# Tagged Questions

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

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### Simple algorithm for online outlier detection of a generic time series

I am working with a large amount of time series. These time series are basically network measurements coming every 10 minutes, and some of them are periodic (i.e. the bandwidth), while some other aren'...
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### Do we have a problem of “pity upvotes”?

I know, this may sound like it is off-topic, but hear me out. At Stack Overflow and here we get votes on posts, this is all stored in a tabular form. E.g.: post id voter id vote type ...
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### Books for self-studying time series analysis?

I started by Time Series Analysis by Hamilton, but I am lost hopelessly. This book is really too theoretical for me to learn by myself. Does anybody have a recommendation for a textbook on time ...
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### What is wrong with extrapolation?

I remember sitting in stats courses as an undergrad hearing about why extrapolation was a bad idea. Furthermore, there are a variety of sources online which comment on this. There's also a mention of ...
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### Proper way of using recurrent neural network for time series analysis

Recurrent neural networks differ from "regular" ones by the fact that they have a "memory" layer. Due to this layer, recurrent NN's are supposed to be useful in time series modelling. However, I'm not ...
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### Pitfalls in time series analysis

I am just starting out self-learning in time series analysis. I have noticed that there are a number of potential pitfalls that are not applicable to general statistics. So, building on What are ...
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### Using deep learning for time series prediction

I'm new in area of deep learning and for me first step was to read interesting articles from deeplearning.net site. In papers about deep learning, Hinton and others mostly talk about applying it to ...
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### Efficient online linear regression

I'm analysing some data where I would like to perform ordinary linear regression, however this is not possible as I am dealing with an on-line setting with a continuous stream of input data (which ...
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### How to apply Neural Network to time series forecasting?

I'm new to machine learning, and I have been trying to figure out how to apply neural network to time series forecasting. I have found resource related to my query, but I seem to still be a bit lost. ...
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### Is it possible to do time-series clustering based on curve shape?

I have sales data for a series of outlets, and want to categorise them based on the shape of their curves over time. The data looks roughly like this (but obviously isn't random, and has some missing ...
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### Why does a time series have to be stationary?

I understand that a stationary time series is one whose mean and variance is constant over time. Can someone please explain why we have to make sure our data set is stationary before we can run ...
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### Time series 'clustering' in R

I have a set of time series data. Each series covers the same period, although the actual dates in each time series may not all 'line up' exactly. That is to say, if the Time series were to be read ...
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### How to make a time series stationary?

Besides taking differences, what are other techniques for making a non-stationary time series, stationary? Ordinarily one refers to a series as "integrated of order p" if it can be made stationary ...
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### Period detection of a generic time series

This post is the continuation of another post related to a generic method for outlier detection in time series. Basically, at this point I'm interested in a robust way to discover the periodicity/...
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### What are disadvantages of state-space models and Kalman Filter for time-series modelling?

Given all good properties of state-space models and KF, I wonder - what are disadvantages of state-space modelling and using Kalman Filter (or EKF, UKF or particle filter) for estimation? Over let's ...
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### Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ridge regression)

I use the auto.arima() function in the forecast package to fit ARMAX models with a variety of covariates. However, I often have a large number of variables to select from and usually end up with a ...
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### STL trend of time series using R

I am new to R and to time series analysis. I am trying to find the trend of a long (40 years) daily temperature time series and tried to different approximations. First one is just a simple linear ...
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### Time series for count data, with counts < 20

I recently started working for a tuberculosis clinic. We meet periodically to discuss the number of TB cases we're currently treating, the number of tests administered, etc. I'd like to start ...
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### How to find a good fit for semi-sinusoidal model in R?

I want to assume that the sea surface temperature of the Baltic Sea is the same year after year, and then describe that with a function / linear model. The idea I had was to just input year as a ...
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### Application of wavelets to time-series-based anomaly detection algorithms

I've been beginning to work my way through Statistical Data Mining Tutorials by Andrew Moore (highly recommended for anyone else first venturing into this field). I started by reading this extremely ...
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### Ways to reduce high dimensional data for visualization

I'm working on a 2D physical simulation and I am collecting data in time at several points. These discrete points are along vertical lines, with multiple lines in the axial direction. This makes the ...
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### Detecting Outliers in Time Series (LS/AO/TC) using tsoutliers package in R. How to represent outliers in equation format?

