Questions tagged [time-series]
The analysis and inference about data observed over a general(continuous or discrete) time space. Usually related to stochastic processes and will probably receive better response under that tag.
15 questions with no upvoted or accepted answers
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Theoretical justification of time-series forecasting using Takens' embedding
This is a cross-posting
where I couldn't get an answer. In the meantime I have tried to improve the original logic:
As in Takens original paper about his embedding theorem, consider a compact $m$-...
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An infinite moving average is stationary iff its innovations are stationary
Let $(a_j)_{j \in \mathbb{N}_0}$ be a real-valued sequence such that $\sum_{j = 0}^\infty a_j^2 < \infty$.
Further, define an infinite moving average time series $X = \{ X(t), t \in \mathbb{Z}\}$ ...
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Probability measure on $\mathbb{R}^n$ with given marginals and given correlation matrix
In all what follows, let $\mathcal{P}(\mathbb{R}^n)$ denote the set of probability measures on $(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n))$ and $\mathcal{C}_n$ the set of $n \times n$ correlation ...
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Convergence of random operators
I'm a statistician not versed in functional analysis and operator theory. I wish that I might not find a wrong place for my question. All my questions are trivial in the scalar time series case, but ...
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Cointegration of (multiple) time series
Some time ago I stumbled upon the notion of cointegration of time series (see the wiki for some basic fact).
Unfortunately, my knowledge of time series is a bit sketchy, and moreover I was able to ...
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81
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Urn model with delayed replacement
Suppose I have x red and y blue balls. At each timestep I draw a ball with probability $$P(\text{red ball}) = (x/(x+y))^z, P(\text{blue ball}) = 1-P(\text{red ball})$$ where z is fixed.
Each ball is ...
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Subordinated non-deterministic Gaussian process is non-deterministic
Let $X = \{ X(k), k \in \mathbb{Z} \}$ be a strictly stationary, Gaussian time series whose spectral density $f_X$ exists.
Furthermore, let $X$ be non-deterministic, i.e.
$$
\mathbb{E}\big[ \vert X(n +...
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How do the singular values of a Hankel matrix, generated by some data time series, change when we add/remove rows and columns?
Suppose I have a smooth time series $C(t)$ defined on the interval $t=[0,T]$, from which I extract the sub-series $c=\{x_1,\cdots,x_N\}$ of $N$ entries, where $x_i=C(i*T/N)$. Naturally, the number $N$ ...
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Deriving periodical processes from a finite time series
Suppose we have a finite time series of real-world events measured at $(t_k), k \in \mathbb{N}$ with $(t_{k-1} < t_k)$. The content of the actual events is irrelevant.
I would like an automated ...
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Calculating right values of Periodogram using Fourier Analysis
In the book, Economic Cycles: There Law and Cause By Henry Ludwell Moore, he plots Periodogram of rainfall of Ohio valley. He uses 72 years data (1839-1910) and tries to find the most dominant cycle ...
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How to analyze a nonlinear time series dataset?
I have a time series that appears chaotic that I would like to analyze with Python. To draw its logistic map, I must use the logistic equation: $$x_{t+1}=rx_{t}(1-x_{t})$$
I have the data in a text ...
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Given a set of time-series data, how would I determine another time-series is a linear combination of the set?
In other words, determine if sum linear combination of existing time-series could result in the desired time-series. I'm unsure if assumptions about the time-series may clarify the problem better, so ...
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How to calculate the power transformation of a spectral density function
There is a problem I have been trying to solve for a while. Let $X_t$ be a stationary (univariate) time series. The spectral density of the moving average process $$X_t=\sum^{\infty}_{j=-\infty}a_je_{...
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Distribution of bivariate vectors for strictly stationary processes
Consider a strictly stationary process $X_t$, $t\in\mathbb{Z}_{\geq 1}$. Could you help me to disprove the following statement:
"For $t, s > 0$, the bivariate vectors $(X_s, X_t)$ and $(X_t, ...
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A new method for processing music scores?
I have developed a method and python script:
https://github.com/githubuser1983/algorithmic_python_music
which allows the user to input a midi file and then chose a few numbers as parameters, and the ...
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