# Questions tagged [random-walk]

A stochastic process that describes a path arising from a succession of random steps.

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### Random walk on the edges of a cube

An ant is placed in a corner of a cube and cannot move. A spider starts from the opposite corner, and can move along the cube's edges in any direction $(x,y,z)$ with equal probability $1/3$. On ...
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### Why does the variance of the Random walk increase?

The random walk that is defined as $Y_{t} = Y_{t-1} + e_t$, where $e_t$ is white noise. Denotes that the current position is the sum of the previous position + an unpredicted term. You can prove that ...
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### Why are random walks intercorrelated?

I have observed that, on average, the absolute value of Pearson correlation coefficient is a constant close to 0.560.42 for any ...
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### Hamiltonian Monte Carlo vs. Sequential Monte Carlo

I am trying to get a feel for the relative merits and drawbacks, as well as different application domains of these two MCMC schemes. When would you use which and why? When might one fail but the ...
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### The magic money tree problem

I thought of this problem in the shower, it was inspired by investment strategies. Let's say there was a magic money tree. Every day, you can offer an amount of money to the money tree and it will ...
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### MCMC on a bounded parameter space?

I am trying to apply MCMC on a problem, but my priors(in my case they are $\alpha\in[0,1],\beta\in[0,1]$)) are restricted to an area? Can I use normal MCMC and ignore the samples that fall outside of ...
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### Random walk with momentum

Consider an integer random walk starting at 0 with the following conditions: The first step is plus or minus 1, with equal probability. Every future step is: 60% likely to be in the same direction ...
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### What does it mean to say that an event “happens eventually”?

Consider a 1 dimensional random walk on the integers $\mathbb{Z}$ with initial state $x\in\mathbb{Z}$: $$S_n=x+\sum^n_{i=1}\xi_i$$ where the increments $\xi_i$ are I.I.D ...
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### What is the autocorrelation for a random walk?

Seems like it is really high, but this is counterintuitive to me. Can somebody please explain? I am very confused by this issue and would appreciate a detailed, insightful explanation. Thanks a lot in ...
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### Random walk estimation with AR(1)

When I estimate a random walk with an AR(1), the coefficient is very close to 1 but always less. What is the math reason that the coefficient is not greater than one?
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### Why is a random walk not a stationary process? [duplicate]

In the book Analysis of Financial Time Series by Rue Tsay, I read: A time series $\{p_t\}$ is a random walk if it satisfies $p_t = p_{tā1} + a_t$ where $p_0$ is a real number denoting the ...
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### Random walk: kings on a chessboard

I have a question about the random walk of two kings in a 3×3 chessboard. Each king is moving randomly with equal probability on this chessboard - vertically, horizontally and diagonally. Ī¤he ...
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### How to interpret ARIMA(0,1,0)?

I ran the auto.arima()command in R on a set of data and it chose the appropriate model to be ARIMA(0,1,0). I know ARIMA(0,0,0) is just white noise, but what does ...
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### How to prove that the probability of spurious correlation increases with random walk length?

Define a simple random walk $y_{t}$ as: $$y_{t} = y_{t-1} + 2\times Bernoulli\left(0.5\right)-1,$$ so that at time $t$ the value of $y$ equals its previous value plus a perturbation from the "flip-a-...
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### How can we verify the intuition that in the RW-Metropolis-Hastings algorithm with Gaussian proposal too small and too large variances are bad choices

Let $d\in\mathbb N$ and consider the Random Walk Metropolis-Hastings algorithm with a Gaussian proposal kernel $Q$ such that $Q(x,\;\cdot\;)=\mathcal N_d(x,\sigma^2_dI_d)$ for all $x\in\mathbb R^d$. ...