Comments: Firstly I would like to say a big thank you to the author of the new tsoutliers package which implements Chen and Liu's time series outlier detection which was published in the Journal of ...
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### Seeking certain type of ARIMA explanation

This may be hard to find, but I'd like to read a well-explained ARIMA example that uses minimal math extends the discussion beyond building a model into using that model to forecast specific cases ...
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### Difference between forecast and prediction?

I was wondering what difference and relation are between forecast and prediction? Especially in time series and regression? For example, am I correct that: In time series, forecasting seems to mean ...
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### What algorithm should I use to detect anomalies on time-series?

Background I'm working in Network Operations Center, we monitor computer systems and their performance. One of the key metrics to monitor is a number of visitors\customers currently connected to our ...
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### Testing significance of peaks in spectral density

We sometimes use spectral density plot to analyze periodicity in time series. Normally we analyze the plot by visual inspection and then try to draw a conclusion about the periodicity. But has the ...
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### Choosing seasonal decomposition method

Seasonal adjustment is a crucial step preprocessing the data for further research. Researcher however has a number of options for trend-cycle-seasonal decomposition. The most common (judging by the ...
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### R code for time series forecasting using Kalman filter

Does anybody have a good example for Time Series Forecasting/smoothing using Kalman Filter in R?
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### Can data cleaning worsen the results of statistical analysis?

An increase in the number of cases and deaths occurs during epidemics (sudden increase in numbers) due to a virus circulation (like West Nile Virus in USA in 2002) or decreasing resistance of people ...
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### Simple way to algorithmically identify a spike in recorded errors

We need an early warning system. I am dealing with a server that is known to have performance issues under load. Errors are recorded in a database along with a timestamp. There are some manual ...
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### Logistic Regression and Dataset Structure

I am hoping that I can ask this question the correct way. I have access to play-by-play data, so it's more of an issue with best approach and constructing the data properly. What I am looking to do ...
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### When to log transform a time series before fitting an ARIMA model

I have previously used forecast pro to forecast univariate time series, but am switching my workflow over to R. The forecast package for R contains a lot of useful functions, but one thing it doesn't ...
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### Why are “time series” called such?

Why are “time series” called such? Series means sum of a sequence. Why is it time Series, not time sequence? Is time the independent variable?
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### How to measure smoothness of a time series in R?

Is there a good way to measure smoothness of a time series in R? For example, -1, -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1.0 is much smoother than ...
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### Explanation of what Nate Silver said about loess

In a question I asked recently, I was told that it was a big "no-no" to extrapolate with loess. But, in Nate Silver's most recent article on FiveThirtyEight.com he discussed using loess for making ...
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### Why use vector error correction model?

I am confused about the Vector Error Correction Model (VECM). Technical background: VECM offers a possibility to apply Vector Autoregressive Model (VAR) to integrated multivariate time series. In the ...
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### How to statistically compare two time series?

I have two time series, shown in the plot below: The plot is showing the full detail of both time series, but I can easily reduce it to just the coincident observations if needed. My question is: ...
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### What common forecasting models can be seen as special cases of ARIMA models?

This morning I woke up wondering (this could be due to the fact that last night I didn't get much sleep): since cross-validation seems to be the cornerstone of proper time-series forecasting, what are ...
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### Support vector regression for multivariate time series prediction

Has anyone attempted time series prediction using support vector regression? I understand support vector machines and partially understand support vector regression, but I don't understand how they ...
I've found two definitions in the literature for the autocorrelation time of a weakly stationary time series:  \tau_a = 1+2\sum_{k=1}^\infty \rho_k \quad \text{versus} \quad \tau_b = 1+2\sum_{k=1}^\...