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

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Multivariate time series model evaluation with conditional moments

Consider multivariate time series models that estimate potentially time-varying conditional means, variances, and correlations (one type of model might be a VAR(p)+Garch(1,1)+DCC Gaussian Copula ...
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174 views

How to define train and test sets in financial time series for estimating machine learning parameters

After reading some material, I found few options for defining train and test sets: Just splitting with no change. Accumulating/moving window of train set. Leave a relatively small (warming) period ...
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229 views

Testing threshold cointegration in vector error-correction models

In Hansen and Seo's paper on Testing two regime threshold cointegration in VECM (J. Econometrics, 2002; 110:293), the authors proposed a test based on Lagrange Multiplier for testing treshold in ...
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14 views

Permutation for large sample sizes

I was trying to do a permutation test on a large amount of temperature observations in R. Approximately 1700 temperature observations (g1) from one place and 2 ...
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233 views

Using anomalies to calculate trends of seasonal data

I commonly see people doing trend analysis of (monthly) timeseries data which show a strong inter-annual cycle following this scheme: compute climatological means ("mean January", "mean February", ...
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53 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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132 views

Regression analysis for more than one categorical variable in time series

I have a time series data for shipment with following variables: Year: 2008, 2009, 2010, 2011, 2012, 2013 Month: jan, feb, ..., dec Number of ordering days Shipment Volume I want to know the ...
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12 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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19 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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1answer
238 views

How to fit a simple count time series INAR(1) model in R

I am trying to perform a simple time series analysis with count time series data. My data is a sequence of small integer values like 0,1,2 and 3. I learned from various sources that INAR model would ...
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752 views

Simple interrupted time series analysis

I have a weekly time series representing costs for a cohort. I want to tell whether an intervention on the cohort (we can assume it happened in a single week) has decreased costs for the cohort. I ...
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57 views

How accurate is F test in panel data

I heard that the F-test is to advice you whether to use fixed effects or pooled OLS. However, I didn't find any details about it in books. Only in a very few studies. What is the hypothesis of the ...
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5 views

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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140 views

Handling stationarity issues in proc ucm/state space time series models

Hope I'm able to find someone who can answer this question. The previous one didn't get answered! Proc ucm is the SAS implementation (using state space concepts) to isolate the unobserved trend, ...
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12 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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148 views

Forecasting the target variable vs building a causal model and forecasting causal variables

I want to know the approaches people use to forecast lets say unemployment rate .... By itself it might not fit a time series model (ARMA) very well as the trend is dependent on many external factors. ...
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10 views

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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4answers
1k views

Lagging over a grouped time series

I have a few tens of thousands of observations that are in a time series but grouped by locations. For example: ...
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97 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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19 views

Beta and Alpha Interpretation [on hold]

I have been given some outputs as part of a group project. The model is a deterministic time-varying coefficient model weighted using a Gaussian kernel. I am ok for most of the output although the ...
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12 views

Interpretation of a Panel SVAR with demeaned data

I am running a Panel SVAR on country data with LR restrictions using MATLAB. I have 15 countries with 77 observations each. All my variables are demeaned. The structural VAR is constructed as ...
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1answer
140 views

What is the implication of unit root of MA?

A ARMA(p,q) process is weakly stationary, iff the root of its AR part is not on the unit circle. So its weak stationarity doesn't depend on its MA part. But what can the positions of the roots of its ...
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1answer
107 views

Diagnostic for VAR model. non normal

I have some problem about my model. my model is based on VAR. (vector auto-.) well, I've tested ARCH test, BG test(autocorrelation p) and jarque.bera.test. Model is stable. Also I got good result for ...
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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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78 views

How to test for Pearson correlation when one variable is fixed on date?

I have 4 groups of different respondents, each group surveyed on four different dates (points of time). All respondents have answered a psychological questionnaire related to their perception of death ...
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1answer
88 views

Markov Switching Forecast. How can I derive this?

Consider the autoregressive model, $\left[ \begin{array}{l} y^{\ast}_t\\ x_t^{\ast} \end{array} \right] = \left[ \begin{array}{l} a_{11}\\ a_{21} \end{array} \begin{array}{l} a_{12}\\ ...
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24 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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3answers
75 views

Test if advertising raised sales?

I have an (offline) advertising campaign that I'm running in one city. I'm trying to figure out how to answer the following questions: What are the chances that the advertising campaign has no ...
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1answer
35 views

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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11 views

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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1answer
118 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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16 views

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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Subset data by month in R

I am working with a time series of meteorological data and want to extract just the summer months. The data frame looks like this: ...
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180 views

Is there a convenient form for this large covariance matrix?

Consider the following bivariate vector autoregression: $$X_t=\mu +X_{t-1}A+\varepsilon_t,\ \varepsilon_t \overset{iid}{\sim} MVN(0, V),\ X_t=(X_{1,t},X_{2,t})',$$ where the assumptions on the ...
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2answers
23 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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2answers
60 views

Time series - correlation and lag time

I am studying the correlation between a set of input variables and a response variable, price. These are all in time series. 1) Is it necessary that I smooth out the curve where the input variable is ...
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1answer
289 views

Quantile regression

I have a question regarding quantile regression. Supposing that I have 10000 observations with one response variable and several predictor variables in a dataset collected each year over several ...
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94 views

Library routine for rolling window lag 1 autocorrelation?

I am looking for a library routine that will calculate the lag 1 autocorrelation of a time series with a rolling window; meaning "slide a window of size N points along the time series, calculate the ...
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1answer
60 views

$R^2$ correspondence for nonlinear time series

Is there a statistical measure for nonlinear time series data that is comparable to $R^2$ value in linear regression (giving an idea of how well the fit is)? The data is not monotonic, so I cannot ...
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1answer
140 views

Generating IMA(1,1) series

I'd like to generate a series that follows an IMA(1,1) process, where $θ$ is the moving average parameter. I generated the series based on different representations and I got different results, I'm ...
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1answer
167 views

Forecasting model inputs that are both auto-correlated and are calibrated over time?

How does one account for model inputs that are both a) auto-correlated and b) calibrated over time? I'm interested in forecasting the outcomes of sporting events. Let's say that each team has a score ...
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2answers
1k views

Analysis of time series with many zero values

This problem is actually about fire detection, but it is strongly analogous to some radioactive decay detection problems. The phenomena being observed is both sporadic and highly variable; thus, a ...
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30 views

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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1answer
184 views

What's a stationary VAR?

What is a stationary VAR (vector autoregression)? Can a VAR with non-stationary variables be stationary? How do you test whether a VAR is stationary or non-stationary? (Example in ...
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14 views

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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446 views

Least stupid way to forecast a short multivariate time series

I need to forecast the following 4 variables for the 29th unit of time. I have roughly 2 years worth of historical data, where 1 and 14 and 27 are all the same period (or time of year). In the end, I ...
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1answer
28 views

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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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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1answer
196 views

Time-varying Coefficients

I have time series data on fish catches from 1950-2011. I wish to implement a regression model with varying coefficients. I'm aware that cox models etc. exist and implementation via the ...
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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