# Tagged Questions

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

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### Can a classification tree model “know” to predict only one of every class for every subset in a data?

In order to help recipients understand my question, there will be context added. I don't know a whole lot of semantics so please bare with me. Draper is hosting a competition on Kaggle to classify ...
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### How is the augmented Dickey–Fuller test (ADF) table of critical values calculated?

Could you please explain in simple terms how the table of critical values for the augmented Dickey–Fuller (ADF) test is created?
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### Estimation of the local trend models (State Space) through ML

Tsay, R. S. (2010), Analysis of Financial Time Series, 2nd Edition, discusses on page 504 the estimation of local trend models (state space). The measurement and the transition equations are as ...
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### Estimating the uncertainty in the peak of a non-stationary poisson process

I have daily counts of observed disease cases for a single location. I am interested in the peak timing of the outbreak of the disease and want to assess the uncertainty in the peak estimate. In other ...
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### Obtaining $T$ residuals from AR($p$) model

I have my estimates for an AR(3). To obtain the residuals I'm supposed to use $$Y_t-\hat\phi_0-\hat\phi_1Y_{t-1}-\hat\phi_2Y_{t-2}-\hat\phi_3Y_{t-3},$$ where the $Y$'s are from the dataset. If I ...
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### Variance Estimation of MA(1) with known autocovariance function

I haven't worked with time-series in a while now and stumbled upon them in a different setting. Given $X_t\sim\mathcal{N}(0,\sigma^2)$ for $t=1,\ldots,n$ and the process $Y_t$ for $t=1,\ldots,n-1$ ...
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### ARDL bounds testing: model specification and selection

I am performing ARDL bounds testing. In particular, my variables are GDP, renewable and non-renewable electricity, carbon emissions and 2 other control variables, capital and labour. I have seen that ...
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### Multilevel modeling of time series coss sectional data with a binary outcome using glmer

Background Although my data should have a multinomial dependent variable, I have settled for a binary as I could not understand too much of MCMCglmm. The data is a time series cross sectional, so am ...
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### Testing intervention for a random walk using ARIMAX model

I am trying to analyze whether the intervention has an causal effect on $Y_{t}$. By ACF and PACF, it looks like the data is a random walk. I further use an ARIMAX model to examine the effect of the ...
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### Decomposing a multi seasonal time series using tbats in R

Can I decompose a time series with multiple seasonalities (an msts object) using tbats (in the ...
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### logarithm and absolute value in returns of stocks

I'm interested in model a GARCH for a serie. The original serie is $y_t$ (price index of a Stock Market), which has a unit root. So I created the returns: $x_t = \ln(y_t) - \ln(y_{t-1})$. Now, I'm ...
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### Compare time-varying series

I want to compare how the position angle during reach 2 (green) and 3 (blue) varies from the control reach 1 (red). It is mainly the middle section of the reach that I am concerned with, at the ...
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### Analysis for evolution of resistance

I am looking for help on an approach for analyzing evolution of resistance. I conducted an experiment in which I exposed pathogens to a constant drug concentration over 6 weeks. At each week, I tested ...
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### Alternative construction of ARMA(1,1) process

My question is related to the exercise 2.9, p. 79 in Brockwell & Davis, An Introduction to Time Series Analysis and Forecasting, 2nd edition, New-York, Springer, 2002 (It is also related to ...
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### Scaling variables for support vector regression for time series prediction

I am confused how to best scale variables for support vector regression for time series prediction. I want to predict the next value for a time series using past values of the series (e. g. the 10 ...
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### Ljung-Box test for ARMA residuals: is my ARMA model fine?

I have an ARMA($p$,$q$) model. $p=q=2$ gave me the lowest BIC value, and hence I stuck to it. I know people do something with the Ljung-Box $Q$-test test for autocorrelations. I did this on Matlab ...
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### Weakly stationary time series questions

Say I have the following model: $y_t = 0.5y_{t−1} +x_t +v_{1t}$, and $x_t = 0.5x_{t−1} +v_{2t}$, where both $v_{1t}$ and $v_{2t}$ follow IID normal distribution ∼ (0,1). The following statements ...
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### Does aggregating features/prediction over samples with LSTM always give a better accuracy?

Here the task is classification of videos. One sample is a single frame. A group of samples is consecutive frames of a video. I have a Neural network that gives me an accuracy of 65% for a single ...
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### Are these time series answers correct?

I've only started looking into higher level statistics and this is my first time on this website. Should I ask each of these small qs individually or can we go through them all in one go? I've have ...
### $c(n)$ is trend, $r(n)$ is fluctuation. Should $\text{cov}[c(n),r(n)]/\text{var}[r(n)]$ be close to zero?
Suppose $y(n)$ is a random time series given as function of the discrete-time variable $n$. Suppose we can decompose it into $y(n) = c(n) + r(n)$, where $r(n)$ is a strict stationary residual ...