Linked Questions
31 questions linked to/from Is a time series the same as a stochastic process?
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Why do stochastic processes involve time? [duplicate]
We define random variables as functions on a sample space $X(ω), ω ∈ Ω$. Here I do not see time being involved.
A stochastic process is a family of random variables, but they also are functions of ...
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What is a time-series signal? [duplicate]
Let's assume we have a CNC machine cutting an aluminium block and we are monitoring its RMS power consumption at a constant sample rate e.g. 1Hz (see figure below for example). Can this considered to ...
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Time series data [duplicate]
Is the following M4_regular_matrix time series data? I am a bit confused since The rows indicate locations although the columns consist of time. We actually ...
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When is a data set a time series?
Time is a concept from the real world. In mathematics and statistics, however, we operate on numbers. When does a number, as a mathematical abstraction, correspond to "time"? Any data set ...
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why independence assumption not applicable on time series analysis?
I just started my course in time series analysis. I saw a statement there: "Statistical methods that depend on independence assumption are no longer applicable in time series analysis". Why it so?
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Definition of random walk as a summation of independent random processes
I have a complete beginner question on random walk.
As per this paper
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How to show that an MA(2) process is strictly stationary?
I have a question about MA(2) model $X_t = e_t + 0.5e_{t−1} + 0.4e_{t−2}$ with $e_t \sim IID(0, σ^2_e $).
I know by construction, MA process is (weakly) stationary, but can it be strictly stationary ...
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Time series and random variable
I would like to know if the $n$ realizations of a variable, say $Y$ expressed in the form of a time series constitutes $n$ random variables or just a single random variable $Y$? For example, the ...
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Backshift Operator: Is it well-defined?
I have seen the backshift operator $B$ defined as $Y_{t-1} = BY_t$ in class. But I don't understand why this is a reasonable thing to do. Does the backshift operator exist for all discrete time ...
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Definition of the dirichlet process: what is the sequence of random variables
Reference material by Dr. Teh
Definition
Given a measureable set S, a base probability distribution H and a
positive real number $\alpha$, the Dirichlet process $DP(H, \alpha)$
is a stochastic ...
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Time series models (e.g. ARMA) a type or extension of GLM? Particular/stipulated forms of dependence in time series models
I am trying to understand the relationship between ARMA Time Series models and the GLM (Generalized Linear Model) family of models. As far I know, all GLMs have the following 3 components: 1) random ...
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Relation and difference between time series and stochastic processes?
Partly inspired by the following post: Relation and difference between time series and regression?
After thinking carefully into these two subjects, I kind of wondering for what kind of data/...
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Understanding stationarity in stochastic processes and time series
I am having trouble fully grasping the concept of stationarity in time series.
Here is what I have gathered so far.
A stochastic process is a collection of random variables with mean $\mu$ and ...
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What is the difference between an AR process and autocorrelation?
Or is it maybe the same thing? I see that autocorrelation is when Yt is correlated with its lag Yt-1. But isn't that essentially what an AR process (say AR(1)) is? We are assuming that there IS ...
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What is a Stochastic Process?
Online I found many definitions of stochastic processes, but none of them was intuitive or easy to understand. I was wondering if someone could provide me with some example and definition to deeply ...