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Questions tagged [time-series]

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

Overview

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

Time series analysis includes trend identification, temporal pattern recognition, spectral analysis, and forecasting future values based on the past.

The salient characteristic of methods of time series analysis (as opposed to more general methods to analyze relationships among data) is accounting for the possibility of serial correlation (also known as autocorrelation and temporal correlation) among the data. Positive serial correlation means successive observations in time tend to be close to one another, whereas negative serial correlation means successive observations tend to oscillate between extremes. Time series analysis also differs from analyses of more general stochastic processes by focusing on the inherent direction of time, creating a potential asymmetry between past and future.

References

The following threads contain a list of references on time series:

The following journals are dedicated to researching time series:

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Estimating same model over multiple time series

I have a novice background in time series (some ARIMA estimation/forecasting) and am facing a problem I don't fully understand. Any help would be greatly appreciated. I am analyzing multiple time series, all over the same time interval and all of…
sparc_spread
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How to interpret these acf and pacf plots

Following are acf and pacf plots of a monthly data series. The second plot is acf with ci.type='ma': The persistence of high values in acf plot probably represent a long term positive trend. The question is if this represent seasonal variation? I…
rnso
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What is a white noise process?

What is the best way of defining white noise process so it is intuitive and easy to understand?
user333
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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, which is the number of lags to be tested. Some…
user2875
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Correlation between two time series

What is the easiest way / method to compute the correlation between two time series that are exactly the same size? I thought of multiplying $(x[t]-\mu_x)$ and $(y[t] - \mu_y)$, and adding up the multiplication. So if this single number was…
BBSysDyn
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Is AR(1) a Markov process?

Is AR(1) process such as $y_t=\rho y_{t-1}+\varepsilon_t$ a Markov process? If it is, then VAR(1) is the vector version of Markov process?
Flying pig
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How to interpret negative ACF (autocorrelation function)?

So I plotted the ACF/PACF of oil returns and was expecting to see some positive autocorrelation but to my surprise I only get negative significant autocorrelation. How should I interpret the above graph? They seem to indicate that there is a…
ankc
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What methods can be used to determine the Order of Integration of a time series?

Econometricians often talk about a time series being integrated with order k, I(k). k being the minimum number of differences required to obtain a stationary time series. What methods or statistical tests can be used to determine, given a level of…
brotchie
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What is a second order stationary process?

I was wondering how his "second-order stationary process" is defined in Brockwell and Davis' Introduction to Time Series and Forecasting: The class of linear time series models, which includes the class of autoregressive moving-average (ARMA)…
Tim
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How to compare difference between two time series?

I am working on my thesis where I'm examining how strong emotion people show to different events. My problem is (1) that I have VERY little experience with statistics and math, so I'm kind of lost with all different methods and would be really happy…
Sara
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How to interpret autocorrelation of residuals and what to do with it?

I was wondering what does it mean when time series residuals have autocorrelation? How should I deal with it?
jjepsuomi
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How do I investigate how long it takes one variable to affect another in a time series

I am a total newbie when it comes to time series, so it is quite possible this question is duplicated somewhere else, only that I cannot find it because I don't know what this feature is called. My data: I have weekly measurements of a variable…
Alex
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Explaining the beveridge nelson decomposition

Can someone explain how the Beveridge-Nelson Decomposition works? So far all I know is it estimates trend cycles in non stationary time series data. I looked at multiple journal articles and I am still confused on how it…
user3084006
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Best algorithm for classifying time series motor data

I am working on a machine control project. We can measure the motor's current during operation. Sample data from two motors performing an operation successfully is below. The red trace shows the current from one motor, the blue trace the current…
fred basset
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What temporal resolution for time series significance test?

I need some guidance on the appropriate level of pooling to use for difference of means tests on time series data. I am concerned about temporal and sacrificial pseudo-replication, which seem to be in tension on this application. This is in…
user2948
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