Time series are data observed over time (either in continuous time or at discrete time periods).

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12
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267 views

Help in how the paper derives the CRLB for Gaussian ARMA model

An univariate autoregressive process AR(p) process is expressed as $$y(n) = \sum_{j=1}^p a_jy(n-j) + u(n) $$ is excited by Gaussian sequence, $u$. Paper : On the Computation of the Cramer-Rao Bound ...
11
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459 views

Link Anomaly Detection in Temporal Network

I came across this paper that uses link anomaly detection to predict trending topics, and I found it incredibly intriguing: The paper is "Discovering Emerging Topics in Social Streams via Link Anomaly ...
9
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890 views

Simulating time-series given power and cross spectral densities

I am having trouble generating a set of stationary colored time-series, given the covariance matrix (their PSDs and CSDs). I know that, given two time-series $y_{I}(t)$ and $y_{J}(t)$, I can ...
8
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172 views

Implementation of CoVaR (a systemic risk measure) in R

I'm trying to estimate CoVaR using bivariate DCC GARCH in R. The concept of CoVaR is the dependence adjusted of VaR, which was first introduced by Adrian and Brunnermeier (2011). However, this ...
7
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132 views

Confidence intervals for difference in time series

I have a stochastic model used to simulate time series of some process. I am interested in the effect of changing one parameter to a specific value and want to show the difference between the time ...
6
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431 views

Dealing with missing data in an exponential smoothing model

There does not seem to be a standard way to deal with missing data in the context of the exponential smoothing family of models. In particular, the R implementation called ets in the forecast package ...
6
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367 views

Clustering & Time Series

I have a multivariate dataset that changes over time. I have extracted (and normalised) some features and used k-means to generate clusters over the entire span of the dataset. Now I want to see ...
6
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218 views

Examining correlation and long range dependence in time series data with strong diurnal effects

I have data sets of network traffic that exhibit strong diurnal effects making them non-stationary. One of the analysis that I want to run is to show correlation between days. If we chopped up the ...
6
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855 views

Measure score change over time while accounting for baseline differences

I'd like to test for and estimate group differences in NIHSS (National Institute of Health Stroke Scale) change between hospital discharge and three months after hospital discharge. Because the score ...
6
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3k views

Intuitive explanation of stationarity

I was wrestling with stationarity in my head for a while... Is this how you think about it? Any comments or further thoughts will be appreciated. Stationary process is the one which generates ...
5
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66 views

What's the variance of the following stochastic integral and is it weakly stationary?

The stochastic integral is defined as $$u_t = \int_{t-1}^t e^{-\kappa(t-s)}\int_0^s e^{-c(s-r)} \, dW(r) \, ds.$$ where $W(t)$ is a standard Brownian motion, $\kappa$ and $c$ are both positive. I ...
5
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184 views

Regularization for ARIMA models

I am aware of LASSO, ridge and elastic-net type of regularization in linear regression models. Question: Can this (or a similar) kind of regularization be applied to ARIMA modelling (with a non-...
5
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156 views

Generalized Linear Models vs Timseries models for forecasting

What are the differences in using Generalized Linear Models, such as Automatic Relevance Determination (ARD) and Ridge regression, versus Time series models like Box-Jenkins (ARIMA) or Exponential ...
5
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114 views

How to decide the p and q for GARCH model?

My question is simple. When shall I stop when trying the value for p and q? I have got the loglikelihood from ARCH(1) to ARCH(10). It's increasing. And then I tried GARCH(1,1), GARCH(2,1) etc. The ...
5
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0answers
334 views

Interpretation of the partial autocorrelation function for a pure MA process

I have been working with some time-series theory and I noticed something that I can understand "mathematically", but not based on the intuitive explanations of what the partial auto-correlation ...
5
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482 views

Better understanding of GARCH and ARCH models

I want to make a function that does GARCH and ARCH in python for calculating variance. But I only have a general understanding of the model. Are there any good papers that can be recommend to give me ...
5
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823 views

