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

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Markov Chain State Transition Probability in R

I have a dataset which shows the states (3 states) across 11 time points for each participant. I wanted to estimate the Markov Chain state transition probability matrices for time points 2-11 using R. ...
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Project using arima

Year Ageing population 1974 32239 1975 33111 1976 34343 1977 35096 1978 35977 1979 37918 1980 39473 1981 40366 1982 42201 1983 43488 1984 44232 1985 45206 1986 ...
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Estimation of VECM via ML and OLS

Take a vector error correction (VECM) model: $$\;\;\;\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta y_{t-(p-1)}+\varepsilon_t$$ where $\Pi=\alpha \beta'$ and each row of ...
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56 views

OLS versus ML estimation of VECM

A vector error correction (VECM) model has an equivalent vector autoregression (VAR) representation. (VECM) $\;\;\;\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta ...
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19 views

Multivariate Gaussian distribution - covariance and variance

In my previous question Density function for AR model, the density function of AR model has the covariance-variance matrix given as $\sigma^2 *V_p$. In multivariate gaussian distribution, the pdf ...
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Skewed posterior distribution on constrained parameter space for Bayesian inference of MCMC. Advice on what to do?

I am running a fully Bayesian MCMC procedure to estimate some time series models, and my model has a lot of parameter estimates. In particular, one of these parameters, $\phi$, is $\in [-1,1]$. The ...
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202 views

Evaluating Time Series Prediction Performance

I have a Dynamic Naive Bayes Model trained on a couple of temporal variables. The output of the model is the prediction of P(Event) @ t+1, estimated at each ...
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290 views

How can I form ARIMA equation given MA and AR terms

Above is output from SAS. What would be the corresponding ARIMAX equation? I would appreciate if someone could help me write the mathematical equation, preferably in the following form: $$ Y(t)= ...
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6 views

Two ways to model pre/post/treatment setting. Which one is preferred and why?

I have 20 individuals randomly distributed into two groups(treatment vs non-treatment) and test_score was measured before/after the treatment. My central goal is to measure the effect of the ...
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258 views
+500

Intervention With Differencing

When conducting an intervention analysis with time series data (aka Interrupted Time series) as discussed here for example one requirement I have is to estimate the total gain (or loss) due to the ...
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17 views

Time series tracking queue optimization problem

In order to track prices of many different products from different sources, I must optimally schedule a group of trackers dedicated to price collection (ie. collect one price at a time for each ...
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10 views

Estimation of parameter depending on other paremeters

PROBLEM STATEMENT: Let $X$ be random variable in $m$ dimensional space. The distance between each pair of vectors $x_i^m,x_j^m$ is $D_{i,j}^m =d(x_i^m,x_j^m)$. There is a measure - Correlation Sum, ...
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62 views

Transfer function in forecasting models - interpretation

I am occupied with ARIMA modelling augmented with exogenous variables for promotional modelling purposes and i have hard time explaining it to business users. In some cases software packages end up ...
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13 views

Holdout MAPEs in SAS PROC ARIMA and SAS Forecast Studio don't match

I have a Time Series (ARIMA) model in SAS, modelled using proc ARIMA which I am trying to replicate in SAS Forecasting Studio. What I see is that The parameter estimates in both are very similar ...
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1answer
202 views

Finding structural breaks in heteroskedastic time series

I'm trying to identify structural breaks in the movement of reserve currencies. I'm not yet all that versed in the finer details of time series, but I've been reading up on ARCH and GARCH estimators. ...
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95 views

find the point at which the curve significantly shoots up

so this is getting a little complex for me and hope someone can help me out. I do not have a mathematical background. I have a time series of daily rainfall for 50 years for a particular location. ...
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65 views

Outlier Detection in Time-Series: How to reduce false positives?

I'm trying to automate outlier detection in time-series and I used a modification of the solution proposed by Rob Hyndman here. Say, I measure daily visits to a website from various countries. For ...
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1answer
231 views

How to plot spectra of an AR(2) process

I am stuggling with this problem and was hoping to find some guidance to answer it. Let $y_t=\phi_1y_{t-1}+\phi_2y_{t-2}+\epsilon_t$, with $\epsilon_t\sim N(0,1)$. Now, I want to plot the spectra ...
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100 views

VAR and Granger causality test

Is it necessary to calculate VAR before Granger causality test so that we can have the lag length to be used in Granger causality test
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Matlab: Time lagged time series and its correlation

Let, $x_t = [y_t,y_{t-1},...,y_{t-p}]'$ where $y_t$ is the output of an autoregressive process of order p=2 excited by Gaussian white noise of zero mean. $y_t$ is a vector output of the AR process: ...
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107 views

How to model a linear regression based on time?

I have some training set data variables $x_1$, $x_2$, $x_3$, $x_4$, and $x_5$ and a response variable $y$. But these are time series data. So the for the same set of values of $x_1$, $x_2$, $x_3$, ...
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12 views

AR(n) model with exponents

When we discuss a (time-series) model $AR(n) = \Sigma_{i=0}^n Y_{t-i} + \cdots + \epsilon_t$, we use $n$ to refer to the number of time steps back the autoregression includes. In other such models, we ...
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8 views

A question about Dickey-Fuller Unit-Root Test

I am reading Dickey-Fuller Unit-Root Test in Time Series Analysis with Applications in R by Cryer and Chan and have trouble understanding some discussion on equation (6.4.1). So they took this ...
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1answer
77 views

Checking that values are piecewise uniform

I have a set of values and I wish to check if they are piecewise uniform. I hope I'm using the correct terms, but I'll explain what I mean. Consider the following values - 100,105,100,103,98. We ...
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181 views

Statistical comparison of two signals

I need to develop an algorithm that will compare two signals and generate some metric(s) to describe changes between them. Signal processing and analysis isn’t my strong point so I would appreciate ...
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29 views

How to predict the time series data

I have no background of advanced stats. I am an engineer and I have the following data. I am representing it as a decent graph for better understanding. I want to forecast the collision for the next ...
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23 views

Time Series Decomposition - autocorrelation of error term

I would like to do time series decomposition, but the error term has a serial autocorrelation at the end and I am freaking out because I have really no idea what to do with that. How I did it? I ...
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101 views

How to interpret PCA on time-series data?

