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

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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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11 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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37 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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55 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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39 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 point ...
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11 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, y_{t-k}|y_{t-1}...y_{t-k+1})}{\sqrt{var(y_t|y_{t-1}...y_{...
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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 | 24/...
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14 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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28 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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32 views

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
143 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
98 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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58 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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21 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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159 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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43 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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18 views

References on ARDL model

Please suggest books/references on ARDL model and ARDL bounds test approach to study.
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16 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
99 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, x3)...
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32 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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56 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. I'...
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39 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 half-...
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81 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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27 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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169 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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46 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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25 views

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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12 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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15 views

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 will ...
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45 views

Multiple regression with autocorrelated errors

I have a multiple regression model in R: ...
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64 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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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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46 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 are ...
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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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68 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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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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$c(n)$ 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 ...
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19 views

Causal Impact and using multiple control series with their regressors

Hi all I am analyzing several DMA's for campaign effectiveness using the CausalImpact package by Kay Brodersen. I have data for participants and non-participants INCLUDING their contemporaneous ...
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R Why auto.arima omits arima(0,1,0)(0,1,0)[6]? [duplicate]

auto.arima gives me that the best model is arima(0,1,0). But using Arima and fitting ...
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Using Covariance and Correlation for Similarity matching

I am trying to find if a particular pattern exists in a time series. I have found that I could try using Covariance or correlation for the task. I have used a sliding window technique for doing this. ...
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43 views

Modelling Periodic Features

I am trying to do a simple regression (either polynomial or support vector regression) for solar power prediction, as a project to learn machine learning. However the data I have is time series data ...
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turning back forecasted differenced data to be in terms of the original non stationary form

i had non stationary inflation data that i needed to forecast.i turned the data to be stationary by differencing it thrice ,then found an arima model which i used to forecast the data using R.i ...
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25 views

Markov Switching Model Forecasting

Let's say I have the following Markov switching model: $$r_t = 1.36 + a_t$$ $$a_t = \sigma_t \epsilon_t $$ $$ \sigma_t^2 = \left\{\begin{aligned} &0.15a_{t-1}^2 + 0.82\sigma_{t-1}^2 &&: ...
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26 views

How to fit a short time series model using ARIMA?

I want to make predictions use ARIMA in forecast package. I find that basically the prediction is just a lag of the actuals. Is there any way that I can better fit the model or any other approach ...
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28 views

Testing the independence of a time series

I’d like to test whether my time series of consecutive payments is independent or not and thought that since this is a pretty common condition in statistics it should be easy. Well, turns out is isn’t ...