Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [discrete-time]

46 questions
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Is average stopping time a continuous function of Bernoulli parameter?

Consider an infinite sequence $X = (X_i)_{i \in \mathbb N}$ of i.i.d Bernoulli random variables with (unknown) parameter $p \in (0,1)$, and let $N$ be a stopping time on $X$. Is it always the case that $\mathrm E[N]$ is a continuous function of…
Luis Mendo
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How to forecast integer time series in R?

For a while now I used to forecast integer/count time series as I would do for any other continuous time series, meaning : I use models like ARIMA, ETS, THETA, TBATS ... And then I simply round the results. So I wonder is there some models designed…
Taha
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Describe AR process with additive white noise using ARMA process

Disclaimer: This is a homework problem This is a problem from "Adaptive Filter Theory" by Haykin. Problem 2.10 (2nd edition). Problem A discrete-time stochastic process $\{x(n)\}$ that is real-valued consists of an AR process $\{u(n)\}$ and additive…
jodag
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Calculating the expected number of visits to a state by a DTMC

Suppose we have a DTMC $X$ : $\{X_n : n = 0, 1,2,\dots\}$, a transition probability matrix $P$, and state space $S = \{1,2,3\}$. Suppose I want to calculate the expected amount of times we visit state $3$ in $T$ periods given that we start our chain…
hkj447
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Simulation -Discrete Time Hazard model

How we can simulate the survival times for fitting discrete time hazard model?
has87
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4
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discrete time survival analysis

I would greatly appreciate if you could let me know how to do discrete time survival analysis with time varying covariates. Some part of my data set is as follows: ID TIME EVENT x1 x2 x3 x4 x5 1 1 0 1.28 0.02 0.87 1.22 0.06 1 …
ebrahimi
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Conditional probabilities with Discrete Time Markov Chain non-perishable inventory

Suppose $\{X_n : n =0,1,2,\dots \}$ is a DTMC that represents the inventory level at the end of day $n$. We have inventory policy $(2,4)$, i.e., if $X_n < 2$, we order enough units to have inventory level equal to $4$ by the beginning of the next…
hkj447
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What statistical tests allow for a comparison of the "roughness" of discrete functions?

I have a data set of the revenues of 10 different large companies from the years 2000 through 2019. Here they are all plotted in one graph. The y-axis has a unit of billions of Euros:                                                 What I found…
Max Muller
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Z transform of $ 2^{-|n|} $

Dears, I'm trying to compute the Z-transform of $$ x(n) = 2^{-|n|} $$. My procedure is as follows: Using definition of Z transform: $$ X(z) = \sum_{n=-\infty}^{\infty}2^{-|n|} z^{-n} = \sum_{n=-\infty}^{0}2^{-|n|} z^{-n} +…
Julius Max
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best statistical approach to study the time evolution of clustering in a data set

I am using a stochastic method for the clustering of a data set. The number of clusters that this approach returns, can differ in each iteration. On the other hand, I would like to study the evolution of clustering at different snapshot of the data.…
Dalek
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Interpreting a (integer valued) discrete predictor as a continuous variable?

I am currently working on a multiple linear regression in order to evaluate the impact of some variables on a contract's length, which can only take integer values (years). As I am only interested in which variables have a significative effect on…
allo
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Discrete time generator of stochastic process

While looking at one paper about Metropolic Hasting optimal convergence rates, I came accross a discrete time generator of Markov chain. It is defined as follows: $$G V(x)=nE\left [ \left( V(y)-V(x)\right )\left(1\wedge \frac{\pi(y)}{\pi(x)}\right )…
Tomas
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Variable data measured discretely with poor resolution

Is there an appropriate method for estimating variation when variable data is measured discretely where the resolution is poor. Here's an example: You are looking at how long it takes for a solid to degrade while in solution, and you check it twice…
KoldBeans
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Proving/showing that the Markov property holds in discrete time Markov chain example

I am currently studying the textbook Introduction to Modeling and Analysis of Stochastic Systems, Second Edition, by V. G. Kulkarni. In a section on discrete-time Markov chains, the author presents the following example: Example 2.2. (Machine…
The Pointer
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Statistical modeling multidimensional discrete system

I have a system which its state is described by a vector $v=(a, b, c)$, where $a$, $b$ and $c$ can take any value between $0$ and $100$ and where $a+b+c <= 100$. I have observations of the state of the system for about 10 years (one per year, so 10…
Giulia Martini
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