I am trying to understand the use of PCA in a recent journal article titled "Mapping brain activity at scale with cluster computing" Freeman et al., 2014 (free pdf available on the lab website). They ...
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Comparing influence of single independent variable on two dependent variables (time series)

Scenario description: Temperature has been measured at $k+2$ different depths in a borehole. Measurements of the temperature were taken once each hour over a period of about 3 months. So observed data ...
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58 views

Can I use the correlation value to measure the correlation between two variables when observations in each variable have auto-correlation?

I have two variables: urban areas protected areas. My observations are urban areas and protected areas in each year. But these observations are the cumulative ones, so observations in each ...
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35 views

Is time-series an appropriate method to model data sampled at widely irregular time intervals ?

I am relatively inexperienced with data analysis. My question: Is time-series an appropriate method to fit trends to data sampled at widely-irregular time intervals such as forests of different ages ...
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115 views

Contingency table with 2 different time series

I am trying to put the two time series of my Excel spreadsheet (see link below), into a contingency table. https://www.dropbox.com/s/2f96oylxj97fuih/example.xls The first series is the number of ...
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Augmented Dickey Fuller says it's okay. But is it really?

This is original sales data. The biggest spike occurs during winter holidays with a consequent customer inactivity around early January. My Augmented Dickey Fuller Unit Root test is quite significant ...
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147 views

How to form a predictive model in R?

I have two data sets whose structure is like this: DATA SET 1: ...
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811 views

ARIMA vs ARMA on the differenced series

In R (2.15.2) I fitted once an ARIMA(3,1,3) on a time series and once an ARMA(3,3) on the once differenced timeseries. The fitted parameters differ, which I attributed to the fitting method in ARIMA. ...
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132 views

How to implement model in R?

i would like your help to implement this model in R or more explicity where yt = monthly mean values μi = mean value in month i, i = 1 . . . 12 . I1;t = Indicator series for month i of the ...
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125 views

Time Series Data Mining Library?

Can anyone recommend a library for time series data mining tasks other than predictive modeling and statistical analysis? There seem to be a number for these purposes (e.g., Gretl), but nothing for ...
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2answers
290 views

Correlating time series for 20 regions (SPSS)

I have a question to which I can't find an answer although I spent really awfully lot of time searching. I have time series data for about 20 regions of a country. Each time series covers 20 years. ...
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205 views

How to use error term in AR (2) model for predicting future values?

We use turbidity to estimate suspended-sediment concentration (SSC)- our data was serially correlated. We ran an ARMA process and ended up with a AR (2) model. Our equation in log form is: ...
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113 views

How can i find the significance of the cointegrating coefficients in output cajorls-function in R?

I investigate the long-term relationship of some variables but in the output provided by cajorls-function, I can't see for each coefficient if it is significant? This is provided by the ...
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25 views

Using quadratic programming to fit a piecewise linear model plus seasonality

I am reading this paper on fitting an L1TF model to data using quadratic programming. Section 7.4 states how one could add seasonality to the model however it doesn't go very far into it. I am trying ...
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18 views

One Step Ahead Forecasts Using Predict() in R

I just fit a model to a time series. I am now required to generate a 10-year extrapolation forecast of my model. My model includes a time term, a time^2 term, 12 seasonal dummies, and 4 lagged ...
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336 views

Trying to use Holt-Winters to fit this data

I'm trying to fit the data in this message (daily temperatures) using the Holt–Winters technique in R, but can't get the seasonal example in here to work. Is this not possible with these data, or am I ...
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Stationarity ⇒ homoscedasticity? [duplicate]

If my data is stationary, can I also write that it is homoscedastic? Does stationarity imply homoscedasticity of the data?
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123 views

Does it make sense to use dynamic time warping when clustering time series that all have the same length and sampling interval?

Comparing Euclidean distances with dynamic time warping (DTW): Will Euclidean distance perform better than DTW when clustering time series that all have the same length and sampling interval? Are ...
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20 views

Selecting an appropriate VAR model

I would like to receive critical comments on an idea explained below. Suppose I have variables $x_1$ through $x_K$, and this is a time series setting. My aim is to forecast variable $x_1$. I know ...
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94 views

How should I set up my data for classification when there is a time component?

I am assuming there is an optimal why to set up my data to achieve my goal of predicting who will retire next year. I can think of two methods. Which do you think is the most appropriate and why? Or ...
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Basic questions about stochastic gradient descent / Robbins and Monro algorithm

I have a LOT of time series observations and I would like to estimate a simple AR(1) model $$ y_t =c+ \phi y_{t-1}+ \varepsilon_t \qquad \varepsilon_t \sim \text{N}(0, \sigma^{2}) $$ with parameters ...
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108 views

Time Series Anomaly Detection with Python

I need to implement anomaly detection on several time-series datasets. I've never done this before and was hoping for some advice. I'm very comfortable with python, so I would prefer the solution be ...
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379 views

How to apply an AR(MA) model to a prewhitened signal?

I have two (vehicle velocity) signals that should consist of similar "latent" drivers, but have different autocorrelation structures. The driver-signals are quite nasty statistically, so I'm not ...