 -15.15143 0.0000
@TREND 9.03E-07 6.68E-07 1.352241 0.1763
The t-Statistic and its corresponding probability says that the trend of the whole sample (118-6736 bars) can be neglected. This is not surprising as there are most likely no trends in large samples.
Let's take a window size sample = 118 bars. The picture is different.
Dependent Variable: EURUSD
Method: Dynamic Least Squares (DOLS)
Date: 04/28/12 Time: 15:00
Sample: 118 236
Included observations: 119
Cointegrating equation deterministics: C @TREND
Automatic leads and lags specification (lead=1 and lag=0 based on AIC
criterion, max=12)
Long-run variance estimate (Bartlett kernel, Newey-West fixed bandwidth =
5.0000)
No d.f. adjustment for standard errors & covariance
Variable Coefficient Std. Error t-Statistic Prob.
GBPUSD 0.410017 0.131928 3.107892 0.0024
C 0.652893 0.209209 3.120769 0.0023
@TREND 0.000202 1.90E-05 10.59269 0.0000
There seems to be a trend, but the t-Statistic values are too low , which suggests a huge error in the estimated coefficient.
From this we conclude that detrending should always be done. But it is not a linear trend. I have certain limitations on the trend equation. You could use a Hodrick-Prescott filter, for example.
Here is the result of including two deterministic trends
Dependent Variable: EURUSD
Method: Dynamic Least Squares (DOLS)
Date: 04/28/12 Time: 15:06
Sample: 118,236
Included observations: 119
Cointegrating equation deterministics: HP_EUR HP_GBP
Automatic leads and lags specification (lead=0 and lag=0 based on AIC
criterion, max=12)
Long-run variance estimate (Bartlett kernel, Newey-West fixed bandwidth =
5.0000)
No d.f. adjustment for standard errors & covariance
Variable Coefficient Std. Error t-Statistic Prob.
GBPUSD 0.604971 0.094954 6.371191 0.0000
HP_EUR 1.002990 0.028777 34.85379 0.0000
HP_GBP -0.607497 0.096679 -6.283619 0.0000
Much more decent than the previous case. The main thing is that this thing is more stable when shifted by one bar.
I did. Almost.
Pair trading. Fixed lot=1. 1036 bars on H1.
Quote charts
Balance without spreads.
Left - increment, i.e. 0.8 = 8000 pips
Graph of trade results
Total statistics for two currency pairs:
profit.factor
[1] 6.210877
> profit.plus
[1] 1.1192 = * 10000 = 11192 pips
> profit.minus
[1] 0.1802 = *10000 = 1802 pips
> sd(profit) - sko
[1] 0.001738898 * 10000 = 17 pips
> summary(profit)
Min. ......1st Qu.... Median Mean ....... 3rd Qu. Max.
-0.0047000 0.0000000 0.0006000 0.0009064 0.0015000 0.0192000
From the last line: max. drawdown in pips = 47 pips. Maximum profitable trade = 192 pips.
Libraries were used to build the trading system:
library(mFilter)
library(tsDyn)
library(lmtest)
library(fUnitRoots)
library(zoo)
Moved here.
Here is another section, the number of bars is 2.5 times higher on H1
The last 1000 bars of the balance
And this is the final statistic.
> profit.factor
[1] 6.843426
> profit.plus
[1] 2.8366
> profit.minus
[1] 0.4145
> sd(profit)
[1] 0.001760334
> summary(profit)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.004000 0.000100 0.000700 0.001054 0.001700 0.017300
Please note that the profit factor and drawdown have not changed much.
Waiting for specific results to compare with (18).