# Questions tagged [stochastic-processes]

A stochastic process describes the evolution of random variables/systems over time and/or space and/or any other index set. It has applications in areas such as econometrics, weather, signal processing, etc. Examples: Gaussian process, Markov process, etc.

1,280 questions
Filter by
Sorted by
Tagged with
17 views

### What is the cubic expectation (third-order moment) of a complex gaussian vector (say, E[$aa^{T}a$])?

Note: I also posted this question on MATHEMATICS. For a real gaussian vector, an explicit formula for the cubic expectation can be found in Matrix Reference Manual (search 'Cubic Expectations' in this ...
1 vote
61 views

### What's the transition probability according to this PDE?

I'm trying to figure out how I can simulate markov chains based on an ODE: dN/dt = alpha N (1 - N / K) - beta N Thus N denotes ...
• 113
1 vote
14 views

### Moving Average with non-increasing coefficients

Suppose I have a Moving Average $MA(q)$. $$X_t = \sum_{j=0}^q \psi_j \epsilon_{t-j}, \quad (\epsilon_t)_{t\in \mathbb{Z}}\,\,\ i.i.d.$$ I know that there is no imposition regarding the monoticity of ...
• 877
1 vote
46 views

### How to simulate non-gaussian stochastic paths

(Edited to be clearer) I am trying to replicate simulating Geometric Brownian Motion (GBM) but instead of the stochastic increment following a normal distribution, I would like it to follow a ...
• 13
6 views

### Variance of random walks in time series analysis [duplicate]

“For a random walk stochastic process, the variance is infinite.” Do you agree? Why?
26 views

$x_t=2.1+0.73x_{t-1}+ε_t$ $ε_t \sim iid(0,σ_ε^2)$ Given the stochastic process with deep Gaussian process above, is x_t an ergodic stochastic process? If possible, I would like to know the reason.
• 1
10 views

• 511
31 views

### Alternative to SimPy for continuous event simulation?

The python library, SimPy, is pretty explicit that it only handles discrete event simulation. Though it is theoretically possible to do continuous simulations with SimPy, it has no features that help ...
• 1,700
11 views

### Numerically solving the Forward equation to estimate SDEs

In books [1] dealing with inference for SDEs, why is the approach of numerically solving the forward PDE to obtain numerical estimate of the PTD not studied? One could then use this PTD to perform a ...
• 101
48 views

### Stationarity and ergodicity of a process conditional on a finite trajectory

Let us say we are interested in a single time series, e.g. the daily closing share price of Tesla. We can model it as a realization of a stochastic process $\{Y_t(\omega)\}$. It corresponds to a ...
• 55.5k
15 views

### First order PDF of a stochastic process

I've started studying about stochastic processes and I need some help in this question. A random number generator is making numbers by this process: First number (X0) is a sample from Normal Standard ...
71 views

### Stochastic modelling, distribution and ergodicity of a particular time series with a given finite history

Let $\Omega$ be a sample space. A stochastic process $\{Y_t\}$ is a function of both time $t \in \{1, 2, 3, \ldots\}$ and outcome $\omega \in \Omega$. For any time $t$, $Y_t$ is a random variable (i....
• 55.5k
1 vote
30 views

### Question about autocorrelation of time series

I have a time series $S(t)$ for $t\in I$ where $I=[0,t_\text{max}]$ is an interval. The time series is very regular, $S(t) = \sin(t)$, although my following question is independent of the explicit ...
• 213
74 views

### What is wrong with using t-SNE for predictions?

If I have a dataset with hundreds of samples and thousands of features, and t-SNE does a good job of separating classes compared to others classifiers, I don't understand why I can't rerun the ...
• 81
10 views

26 views

### A nondeterministic covariance-stationary process approximated by an ARMA process

We know that the Wold Decomposition Theorem says that any purely nondeterministic covariance-stationary process, $x = [x_t : t \in \mathbb{Z}]$, can be written as a linear combination of lagged values ...
• 877
71 views

### Winning at tennis

What is your probability of winning a game of tennis, starting from the even score Deuce(40-40), if your probability of winning each point is 0.3 and your opponent's is 0.7? My answer: I think the ...
1 vote
54 views

### Modeling Urns and Balls System as a Markov Chain

Suppose I have $q$ urns each of which hold up to $n$ distinguishable balls, but only $1$ of each type of ball (there being $n$ types of balls too). I would like to make any particular configuration of ...
• 151
56 views

### Show that two white noise definitions are equivalent

Given $(\varepsilon_t)\sim WN(0,\sigma^2)$ a white noise. By definition $$E(\varepsilon_t)=0,\,\, E(\varepsilon_t^2)=\sigma^2 \quad \forall t$$ and $$E(\varepsilon_t \varepsilon_s) = 0, \quad s\neq t$$...
• 877
42 views

### A conceptual question about the limitation of the MA processes

We know that linear time-series techniques are frequently used in macroeconometrics. The Wold Representation Theorem states that any covariance-stationary process may be expressed as an MA process ...
• 877
16 views

### Coefficients for higher dimensional NIPC (non intrusive polynomial chaos expansion) heavily biased towards 0 degree function

Currently, I am trying to apply the PCE to the thermal fin problem as solved using finite element. Although I cannot attach the code I use, suffice to say I solve a linear system $AU=F$ where $F$ is ...
• 111
35 views

### Simulating paths of stochastic process from density

I need yout help! I have a stochastic process $X_t$ and I know its density function $f(x,t)$, which is defined for $x>t$. I'm looking for a code in R that simulates the paths of the process, so I ...
1 vote
13 views

### What would be a continuous-time version of a VAR process?

It is often said that a AR(1) process can be viewed as a discretized version of the continuous-time Ornstein-Uhlenbeck process. Can we really claim this to be valid considering that the Ornstein-...
• 299
1 vote
26 views

### Purpose of negative indices in time series

In the book Time-series analysis by Hamilton we find the following passage: A time series is a collection of observations indexed by the date of each observation. Usually we have collected data ...
43 views

### Why is the difference between 2 time series drawn from the same process not White Noise?

I take the difference between 2 time series (each with 200,000 observations) drawn from the same ARMA(2,1) process and find that (at least the first 1000 observations of) this difference looks like ...
• 3,242
17 views

### Derivation of autocovariances of squared shocks

I have two shocks: $\varepsilon_{1t}$ has constant volatility $E[\varepsilon_{1t}^2]$ = $\sigma^2_1$ while $\varepsilon_{2t}$ has time varying volatility $E[\varepsilon_{2t}^2]$ = $\sigma^2_{2,t}$. I ...
• 137