# 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.

**-1**

votes

**0**answers

34 views

### 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 ...

**0**

votes

**0**answers

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 ...

**-4**

votes

**1**answer

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 ...

**4**

votes

**0**answers

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**

votes

**1**answer

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 ...

**0**

votes

**0**answers

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 ...

**1**

vote

**1**answer

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 ...

**1**

vote

**0**answers

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 ...

**2**

votes

**1**answer

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**

votes

**1**answer

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 ...

**0**

votes

**1**answer

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 ...

**0**

votes

**0**answers

137 views

### Solving overdetermined, “polynomial time dependent” linear system

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

**8**

votes

**1**answer

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 ...