Remembering veterans: Box and Jenkins - page 4
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faa, please explain in simple terms the terms in the table you gave on the first page of the thread. What is t-statistic, Akaike, Schwarz etc.
Some understand them, but they are unknown to most. Take the popularisation from the start. The occasion has just arrived - Boxing and Jenkins. The sign:
Don't be too hasty. It's OK if you explain one term at a time in one post.
The question in reply is: what should be the point?
faa1947: Доверять тестированию и форвард тесту можно только в том случае, если остаток = котир - ТС стационарен! т.е проходит тест единичного корня.
faa, please explain in simple terms the terms in the table you gave on the first page of the thread. What are t-statistic, Akaike, Schwarz, etc.
Some understand them, but they are unknown to most. Popularise it from the beginning. The occasion has just come up - Boxing and Jenkins. A plaque:
Yes, please. From top to bottom.
The dependent variable EURUSD is a function. Bottom down in the table are the arguments of that function.
C is a constant, an offset. It coincides with the quote, i.e. it shifts to the axis.
@TREND - sloping straight line by 45 degrees.
AR(1) - EURUSD (-1)
MA(1) - one bar error, which I think is the difference between the kotir and the AR
Table. Columns.
Coef - estimation of coefficients of arguments (regressors, independent variables) of the equation.
Std.Error - standard error of the coefficient value. For us the most interesting conclusion is that the coefficient from the previous column is not a constant but a random variable with a range and its distribution law is normal.
t-statistica - I won't go into the theory, but = coefficient/Std.Error. If you divide 100% by this value you will get error in percent.
Prob - roughly this is the probability that the coefficient is equal to zero.
Further, some values from the lower part of the table.
R-squared - it reflects the degree of adjustment of the quote. For us it is 98%.
S.E. of regression - standard error of equation fitting to the quoted price
Akaike info criterion, Schwarz criterion - so called info criteria. They are used for comparing two different equations. the smaller the better
Durbin-Watson stat - statistics saying how close the residue is to the normal law. If it is equal to 2, then it is a normal law. Deviations indicate the presence of tails. In practice it is considered to be a normal law if it is from 1.7 to 2.3.
The last two lines.
The so called roots. The closer to 1, the worse. Speaks to the stability of the equation. If => 1, the fitting error will grow indefinitely fast.
All exact definitions can be found. specifically, in your own words, thinking it is clearer that way.
The point must be in the quid.
How do I do a unit root test of future data? For example, past data passes the unit root test. How can I be sure that future data will also pass the unit root test?
Another idea. Take the RT and calculate the difference between the RT and the quotient. If this BP passes the unit root test, then you can be sure that in the future the residual from the TS used will also be stationary, because this TS has once defeated the non-stationarity of the quotient. It has this property. One can turn a blind eye to this, not do the unit root test, and trust the forward test.
faa1947: Другая идея. Берем ТС и вычисляем разницу между ТС и котиром. Если этот ВР проходит тест единичного корня, то появляется уверенность, что в будущем остаток от используемой ТС будет также стационарен, так как эта ТС один раз поборола нестационарность котира. Она таким свойством обладает. Можно закрыть на это глаза, не заниматься тестом единичного корня, и верить форвард тесту.
Not so sure. If the TS once defeated a non-stationarity, how can we be sure that it will also defeat other non-stationarity in other (future) conditions? And it should be understood that the non-stationarity it has beaten will not be similar to the stationarity it will have to beat.
You can't be sure of anything at all on the market.
I am considering situations.
(1) Test, forward test and on the real. This is the usual way. Holy faith in the forward test. No forward test solves any problems.
(2) We create a TC. Calculate the remainder and check for a unit root. If the residue is non-stationary, we create a new TS, because our current TS is hopeless and no positive tests, including forward test, do not matter. It will surely fail.
(3) Create TS. The balance is stationary. We test it including a forward test. We have a reasonable belief that it will be so in the future. Especially if it's not a randomly obtained stationary residue, but the result of purposeful modeling, such as GARCH. I haven't yet been able to create a TS in which a stationary residue is guaranteed. But the stationarity residual test at least allows you to wait out the market if the TS does not contain the means to simulate a particular quotient area.
Here's the point. You don't have to predict quotes on every bar - it's not necessary for trading. It is important to predict those moments (specific bars) when you need to open (and/or close) a position in time - it is necessary for trading.
We are talking about the past. You need a certain number of bars for testing.
What you are talking about is a tactic of every TS, a matter of taste maybe.