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

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Testing significance of a treatment inducing correlations over a time series

Example data In the example dataset, there are 3 distinct biological measurements, over 3 time points (0,12,24hrs) for 19 individuals. These individuals have been divided into 2 groups: treatment and ...
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Modeling time series data that is bimodal and non-Gaussian

I'm trying to model time series data that is bimodal and non-Gaussian. The 2 modes are due to weekday points versus weekend points. I keep thinking that I just need to split the data up to model ...
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38 views

Removing Time-Series Variance from Panel Data

We are working with panel data. But we want to study only the cross-section part of the panel data. So can anybody please tell me how to do any kind of data transformation, so that I can remove the ...
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181 views

Predicting time to finish

Out of curiosity, I want to understand how to model this problem. I've been hearing people suggest the use of linear regression but I am not sure how to encode this problem (included my attempt below) ...
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Rule of Thumb for minimum length of time series for Autocorrection estimation

I had a related question answered here: Rule of Thumb for minimum length of time series for AR(1) estimation However the answer gives rise to a new question. I want to be able to estimate the Auto ...
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What is the error on measuring the phase of a sine wave? [duplicate]

Let's say I have a wave, with frequency $\omega$ and phase $\phi$, of the form: $$y(t)=1+A\sin(\omega t+\phi)$$ where $A<1$. I have $N$ measures of $(\hat{y}_i, \hat{t}_i)$, that are assumed to ...
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23 views

Data transformation

I was writing with a question regarding a time-varying state space model of the form: \begin{align} y(t) &= \mu_1(t) + A(t)x(t) + v(t); &v(t) &\sim (0, R(t)) \\ x(t) &= ...
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30 views

Rule of Thumb for minimum length of time series for AR(1) estimation

I have a data set of 350 points, I want to estimate the lag 1 auto correlation for different sub-sets of the data. More precisely I want to take non overlapping windows of length 1,2,3....n and ...
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18 views

Most efficient vector construction for Dynamic Time Warping

I'm in the process of folding FastDTW into my SVM and the question now is how to best format my data (irrespective of normalization). Here's an example of what I'm attempting to do - given two 3d ...
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31 views

Financial time series model

I have an interesting question that I think has not been asked yet here. I am building an AI that has as goal to predict how wrong a standard based-on-history model is. This is done based on Natural ...
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unconditional volatility from an Arma-Garch process

I know that one can easily get variance (unconditional) of a Garch (r,s) process : $\sigma^2= \frac { \alpha_0 } { (1- \Sigma_{i=1}^r \alpha_i - \Sigma_{j=1}^s \beta_j ) }$ However I am struggling ...
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38 views

How to fit an ARMAX model with more than one exogenous time series?

I am trying to fit an ARMAX with two exogenous time series with the following code but it gives me an "computationally singular" error. I know it is about defining more than 2 time series for ...
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What is the “scale” parameter in “continuous autoregressive model” in cts package?

I am trying to use the "car" command in "cts package" in R program and I see the "scale" parameter there. I wonder whether this can be assumed to be equivalent to time intervals for time series ...
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28 views

Bias in lagged dependent variable [duplicate]

$$ y_t = θy_{t−1} + u_t \\ t = 1,...,T; $$ I need to derive a formula for $y_t$ and show that $$ E\left[\frac{\Sigma y_{t-1}u_t}{ \Sigma(y_{t-1})^2}\right] \neq 0 $$
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Modeling a non-stationary bounded series

I'm trying to model a time series variable that represents a percentage, strictly bounded between 0 and 1, that is also non-stationary about the mean. Is there a model form that is able to account ...
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Is time-delay embedding/attractor reconstruction used in some machine learning algorithm?

I try to model/forecast blood glucose levels from my diabetes diary, so I have to deal with some 5-7 daily measurements of estimated carbohydrates, physical activity, insulin doses and measured blood ...
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120 views

Doubts in linear regression

If a linear regression model has a constant term say 1 or 0.2, for example if the original model is $y(t) = 0.2 + ay(t-1) $, then what does this constant term imply? Will it hamper the estimates if ...
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Arima model for non-negative data

I have been reading a tutorial for an introduction to time series. It contains a dataset, with an $Arima(2,0,0)$ forecast along with a 80% and 95% prediction interval. It looks like this: This ...
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2answers
24 views

Confidence bands for difference of time series

Assume that I have two time series $Y_{1t}$ and $Y_{2t}$ that are sampled at the same frequency. Is there a way to quantify the uncertainty in their difference $Y_{1t} - Y_{2t}$? That is, can we get ...
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1answer
29 views

Testing the hypothesis on clustering

I have a number of samples. For each, there is a time course of multivariate data defined, with $t$ timepoints ($t < 50$) and $n$ variables ($n > 100$). We have noted that the time courses of a ...
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1answer
113 views

Can we skip the lower order terms in interactions? [duplicate]

This question is about three-way interaction and the possibility of applying without second lower terms with keeping the main variables in the equation not like the other questions. In fact the other ...
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Transforming time series to compensate for change in variance

I have a time series (shown below) that comes from a sensor whose calibration was changed in the middle of last year. As part of this change, the sensor's reading of the variance (or volatility) of ...
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Fitting a straight line to components of complex numbers

I have a strange problem that I'm not sure how to solve: I have complex data points in a time series. The amplitude of these complex numbers in the time series forms a straight line, which I have fit ...
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How to get observations from residuals in an ARIMA model?

