# Questions tagged [discrete-time]

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### Determine order of events happening in discrete timespace

At $t=0$ I have a certain (active) population, lets say 1,000 customers. In each time step I expect a certain amount I have a probability of death of 1% and a prepayment rate of 5%. At the end of each ...
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### Probability $X_n=k$ for a Markov Chain over the integers

Let $\{X_n\}$ be a Markov chain with state space $\mathcal{S}=\mathbb{Z}$, and $X_0=0,$ and $p_{0,1}=p_{0,-1}=1/2,$ and $p_{i,i+1}=1$ for all $i \ge 1,$ and $p_{i,i-1}=1$ for all $i\le -1.$ The ...
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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 ...
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### Negative Binomial vs. Discrete Survival

I am trying to model a discrete duration variable (number of weeks) and I am not sure which model to use. Many would argue that durations are modeled using survival models. However, in J. Hilbes ...
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### Any methods for clustering short time series data

I have around 200 different sets of time series data with a semi-annual periodicity. The length of each series varies from 1 to 6 years. I essentially want to build unsupervised clusters by grouping ...
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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 ...
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### Rows and columns of the one-step transition probability matrix

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 introduces ...
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### Regression analysis with small data set

We've performed a regression analysis with 14 data points (Y's) that originate from 9 X's (plant batches were split up). I'm well aware that this is a small data set and there are caveats. However, ...
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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 ...
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### Detecting Significant Changes in Time Series

I’m hoping someone might be able to point me in the right direction for this problem. I’ve anonymised the problem by describing it in terms of supermarket purchase data rather than the real context so ...
175 views

### Posterior distribution from piecewise likelihood

Consider a hierarchical Bayesian model for analysing data from an inhomogeneous Poisson process that we observe in discrete time. Let $Y_i, i = 1,...,n$, be the number of events occurring in the time ...
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### Modeling Time in the Discrete Time Analysis using Left-truncated Data

I am doing multiple-spell, discrete-time analysis to examine factors shaping time to exiting a renter spell, with time-varying covariates at monthly interval. My data has left-truncated spells, ...
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### INAR(1) simulation in R [closed]

How do we simulate values of $Y_t$ for a maximum value of $t=60$ when we have an INAR(1) process as follows: $Y_t=ρ^*Y_{(t-1)}+R_t$ where $t$ takes values from 1 to 60, $ρ=0.3,0.8$, $ρ^*$ is ...
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### Simulating a (discretized) Cox process via binomial sampling

Let X be a Cox process (doubly-stochastic Poisson process) driven by a Poisson process with fixed intensity(rate) $\lambda=50$ , and choose some small time interval $dt=0.01$ . Is the proper way to ...
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### How to recognize an ARMA process?

By looking at the autocovariance, how could you recognise what discrete model (MA(q), AR(p), or ARMA(p,q)) is more appropriate to describe your data?
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### Simulation -Discrete Time Hazard model

How we can simulate the survival times for fitting discrete time hazard model?
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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 ...
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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 ...
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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 ...
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### Gaussian random variable over multiple periods

Let's assume that : $$X_0=X_0$$ $$X_1=(1+R_1)*X_0$$ $$...$$ $$X_N=(1+R_N)*X_{N-1}$$ where $R_i \sim \mathcal{N}(0,u^2)$. I am trying to compute the probability $P(X_N < a)$. How accurate is it to ...
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### Linear mixed model: Time as continuous or discrete variable?

I am analysing a dataset from a randomised controlled trial (2 treatment groups) with measurements at 3 time points (weeks 0, 1 and 8). I am struggling with whether to analyse this with the three time ...
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### Probability distribution for day of the year [closed]

"Day of the year" is an integer from 1 to 365, indicating the day within the year. I'd like to model the day of the year that a particular event occurs. The event must occur between day 100 and day ...
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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: ...
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### parametric survival regression and discrete time survival regression

I would greatly appreciate if you could let me know how to choose among different parametric distributions including gama, Weibull, lognormal, loglogistic and etc for panel (time series cross ...
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### Looking for suitable method to update predictions

consider an e-commerce website which daily updates their transaction data. I take interest in predicting the revenue an account generates over a certain time range, say until the fifth year after the ...
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### Difference between count time and discrete time survival analysis

Is there a practical or theoretical difference between count time survival analysis (e.g. ctset/cttost in Stata), where counts ...
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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 ...
329 views

### 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-...
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### Algorithms for extracting moving average intervals

I have a series of discrete events and a global clock. Whenever an event happens, I record a timestamp and do some processing. Specifically, I am trying to compute "moving average" (not really) ...
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### How to check assumptions for a discrete time survival analysis

What tests are required before and after estimating a discrete time survival model? In other words, how the assumptions should be tested and how the generalization of results should be investigated ...
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### Coefficients in discrete proportional hazards model

I am aware of the rationale behind taking the exponentiated coefficients in a proportional hazards model as representing change in hazard per unit change in the corresponding predictor. This also ...
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### I have a discrete-valued time series and would like to analyse it, but dont know where to start

Due to some health issues, each day at about the same time, I give myself a score which represents the state of my health: specifically, fatigue, with 1 being the worst and 10 the best. In practice, ...
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### How to calculate the probability of death between two discrete time periods using survival curves

I was hoping somebody could help, I am trying to work out the probability of death between two time points on a survival curve. i.e. I have my survival curve as follows (this is an example Kaplan-...
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### When is time treated as a discrete variable?

Time is usually treated as a continuous variable but in some cases it is discrete. An example would be with a drug study and measurements are taken at 1, 2 and 3 hours. Am I right to think an ...
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### Resource request : How to prove the output of a process is random variables?

I am reading through articles which present the spectral properties of chaotic systems such that they can be candidates for generating pseudo random binary sequences. One such article, is http://...