Stationarity tests for time series

I am currently working on time series modeling, especially on stationarity tests. For this purpose, I am extensively using Pfaff's book "Analysis of integrated and cointegrated time series with R" and ...
5
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283 views

Reference for implementing generalized likelihood ratio test to determine online whether time-series mean has shifted

What is a reference that describes the "generalized likelihood ratio" test to determine online (i.e., meaning that we add an observation, then check, then add an observation, then check) whether the ...
5
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198 views

Forecasting a complex time series by splitting into subseries

I have finance data that I need to forecast out for 7 years. My data is generally debits and credits, and those are split into a number of sub-series which share common traits (e.g. similar ...
5
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1k views

What is the confidence interval calculated in a spectral density periodogram in R?

This question is similar to the one posed here: Testing significance of peaks in spectral density In that post, Pantera asks how to test whether a peak in a periodogram has a spike that is ...
5
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163 views

How to denoise a “Poissonous” time series

I have $N$ time series each of which can be modeled as $$y_{kt}=Ax_{kt}+b+\varepsilon_{kt}\quad(1\le k\le N,1\le t\le T),$$ where $x_{kt}\sim\text{Pois}(\lambda\Delta t)$ and $\varepsilon_{kt}\sim N(0,...
5
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1k views

Exogenous variables in VECM

I found the following posts interesting and I was wondering if any of you guys know of good academic papers that describe methods/relationships of exogenous variables in VECM models. If so could you ...
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42 views

How to parameterize coefficient matrix to restrict eigenvalues?

Consider the $r-$dimensional autoregression $$ y_t = Ay_{t-1} + v_t, v_t \overset{iid}{\sim}N(0,\Sigma). $$ It is well known that if all eigenvalues of $A$ have modulus less than unity then this ...
4
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77 views

Correlation between two multivariate time series

I'd like to quantify correlations in time series of 3D position. Assume: $$ p_1(t) = \left( x_1(t), y_1(t), z_1(t) \right) ;$$ $$ p_2(t) = \left( x_2(t), y_2(t), z_2(t) \right) .$$ where $x, y,$ ...
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84 views

Statistics behind gravitational waves discovery

The recent gravitational waves result is a stunning feat for both physics and engineering. I suspect there may be much to admire on the statistics side as well. For example, the original paper states: ...
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99 views

Seasonally adjusted data used in time series forecasting

I am looking at two time series, from 01/01/2000 to the present: The ISM Manufacturing: New Orders Index, only available seasonally adjusted The manufacturing industry unemployment rate, only ...
4
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26 views

Time series and images : difference and terminology

A time series is an ordered collection of random variables. Considering a one-dimensional time series $A_i = {a_{i1},a_{i2},\ldots,a_{it}}$ where $t$ denotes the time index. So, the time series is a ...
4
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157 views

Analyzing the effects of different scholarships among university students

We have a data set that has data on university students, including their socio-demographic characteristics (sex, first language, ethnicity, residency etc.), GPA and CGPA in each semester (note that ...
4
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122 views

Picking block length in a block bootstrap

I am using the Mann-Kendall test to assess trends in a data time-series. I believe there is autocorrelation in my data and therefore need to use a block bootstrap to correct for it. I have plotted ...
4
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292 views

Attrition Forecasting

I am currently trying to develop a forecast for monthly subscriber attrition that allows me to predict for a future point in time, how many subscribers I have. I have a couple of years worth of ...
4
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157 views

Determining the effect of number of likes

Let's say I have marketing data and I need to determine how effective the marketing is. The marketing strategy is to publish facebook posts at inconsistent intervals. The goal is to see how the ...
4
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56 views

Estimating AR process for Logistic Regression

I'm fitting a time-series model with independent $X$ variables coded as months of the year (so there are 12 of them) and the dependent $y$ variable is some proportion, bounded between 0 and 1. As a ...
4
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195 views

Ideal statistical or machine learning technique to model highly cross-correlated data

