# Questions tagged [random-walk]

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

208 questions
Filter by
Sorted by
Tagged with
2k views

### Moving Average, Exponential Smoothing, and Random Walk for Forecasting

I would like to confirm my understanding. Is it true that a (simple) exponential smoothing model with alpha (smoothing constant) = 1 is the same as MA(1), which is in turn the same as a random walk ...
427 views

### Runs test and Durbin-Watson test yield different outcomes

I have analysed the market return using the runs test and the Durbin-Watson test to determine whether the return series follow the random walk or not. The problem I have found is that some return ...
148 views

### Proof the increment variance of the Scaled Random Walk

Start by defining the Symmetric Random Walk: $$M_t = \sum_{i=1}^{t}X_i, ~~ \text{with}~X_0=0$$ where $X_i$ is equal to 1 or -1 with $p=(1-p)=0.5$. Consider $t > s$, the variance of its ...
357 views

### Is a random walk necessarily a martingale?

I read in the following notes (http://www2.econ.iastate.edu/classes/econ672/Falk/_notes/lecture_4_martingales.pdf, p.2) that "a random walk is a martingale." Although it seems logical with the used ...
92 views

### Estimating error from an autocorrelated random walk

Hello Cross Validated, I am trying to simulate autocorrelated, lognormal values such that their SD matches that of an existing time series. I plan to generate these values using the following ...
559 views

### Error term in Random walk with drift

In random walk model the error term is generally modelled using normal distribution. I have two questions. Q1. How to calculate the parameters of error term in case of Random walk with drift. Q2. ...
66 views

### the length of a random walk in two dimensions

This is a matlab code that could generate a random walk in two dimensions of length 1000: xy = cumsum (-1+2*rand(1000,2),1). The 'stepsize' is between $[-1,1]$. In this case, we are talking about ...
599 views

### Estimating the white noise of a Random Walk

I want to simulate a random walk without drift to predict a time serie. The random walk model is $X_t = X_{t-1} + \epsilon_t$ where $\epsilon_t$ a white noise with a Normal distribution. It seems ...
66 views

### How to draw a representative gaussian random walk?

I would like to draw (as in, with a pen on paper) a line chart that is representative of a Guassian random walk defined as the sequence of random variables $(Y_t)$ where $t = 0, 1, 2, \dots$, such ...
2k views

### Lag between predicted output and real output in time series prediction (directional prediction)

I modeled a directional prediction of a time series. In every step, I predict next direction of that series (up or down). Currently I have a lag in predicted outputs compared to real outputs. For ...
814 views

11k views

### How to create a random walk model using {forecast} R package

I have a good understanding of ARIMA models but I've always found significant spikes in ACFs and PACFs that gave me the appropriate AR and MA parameters. Now I'm dealing with a series that is more ...
332 views

### Predicting point forecast using Random walk model coefficients

I have created a random walk model ARIMA(0,1,0) in R. The coefficients and R output is as shown below: ...
81 views

### Learn a random walk process with RTS smoother

I'm trying to learn a random walk process as described at section 7 of http://www.cs.cmu.edu/~epxing/papers/SDM08_Ahmed.pdf I have a set of points over N epochs. Given a set of clusters $K$, every ...
45 views

### probability that noone will have to wait for change [closed]

This is the exact question text: $2n$ children are waiting in a queue for movie ticket. Tickets are priced at a quarter each. Each child pays for the ticket either with a quarter or with half dollar ...
322 views

### continuous vs discrete random walk

For 1D random walk in discrete case the probability of finding walker at position X after N steps(P_N(X)) is binomial distribution(http://mathworld.wolfram.com/RandomWalk1-Dimensional.html), moreover ...