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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1answer
39 views

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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31 views

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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25 views

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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35 views

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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9 views

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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10 views

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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35 views

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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1answer
38 views

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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1answer
35 views

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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23 views

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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10 views

how to prove the PACF(k) equals the regression coefficient of last lag (assume stationary process)

assume AR(p), $$ y_t = \phi_1y_{t-1}+\phi_2y_{t-2}+...+\phi_ky_{t-k}+\epsilon_t $$ $$ corr(y_t, y_{t-k}|y_{t-1}...y_{t-k+1}) = \frac{cov(y_t, ...
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15 views

Find relationship in two time series datasets

I have two datasets: Ingested ingredients at a point in time e.g. | 24/04/2016 11:56:33 | Tomatoe | | 24/04/2016 11:56:33 | White rice | | 24/04/2016 14:34:01 | Mars Bar | Symptoms | ...
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12 views

What n to use for significance of correlations in three different scenarios

I feel these questions might already be answered around here somewhere, but I was not able to find it, so here goes. 1) General case of time-series When determining the significance of a correlation ...
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1answer
26 views

Forecasting beginner question, using regression and historical data

I'm new to forecasting, I wanted to forecast the rise or drop of data traffic considering the number of subscribers I have, I have data from different countires, I used linear regression to get a line ...
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Find the most frequent timespan of event occurrence

I'm working on bike-robbery events dataset. I'm trying to figure out the most frequent timespan of a bike robbery. Most of time, the robbery does not occur when the owner is watching => the declared ...
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3answers
115 views

Seasonality not taken account of in `auto.arima()`

I am having basically the same issue than in this thread, except one thing: The difference, in my case, is that my data is measured weekly and not daily, so the argument of a too high seasonality (> ...
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2answers
53 views

Forecasting with multiple predictors and with multiple seasonalities in R

I have half-hourly electricity data of several homes for a duration of one month. Also, I have ambient temperature at same sampling rate. Now, I need to make half-hourly forecasts using historical ...
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13 views

Parallel processing in ARIMA [migrated]

I have one month half-hourly data (48 readings per day). Using auto.arima() of R forecast package, I forecast the readings of ...
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51 views

How to improve a bad long-term forecasting of time series in common case

I have two time series $d_t(t)$, $d_c(t)$, where I'm modelling charge as a function of time. Lengths of time series, $N$ are equal to $101$ data points. For the $d_t(t)$ (test sample, short-term) the ...
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1answer
18 views

Selecting an appropriate control time series in the R CausalImpact package

I am new to the CausalImpact package in R and wanted to test the effect of a marketing intervention. Now, if we assume that a specific intervention only took place in 2013, is it possible to use time ...
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73 views

Significant difference between time series - Can I do this?

I'd like to know whether the solution proposed below is valid/acceptable and any justification available. We have two biological conditions, and for each condition we measured 3 time series, so at ...
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1answer
35 views

PCA on the time series data yields first PC that has an opposite trend from all original time series

I have time series data with five variables that have common variation and trends and they are very noisy. I want to extract their common variation (most likely the first principal component) and use ...
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1answer
17 views

References on ARDL model

Please suggest books/references on ARDL model and ARDL bounds test approach to study.
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14 views

Quadratic fitting raw time series data vs linear fitting its derivative

I have time series data $f_i(t_i)$. Is there a difference between the following two strategies: Fitting $\hat{f}(t)=at^2+bt+c$ to the original data Fitting $\hat{g}(t)=2at+b$ to the time derivative ...
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3answers
68 views

Forecast time series data with external variables

Currently I'm working on a project to do forecasting of a time series data (monthly data). I am using R to do the forecasting. I have 1 dependent variable (y) and 3 independent variables (x1, x2, ...
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29 views

Understanding recurrent SVM in volatility estimation of GARCH model

I read Chen et al. "Forecasting volatility with support vector machine-based GARCH model" (2010) where they implented a recurrent SVM procedure to estimate volatility by a GARCH based model. The ...
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1answer
46 views

Low performance of SVM (and neural network) in out-of-sample data with high test accuracy of 10-fold cross validation in a financial time series

I'm using SVM and (neural network) for a time series prediction data-set in MATLAB R2016a with 800 samples. Currently I'm using 10-fold cross validation and grid search to find best SVM parameters. ...
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1answer
31 views

Mention day-wise seasonality for forecasting in ARIMA using R

I have half-hourly electricity data of several homes for a duration of one month. This data is represented in xts time-series format. Now, I need to make ...
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20 views

Detecting sustained increases in employee pay (time-series data, non-stationary)

I am seeking guidance with detecting features (specifically, sustained pay-rises) in monthly income data. I haven’t worked much in the time series space so nothing straightforward springs to mind ...
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70 views

Choosing the right ARIMA model when data are already seasonally adjusted

I'm trying to build an ARIMA model to forecast the US unemployment rate month-by-month for the period 2006-2015. To select the model I'm using monthly seasonally adjusted data from 1948 to November ...
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26 views

How to describe my problem when my features are vectors?

My problem is a multivariate time series of measurements from a chemical sensor. There are $n$ different experiments made with as many different substances. Each experiment ranges over $t$ time steps. ...
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165 views

What is the impact of management on tree mortality caused by insect pest?

I am monitoring tree death caused by insects and potential impact of human treatment on yearly amount of tree mortality in areas with and without human intervention. My data are recorded by remote ...
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1answer
45 views

Difference between random walk and martingale

I am trying to understand the diffrence between random walk and martingale. According to my understanding, a random walk without drift is $$ y_{t} = y_{t-1} + u_{t} $$ where $u_{t}$ is $i.i.d.(0, ...
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Weakly stationary time series - what type of model is this?

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). How would I go about showing ...
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11 views

GARCH model is better for index than stock

We have used a standard GARCH(1,1) model with t distributed innovations for daily data of S&P index and JPM stock. Question: is there any financial or statistical reason why the GARCH model ...
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Time-Series Cross-Section or Multi Level

I trying to make a quite complicated model (for me at least) which i cannot figure out myself :/ I have a dependent variable (level of production) (and perhaps more than one - different types of ...
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40 views

Time Series Question

I have put what I thought as below: Q5i) It is weakly stationary. I'm not sure how to justify this ii) Yes, because the process is stationary with some persistence iii) False because bound ...
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42 views

Multiple regression with autocorrelated errors

I have a multiple regression model in R: ...
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1answer
61 views

ergodic theory for markov processes

For an ergodic Markov Chain $$ \frac{1}{N}\sum_{i=1}^n f(X_i) \rightarrow E_\pi[f] $$ where $\pi$ is the invariant distribution. I am also dealing with a Markovian process (a state space model to ...
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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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1answer
32 views

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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9 views

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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1answer
33 views

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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67 views

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 ...
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30 views

Need help interpreting linear/nonlinear time series

I have a set of data, which i am tasked to find out anything that i could from this set of one dimensional data. Im looking at the ACF and PACF plot. Can anyhow determine if below indicates ...
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2answers
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$c(n)$ 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 ...