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4

Beware, oversimplification ahead! (This means that the following is technically not correct, in fact it is false! But: It gives an intuition what is going on!) If you toss a coin and calculate heads as $-1$ and tails as $1$ you get a mean of $0$ with a variance of $1$. When you add up multiple coin tosses, i.e. create a random process $dz(t)$, the mean ...


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 ...


4

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 ...


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

First of all, GNP and GDP are economic time series and they are not economic model. Secondly, you can also get these time series with different frequency, as quarterly data, avalaible on OECD website. In the case you need for lower frequency data you can get it by interpolation (as, for instance, the cubic spline interpolation); This is the Matlab tutorial ...


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 ...


1

If $V_0(\phi) < \Pi(0,x)$ at $t=0$ You sell short the claim and collect $\Pi(0,x)$ You buy the portfolio $\phi$ for $V_0(\phi)$ You put the money $\Pi(0,x) - V_0(\phi)$ in your risk-free instruments at $t=1$ At $t=1$ you'll be liable the payoff of the claim you have shorted. The money you owe the counterpart long the claim is $\Pi(1,x)$. $\phi$ ...


1

Intuitively, because of the central limit theorem: wiener process is a limit of a random walk, and after n steps a random walk moves away from the origin by ~ $\sqrt{n}$ Edit: here is a complete answer. First the formula for the sum. The trick is the following simple observation: if $X_1,.. X_n$ are independent zero mean, then $E(\sum X_i)^2 = ...


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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