Questions tagged [random-walk]
A stochastic process that describes a path arising from a succession of random steps.
292 questions
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Efficient algorithm to approximately sample from random walk
Let $X_0,X_1,X_2,\dots$ be the simple random walk, i.e., $X_0=0$ and each $X_{t+1}$ is sampled uniformly at random from $X_t-1,X_t+1$ independently of everything else.
Given a very large $t$, I want ...
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Probability of hitting time and additional time $X+Y$ in a diffusion process
Let $X$ follow an inverse Gaussian distribution, and $Y\mid X$ a Gaussian distribution.
$$X \sim IG\left( \frac{\alpha}{v_X}, \frac{\alpha^2}{2D_X} \right)$$
$$Y_{\text{given $X=x$}} \sim \mathcal N(...
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Distribution of terms in a random walk on the simplex
It is known that the random walk on the simplex $\Delta^{n}$ given by:
$$
X_{t+1} =(1-b_{t}) X_{t} + b_{t} E_{t}
$$
where $X_{0}$ is any point in the simplex, $b_{t}\sim Beta(1, \gamma)$ are sampled ...
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Detrended Fluctuation Analysis
In R, I am attempting to implement the DFA time series analysis algorithm described in
https://en.wikipedia.org/wiki/Detrended_fluctuation_analysis
and
https://www.kubios.com/blog/hrv-analysis-methods/...
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Best parameter of exponential smoothing when applied on a random walk
Let's say I have a random walk:
$$X_t = X_0 + \sum_{i =1}^t \epsilon_i$$
with the $\epsilon_i \sim \mathcal{N}(0, \sigma^2)$ and independent.
Then what smoothing factor $\alpha$ in an exponential ...
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When regression models outperforms the naive methods?
I followed from this question.
Case1:
I have the following task to do: Training by the consecutive 3 days to predict the each 4th day. Each day data represents one CSV file which has dimension 24x25. ...
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Bayesian posterior predictive distribution for a random walk with drift
Suppose we have a random walk with drift $$ x_i - x_{i-1} = \mu + \varepsilon_i,$$ where the error terms $\varepsilon_i$ are i.i.d. Gaussian with the same variance $\sigma^2$. Given a sequence of $t+1$...
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Expression for discrete Brownian motion with reflection
For a discrete Brownian motion with an absorbing state we can express the distribution of the position as a linear sum of two binimial distributions as described here when the odds for +1 and -1 steps ...
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why does this tumbling tetrahedra result depend on n?
In Section 15.4 of Jaynes' Probability Theory the Logic of Science (pdf here: http://www.med.mcgill.ca/epidemiology/hanley/bios601/GaussianModel/JaynesProbabilityTheory.pdf), he proposes following ...
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Conditional variance of random walk with given start points and ending points
If I have a random walk with 0 drift and I observe that $X_1 = x_1$ and $X_k = x_k$, bu I don't have all the points from $X_i$ for $i \in \{2, ..., k-1 \}$, how do I estimate them and given an CI? I ...
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Why is a coefficient in front of $Y_{t-1}$ in a random walk (equal to 1) not an autocorrelation coefficient? [duplicate]
As it is said everywhere autocorrelation measures the correlation between a time series variable and its lagged values at different time intervals. Then why can't we say that coefficient in front of $...
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How can I simulate the path between two defined points but also define the overall step variance?
As stated in the question. I’m wondering if it’s possible to simulate a random walk between two fixed points (always start at A and finish at B) where the variance of the difference of steps is also ...
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experimenting random price movement
Random price movement
Consider the following:
The price of an apple starts at 1 dollar.
On each day, the price will change -10% or +10%, with equal probability.
You buy this apple on day 1, and sell ...
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Checking if RW() = ARIMA(0,1,0) with drift
I am trying to confirm the following statement that in R fable package: ...
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Gridsearch on ARIMA favours random walk
I am working on a time-series forecasting problem with ARIMA.
Since long-term predictions were not good, I've started using a "rolling ARIMA" like explained here
...
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