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

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How to understand from paper how to derive the CRLB for Gaussian case AR 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, $u$. Is there a resource / reference for a lucid ...
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362 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 ...
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256 views

Algorithm for real-time normalization of time-series data?

I'm working on an algorithm that takes in a vector of the most recent data point from a number of sensor streams and compares the euclidean distance to previous vectors. The problem is that the ...
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303 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 ...
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669 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 ...
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183 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 ...
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287 views

How does pooling and resampling affect variance of sample mean?

Suppose I have $N$ independent random variables $X_n$. I draw a sample of predetermined size $K_n$ from each of them. Denote the average of each sample $\bar{\hat{X}}_n$, and the total number of ...
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683 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 ...
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110 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 ...
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572 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 ...
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564 views

Asynchronous (irregular) Time Series Analysis

I am trying to analyze the lead-lag between time series of two stock prices. In regular time series analysis, we can do Cross Correlaton, VECM (Granger Causality). However how does one handle the ...
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706 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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27 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 ...
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65 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 ...
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79 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 ...
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60 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 ...
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54 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 < ...
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162 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 ...
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103 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 ...
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47 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 ...
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205 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 ...
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105 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 ...
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757 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 ...
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268 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 ...
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229 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 ...
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373 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 ...
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5k views

Confusion with Augmented Dickey Fuller test

I am working on the data set electricity available in R package tsa. My aim is to find out if an ...
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72 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 ...
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2k views

Interpreting time series decomposition using TBATS from R forecast package

I would like to decompose the following time series data into seasonal, trend, and residual componenets. The data is an hourly Cooling Energy Profile from a commercial building: ...
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259 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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229 views

Unit root tests and stationarity

Two common methods of testing whether a time series is stationary are the KPSS and ADF tests. If my understanding is correct, these tests essentially work by measuring the residuals of fitting the ...
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126 views

Visualizing probability of event over time, based on epoch time

I have a list of epoch/unix times at which an event happened. My hypothesis is that there are certain times during the week when this event might happen more frequently. How can I visualize/determine ...
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164 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 ...
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136 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 ...
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183 views

Estimating parameters of an unknown PID controller

Say that I have your standard PID controller at work. To keep it extremely simple imagine I have a target $x^*$ on the variable $x$. Then the controller is: $y(t) = K_p ( x^* - x_t) + K_i \int_0^t ...
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53 views

Estimating a time frame for interventions or judging the extent to which events become “determined” as time goes on

In certain arenas, it's valuable to be able to intervene early on to prevent problems from getting worse, because after a certain point there's not much you can do. Two examples might be public health ...
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138 views

What's the probability a rabbit will return to a (certain) forest?

Let's assume we have a forest. And there is a breed of rabbits that is visiting that forest all the time. It is possible to distinguish every individual rabbit. There are devices in that forest ...
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786 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 ...
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189 views

How to analyze mood data over time?

I've collected data for individuals on a team about their daily mood. Each day, individuals rate their mood on a scale that is assigned the following values: 0 (bad), 5 (so-so), 10 (good). Using the ...
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207 views

Testing for the existence of dependencies in time series

What methods exist to test for the existence of any sort of dependence in a time series? This is in contrast to something like auto-correlation, which tests for a particular type of dependency. Is ...
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475 views

How to model time-varying correlation

Suppose I have two time-series variables, $\{x_t\}$ and $\{y_t\}$, where $t\in[1,T]$. I would like to model the correlation $\rho(x_t,y_s)$ as some function of $t$,$s$, and the difference $t-s$. In ...
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133 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 ...
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1k 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 ...
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36 views

Analysis of Multiple Time Series Data with Exogenous Shocks

Real Life ProblemThis one is a tough one and some crowd sourcing seems like a good way to get some feedback. I am trying to determine the effect of Non-Farm Payroll surprises on a subsector of the ...
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23 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 ...
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35 views

How to best analyze several time series of speed data? Comparing regression analysis?

So I have several time series of AIS data, aka time, speed and geographical position at that moment for thousands of ships. They all have that in mutual that they are arriving at the same spot, but ...
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57 views

Understanding Chib (1998) Bayesian multiple changepoint model

Ungated link to the paper Chib, S. (1998). Estimation and comparison of multiple change-point models. Journal of Econometrics, 86(2), 221–241. doi:10.1016/S0304-4076(97)00115-2 The context of the ...
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49 views

Sample size for tracking data

I'm currently trying to figure out how to estimate a fitting sample size for a specific problem. The situation is as follows: We've got x people, of whom we are able to track y% - all the time, so we ...
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165 views

How to use lagged dependent variables (panel data) in practice?

Working with a panel data set with a daily time series structure I was told to include a lagged dependent variable. The dependent variable is daily electricity consumption of a medium size sample ...
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55 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 ...