I'm trying to build a model that can predict streamflow for an alpine (snowmelt-fed) watershed using snow albedo (roughly, the energy reflectance of the snow) data. Albedo controls the melt of the ...
4
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481 views

AIC versus cross validation in time series

I am interested in model selection in a time series setting. For concreteness, suppose I want to select an ARMA model from a pool of ARMA models with different lag orders. The ultimate intent is ...
4
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166 views

Seasonal Kendall test and the Mann-Kendall test

I am trying to detect trends using non-parametric methods but I'm a little confused as to when you should apply the Seasonal Kendall test. Don't get me wrong I know you apply it when you have ...
4
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95 views

How do I solve this stochastic differential equation?

So I have a second order stationary process $Y(t), \infty < t < \infty$ which has a continuous sample function, mean $\mu_Y = 1$ and covariance function $r_Y(t) = e^{-|t|}, -\infty < t < \...
4
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1k views

Hold out sample vs. cross validation for time series, and how to perform in R

I think out-of-sample validation testing for accuracy is essential in initially judging what time-series forecasts to use. In any case, I've been doing some reading on the two most common methods, ...
4
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141 views

Determining parameters in AR model for non-stationary time series

I am currently trying to fit an AR model to some financial data. The time series $Y_t$ in levels is clearly non-stationary; however it appears the first differences $dY_t$ are stationary (and this is ...
4
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63 views

“Average” line over irregular log series data

I have simulation data from 1000 runs, plotting some measurable (in this case convergence of the algorithm) as a function of simulation time. Each run produces a discrete set of points ...
4
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261 views

How to fit log-linear poisson autoregressive mixed model?

I have time-series count data $N_{i,j}$ (population sizes in site $i$ and year $j$) and I want to correlate year-to-year changes with the environmental conditions $x_{i,j}$. For this, I want to fit ...
4
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119 views

Probability puzzle about zombies

I am thinking about writing a simple game about zombies. I got stuck trying to calculate how many people should become zombies. Here are my conditions: We have a small rural town of 700 people. One ...
4
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1k views

Time series clustering: Fourier transform and PCA

I have biological time series (9 years long) of the biomass of species which logically exhibit a seasonal pattern. I would like to cluster them into a few groups based on their typical seasonal ...
4
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286 views

Detecting statistically significant clustering of continuous values

I'm working with biological sequence data where each position in the sequence has an associated continuous value. I'm ignoring the sequence content so the data is very similar to a time series with ...
4
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560 views

Standardized dependent variable within a group in panel data models?

Does standardizing of a dependent variable within the identifying group make sense? The following working paper (Deforestation slowdown in the Legal Amazon; Prices or Policies?, pdf) uses a ...
4
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0answers
303 views

Block bootstrap for dependent data with unequal sampling intervals?

I have data from a natural archive (lake sediment). For various reasons it is usually impossible to sample the archive equally in time, and we end up with a time series where essentially we have ...
4
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82 views

How to form a confidence band around the trend fitted from time series data

I have a time series data set. I can decompose it and get the trend but I would like to put confidence ranges around the trend (past) not the forecast-ed component. The decompose function also doesn'...
4
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307 views

detecting circadian rhythm in a time series

I have a sensor that can detect minute changes in distance. It produces a time series. I would like to point it at people and detect things like their sleeping pattern. How would one build a system ...
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423 views

How to design good plots for multiple time series?

I have huge (about 100 000) set of time series. I need to show between 5 to 10 time series, chosen semi-randomly on one chart. Chart estate is very limited - plot for each time series is only 100px x ...
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274 views

Common statistical methods for analyzing weather station data

I have been tasked with analyzing temperature time series from multiple weather stations. I have minute and hour resolution temperature data spanning three years at 4 stations and 35 stations ...
4
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145 views

Relationship between LASSO T and LARS number of steps k

We can see on the figure (cf Least Angle Regression p30, Efron, Hastie, Johnstone, Tibshirani - link: Least Angle Regression) that there is a direct relationship between: LASSO T absolute norm of $\...