If we have residuals of an ARIMA(p,d,q) with known parameters, how can we retrieve the original observations of the time series?
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Is two years enough for panel data analysis?

I have around 800 companies for only two years period. However, around 200 of them have only one year observation. Is it still possible to conduct panel data analysis with such data Thank you
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Is a Gaussian AR process with white noise independent?

I was just wandering if, given the AR process \begin{equation} X_t = \alpha X_{t-1} + \varepsilon_t, \quad \varepsilon_t \overset{iid}{\sim} N(0,1), \end{equation} the $X_t$ values are independent due ...
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State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure ...
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49 views

Four tricky time series questions with a “seasonal twist”

A ski-hotel has the most guests in the third quarter in every year (check the data below after the four questions). Can you answer these four questions (every year has 4 values, the first is quarter ...
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28 views

Reproducing ARIMA error terms

When forecasting a moving average (MA) model using R's forecast, why does using residuals(fit) produce different results than ...
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What does it mean intuitively to say that a time series process is causal ?

What does it mean intuitively to say that a time series process is causal ? And what is the relationship between causality and stationary and invertibility ? If I understand correctly, these 3 ...
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How to handle large .csv file in R? [migrated]

I have a large(>100,000) single column floating point time-series data. I want to find structural changes within the data with respect to time( in my case index). In-order to do that, I am using R ...
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20 views

Using Yule Walker equations for ACF and PACF

When using Using Yule Walker equations for getting ACF and PACF, is it essential that the time series has to be stationary? In other words, do we really need Box-Cox transformations before we use Yule ...
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How do I replicate these simple state space models from Commandeur's book in Stata?

I'm working through the book An introduction to state space time series analysis by Commandeur and Koopman, and I want to replicate a few of the simple models in Stata 13.1. The two related models I'm ...
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Stream classification of time series

I have a set of time series $\mathcal{Y}$, and a test time series $T$ for which I need to find the closest matching time series $Y_i \in \mathcal{Y}$. This has to be done online, i.e., $T$ is a stream ...
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using decompose function for high frequency data

I have a table as Date Time Energy 1/1/2008 10:30 0.89 1/1/2008 11:30 0.76 and so on. The data is recorded for every half an hour. I wish to ...
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Time series Data Analysis and Forecasting by country and time factor

cty year qtr tl Argentina 2009 Q4 3 Argentina 2010 Q1 2 Argentina 2010 Q2 7 Argentina 2010 Q3 7 Argentina 2010 Q4 10 Argentina 2011 Q1 7 Argentina 2011 Q2 7 Argentina 2011 Q3 1 Argentina 2011 ...
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Model validation and verification for Markov Chain switching model

Assuming I have a discrete-time Markov chain with only five states. The chain will be used for the prediction of the macroscopic states which are observable and coming from a timeseries. I use maximum ...
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Homogeneity of variance for time variable

I have four groups of plant treated with different temperatures and I conducted repeated measurement on their growth rate. I use ANOVA with Mixed Model to analyze the data by specifying both ...
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56 views

Are time series variances additive?

I am trying to measure and quantify risk, variance, and standard deviation over a time period $T$. It is broken into two sub-periods $t_1$ and $t_2$. $X_1$ is the time series for $t_1$, and $X_2$ is ...
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Ensemble model performs better with worse performing consitutent models?

I have a forecast model I am developing that uses some very unreliable input data, missing data (due to sensors or comms failures) is the rule, not an exception. The quantity being forecast is a daily ...
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Weighted average of a time series

I am trying to construct an average from a set of points (time series) considering that the more recent points have a bigger weight. I already tried with the formula of exponential moving average ...
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65 views

Does an exponential model fit my data?

I am measuring accumulation of a fluorescent-tagged protein at a particular location within a cell over time. In previous experiments that I have performed, I see a standard exponential distribution ...
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24 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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32 views

Seasonal vs non-seasonal coefficients in R ARIMA

Let's say I have the two following ARIMA models: ARIMA(7,1,1) (no seasonality) ARIMA(6,1,1)(1,0,0)7 (seasonality of period 7). Are they conceptually the same? If so, why is that when I model ...
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22 views

Average Growth Rate for Year 1 across 5 groups

I have a question that pertains to time series or more likely pertains just to simple math. Lets suppose that I am measuring the number of online visitors to 5 websites on a monthly basis, so I have ...
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22 views

Is it possible to measure the independent variable with part of the dependent variable

I have Beta as my independent variable and Economic value added (EVA) as my dependent variable. To calculate EVA I need to use Cost of capital and to calculate that I have to use Beta, so is it ...
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Time Series Cross Sectional Analysis and Forecasting With R

cty time tl Argentina 2009_Q4 3 Argentina 2010_Q1 2 Argentina 2010_Q2 7 Argentina 2010_Q3 7 Argentina 2010_Q4 10 Argentina 2011_Q1 7 Argentina 2011_Q2 7 Argentina ...
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Sales Forecasting using Support Vector Machine

I have sales data for last three years 2011-2013. I want to use Support Vector Machine technique in R to do the predictions. I just wanted to know that the approach that I am using is correct or not? ...
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How to interpret residual plots from time series regression

I am doing a time series regression between 2 variables. I used the dynlm library in R. I'm trying to understand how to interpret the results. Could you please point out where I am getting it wrong: ...
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42 views

The best way to solve particular classification problem?

I got training set (time series) of size approximately 2 million precedents {x,y}. Each x is a vector of size 20 and each y is a binary vector of size 10 like {1,0,0,1,1,0,1,1,1,0}. For a new input x ...