# 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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### 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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### 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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### Dynamic Time Warping Clustering

What would be the approach to use Dynamic Time Warping to perform clustering of time series? I have read about DTW as a way to find similarity between two time series, while they could be shifted in ...
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### Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey

I am used to seeing Ljung-Box test used quite frequently for testing autocorrelation in raw data or in model residuals. I had nearly forgotten that there is another test for autocorrelation, namely, ...
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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 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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### 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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### How do I write a mathematical equation for ARIMA (2,1,0) x (0,2,2) period 12

I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (2,1,0) x (0,2,2) period 12. I'm a little confused with how to go about this. I would prefer an ...
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### How do I write a mathematical equation for ARIMA (0,2,1) x (0,0,1) period 12

I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (0,2,1) x (0,0,1) period 12. I'm a little confused with how to go about this. I would prefer an ...
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### What method can be used to detect seasonality in data?

I want to detect seasonality in data that I receive. There are some methods that I have found like the seasonal subseries plot and the autocorrelation plot but the thing is I don't understand how to ...
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### Estimate ARMA coefficients through ACF and PACF inspection

I know that this is probably a question that's been asked plenty of times, but i haven't seen an answer that's both accurate and simple. How do you estimate the appropriate forecast model for a time ...
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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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### 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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### Best method for short time-series

I have a question related to modeling short time-series. It is not a question if to model them, but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq 20$...
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### How to use Pearson correlation correctly with time series

I have 2 time-series (both smooth) that I would like to cross-correlate to see how correlated they are. I intend to use the Pearson correlation coefficient. Is this appropriate? My second question ...
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### Data has two trends; how to extract independent trendlines?

I have a set of data that is not ordered in any particular way but when plotted clearly has two distinct trends. A simple linear regression would not really be adequate here because of the clear ...
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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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### How to fit an ARIMAX-model with R?

I have four different time series of hourly measurements: The heat consumption inside a house The temperature outside the house The solar radiation The wind speed I want to be able to predict the ...
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### How many lags to use in the Ljung-Box test of a time series?

After an ARMA model is fit to a time series, it is common to check the residuals via the Ljung-Box portmanteau test (among other tests). The Ljung-Box test returns a p value. It has a parameter, h, ...
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### stochastic vs deterministic trend/seasonality in time series forecasting

I have moderate background in time series forecasting. I have looked at several forecasting books, and I don't see the following questions addressed in any of them. I have two questions: How would ...
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### What to make of explanatories in time series?

Having worked mostly with cross sectional data so far and very very recently browsing, scanning stumbling through a bunch of introductory time series literature I wonder what which role explanatory ...
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### How to compare two time series?

I have collected temperature readings for 4 locations on a beach in Cornwall UK using data loggers. The loggers recorded temperature every 15 mins accurate to .1 of a degree (Celsius). The loggers ...
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### Can you compare AIC values as long as the models are based on the same dataset?

I am doing some forecasting in R using Rob Hyndman's forecast package. The paper belonging to the package can be found here. In the paper, after explaining the automatic forecasting algorithms, the ...
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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 know if a time series is stationary or non-stationary?

I am using R, I searched on Google and learnt that kpss.test(), PP.test(), and adf.test() ...
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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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### Good introductions to time series (with R)

I am currently collecting data for an experiment into psychosocial characteristics associated with the experience of pain. As part of this, I am collecting GSR and BP measurements electronically from ...
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### Auto.arima with daily data: how to capture seasonality/periodicity?

I am fitting an ARIMA model on a daily time series. Data are collected daily from 02-01-2010 to 30-07-2011 and are about newspaper sales. Since a weekly pattern in sales can be found (the daily ...
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### Time Series Forecasting with Daily Data: ARIMA with regressor

I'm using a daily time series of sales data that contains about 2 years of daily data points. Based on some of the online-tutorials / examples I tried to identify the seasonality in the data. It seems ...
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### Computing correlation (and the significance of said correlation) between a pair of time series

I have two time series S, and T. they have the same frequency and the same length. I would like to calculate (using R), the correlation between this pair (i.e. S and T), and also be able to calculate ...