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4

I mainly speak as market practitioner when I say that I believe in the end all models that are applied to data and real life pricing issues are discretized. Think about it, even the BS hedge argument is in the end just a "theoretical continuous time overlay" of actual discrete time steps and re-hedges. Thus some of the limiting assumptions re BS. You do not ...


3

If you just want to run some simplistic technical analysis on quotes, then select the last quote for each unique timestamp. That will ensure that you don't have duplicate timestamps. If you must have it evenly spaced (i.e. no gaps from one second to another), then you can reuse the previous quote to fill-in the missing value.


2

You could try net positions: where you continuously buy and sell depending on the signals generated. Net positions may lead to unnecessary commissions/spread nickel-and-diming your profits away. Once you have picked a direction and already have trade entry, your system should instead continue looking for new signals in the BACKGROUND. New signals while in ...


2

The answer depends on the reasoning behind your forecast. Is this a mean-reversion signal? If so, perhaps the presence of a short signal shortly after a long signal indicates that the long signal was very profitable, and you should take profits immediately. Is it a momentum signal? If so, then perhaps the momentum of this stock is very choppy at the ...


2

If you designed the model to predict direction only, I would just use the current signal. You could test whether this is correct by calculating the signals and their 5-second lags, then regress 1-minute forward returns (or 55-second fwd returns) on them both, and see if the coeff on the 5-second lagged signal is significant. If it's not significant, just ...


2

This is the answer to the first version of the question which asked whether a stationary process has an increasing variance over time. No the definition of (weakly) stationary (http://en.wikipedia.org/wiki/Stationary_process) is that the variance is the same for each point in time. In the literature it is often dealt with the covariance function. For ...


2

Note that you can understand the $\Delta$ as an "operator" acting on $r$. So just act on $r$ twice: $$\Delta^2 r_t = r_t - 2 r_{t-1} + r_{t-2}. $$ In fact if you write the $r$ as a vector, $r = (r_1, r_2, \ldots, r_N)$, then $\Delta$ is an $N\times N$ matrix with elements $\Delta_{i,j} = \delta_{i,j} - \delta_{i-1,j}$. The AR(2) model can be written as ...


1

To help you understand why you need to follow recipes (like chrisaycock's) just have a look at your tick data. You will find ticks clustered at some points in time while they seem scarce at others. If you proceed with your recipe 2, you will lose those clusters of activity and stretch them out. In periods of low activity you will condense the market. ...


1

One solution I have been considering is to add a target position parameter with a time decay. For example, given the $t_1$ buy and $t_2$ short signals described in the question and assuming a 5 seconds signal window to simplify, we would have the following time-based target positions: ╔════════════════╦═══════╦═══════╦═══════╦═══════╦═══════╦═══════╦════╗ ║ ...



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