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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.

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PCA on conditional heteroscedastic stochastic process data

What is the correct method of application of Principal Component Analysis (PCA) on time series data? Since the time series may exhibit conditional heteroscedasticity, application of normal PCA might ...
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23 views

IGARCH model property (conditional distribution) when used to model sum of log returns

I already asked this in the quant, crossvalidated, and math SEs, but no help there. I'm not sure many people are familiar with whatever I'm asking, and I tried rewording the question too, but seems ...
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1answer
185 views

Reference request in optimal stopping [closed]

I am given the following task. Distributed over a trading day, I am supposed to buy a certain quantity of a good. The price of this good changes during the day. The goal is to buy the required ...
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44 views

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 $m$-...
4
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1answer
248 views

Support of bivariate joint distribution of stationary and ergodic sequence

Let $\{X_t\}_{t\in \mathbb{N}}$ be a strictly stationary and ergodic sequence of real valued random variables and let the support of $X_1$ equal $[-1,1]$. Can the support of $(X_1,X_2)$ equal the unit ...
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118 views

Why according to Takens' theorem (1981) we need 2m+1 observation functions (or time series) to reconstruct the attractor?

In the paper [1], page 369 we have Theorem 1 which says: Let $M$ be a compact manifold of dimension $m$. For pairs $(\phi,y),\;\phi: M\to M $ a smooth diffeomorphism and $y: M \to \mathbb{R}$ is a ...
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1answer
76 views

Calculate Average and Correlation of WSS Random Processes

Given two stochastic processes, $X[n]$ and $Y[n]$, both being WSS (wide state stationary) and independents. What would be the Average and Autocorrelation function of $Z[n] = Y[n] X[n]$? Is the ...
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41 views

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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1answer
75 views

Quantifying an increasing spacing between data points

Is there a measure or statistic that could quantify a steady increase in the spacing between data points in a time series? For instance, in the figure, the points are clustered and dense near 0, but ...
2
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1answer
70 views

Relation between invertibility and strong mixing of a time series

Setup: I have a sequence of stationary ergodic random variables $(\epsilon_t)_{t\in\mathbb{Z}}$ and a function $\phi:\mathbb{R}\times \mathbb{R} \rightarrow \mathbb{R}$. Define the sequence of random ...
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1answer
61 views

Estimating operators of functional linear processes

Let $H= L^2[0,1]$ be the space of measurable and square integrable functions from $[0,1]$ to $\mathbb{R},$ let $(\varepsilon_k)_{k \in \mathbb{Z}}$ denote the iid (or strict stationary) $H$-valued ...
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137 views

Solving overdetermined, “polynomial time dependent” linear system

Hello & happy new year, let $n \geq m$ be two natural numbers. Furthermore let $W \in \mathbb{R}^{n \times m}, Y \in \mathbb{R}^{n \times n}, \lambda \in \mathbb{R}^n, \mu \in \mathbb{R}^m$. ...
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1answer
531 views

Fourth moments of Gaussian processes

I am working on a topic outside my main research area, so I am afraid I am reproving obvious results, so I would like to ask for a reference. Google didn't help, mostly because I am looking for ...