# Questions tagged [time-series]

This tag is used for question related to time series models such as AR, ARMA, ARCH, GARCH and their properties and techniques used for inference.

855 questions
Filter by
Sorted by
Tagged with
31 views

### Interpretation of Complex Roots of a Linear Difference equation.

I solved this linear difference equation $$x_{k+2} = c_1 x_{k+1} + c_2 x_k$$ to get the general solution \begin{align} x_k = \lambda \left(\frac{c_1 + \sqrt{c_1^2 + 4 c_2}}{2} \right)^k + \mu \left(\...
15 views

### Is it possible to represent two time series as a common and different component?

First of all, thank you for reading my question. I would like to know if it is possible to rearrange two correlated time series as the sum of two individual components plus a a third common component? ...
19 views

### Moving Average for Speed and Acceleration

I am tracking a person using a set of ultrasound tracking device. The ultrasound system provides (x,y) location data at 8Hz frequency, and there are 131 data points in total. When calculating the ...
22 views

13 views

### How to smooth a projected value obtained with a multiplicator in a time series?

I have a time series chart where each bar interval = 600 seconds. Each bar accumulates a number of transactions in a variable called 'volume'. The goal is, while the current 10 mn bar is forming in ...
6 views

### Impulse response function of the unit root model

Trying to calculate the impulse response function of the unit root model. IRF = enter image description here Where Y = enter image description here Not sure how to derivate that.
26 views

15 views

### Constrained interpolation/smoothing of multi-dimensional time series

Consider an $N$ dimensional time series $x_i(t),~i\in\{0,1,\cdots, N-1\}$ where $x_i(t)$ is smooth. It turns out that for all $t$: $x_i(t)>x_{i-1}(t)$. The multi-dimensional series is sampled at ...
41 views

### Does Portmanteau Test need?

I am studying time series with Ruey S. Tsay Financial time Series(3rd ed). In his text (page 32), he introduced Box & Pierce Portmanteau statistics $$Q^*(m) = T\sum_{l=1}^m\hat{\rho}_l^2$$ for ...
50 views

### Is a ratio of numerical derivatives, $\frac{dx}{dt} / \frac{dy}{dt}$, considered a "partial derivative"?

I am reading a paper on genetic programming by Lipson and Schmidt called "Distilling Free-Form Natural Laws from Experimental Data" at the following link: ...
8 views

### Multinomial model: starting value for time parameter

I’m a beginner data science student and for a course we need to replicate a paper which models multi-party elections in a Bayesian framework. Basically, we understand the model: poll respondents $y$ ...
20 views

### Predicting complex periodic signals without "enough" samples

I was recently reasoning about the analysis of complex periodic signals and about the prediction guarantees that one can achieve without sampling the whole period. Say I have a signal that I know can ...
33 views

### Multivariate time series and machine learning.

I have a question relate to apply machine learning algorithm to time series data. Because time series data has the impact of "order time or sequence" (I am meaning that time indexing, for ...
13 views

100 views

### Approximating the spectral density of white noise by a moving average process

Suppose that $X_t$ is a weakly stationary process; then, its autocovariance function can be represented as: $$\gamma_X(h) = \int_{(-\pi , \pi ]} e^{i h v} dF(v)$$ The function $F$ is called the ...
141 views

### Order of a non-linear autoregressive exogenous (NARX) model

Suppose I have a non-linear autoregressive exogenous (NARX) model of the kind $$y(k+1)=f(y(k), y(k-1), ..., y(k-s), u(k), u(k-1),..., u(k-t))$$ where $y$ and $u$ represent respectively the output and ...