# Questions tagged [random-walk]

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

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### Give a random walk on an interval with specified endpoints & extrema, can I find the probability that the max occurs before the min?

I have some summary measures on a time series process for a large number of time intervals, all of the same length. The summary measures are the initial value (i), which I will take to be zero without ...
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### Is a random walk cointegrated with its own lag?

Can a random walk, or more broadly a unit-root process, be considered cointegrated with its own lag? E.g. if $y_t=y_{t-1}+u_t$ with $u_t\sim$ i.i.d., then $y_t$ is I(1), $x_t:=y_{t-1}$ is I(1) and ...
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### Simple Symmetric Random Walk on $\mathbb{Z}$ is null recurrent

Question: Consider a simple symmetric random walk on integers, where from every state $i$ you move to states $i-1$ and $i+1$ with probability half each. Show that this random walk is is null ...
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### Random walk analysis of a univariate timeseries

As the title describes, I want to conduct a random walk analysis of a univariate time series $Y_t$. What are the tests and steps that you guys would suggest for this purpose? My current thinking: ...
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### Random walks and martingales

In class, our professor explained that the martingale process is the in between case of random walk type I (innovations are i.i.d.) and random walk type II (innovations are serially uncorrelated). ...
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### Different Random Walk Types and the Variance Ratio test

From my knowledge, we distinguish between two types of random walks. Type I, where the innovations are i.i.d. and Type II, where the innovations are serially uncorrelated. I want to conduct several ...
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### Find the expected number of steps [duplicate]

Consider the following problem: Two people $M$ and $T$ walk over a straight line. The steps they take depend on flipping a coin: They move to the left if the result is head and they move to the right ...
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### Random-walk and unit root processes predictable?

I know that a random walk is an AR(1) with a unit root, but there are also higher order autoregressive processes with unit roots. Does the unit root in such a higher order autoregressive process also ...
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### Is every time series that is not predictable a random walk?

The title already reveals my question. I was wondering how specific the characterisitics of a random walk are defined and if every time series that is not predictable belongs to the class of random ...
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### Weak form of market efficiency and random walks

The weak form of market efficiency states that historical prices should not provide predictive information that is not already incorporated in the current price. Hence, predictions based on the past ...
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### Is ARIMA and Random Walk a Nested model?

I have confused about the Radom Walk. If a model restrict some parameter as 0 and the two regressions are the same, which is the Nested model. But in ARIMA model versus Random Walk model, the random ...
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### Expected first passage time for random walk

A random walk on $\{0,1,2.....n\}$ with $p_{0,0} = p_{n,n} = 1$ and $p_{i,i+1} = p = 1-p_{i,i-1} = 1-q$ for $1 \leq i \leq n-1$ .Let $X_0 = i$ and $T$ be the first passage time to either 0 or $n$ ...
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### Confused about stationarity and ARIMA processes

So I am quite confused about stationarity in ARIMA processes. For example, a Random Walk is an ARIMA process with order (1,0,0). Does this mean that a Random walk is stationary? Stationarity implies ...