Autocorrelation is the correlation of a series of data with itself at some lag. This is an important topic particularly in the analysis of time-series data.

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26 views

Is an auto-correlation plot suitable for determining at what point time series data has become random?

A piece of research I am working on requires us to decide at what point time series data has become random. For what it is worth, the time sequence in question is a collection of in-process timings ...
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22 views

High autocorrelation parameters? [on hold]

I plotted the autocorrelation and partial autocorrelation for two of my time series data in R. But it seems that one of the autocorrelation plots of the two has much higher autocorrelation parameters ...
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16 views

Does a high autocorrelation imply high predictability using an AR model?

Assuming that I have a list of time-series which all have significant autocorrelation at lag 1 and no significant autocorrelation at any other lags. So if I want to test for the predictive abilities ...
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16 views

What is the autocorrelation property for this case?

The CRB gives the variance of the estimation error of the estimates and a lower value is preferred. I have computed the cramer rao bound (CRB) of the estimates of the coefficients $\mathbf{h^T}$ for ...
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49 views

Autocorrelated Inter-arrival Times of Extreme Events

I'm using a bunch of techniques and methods from Extreme Value Theory to analyze my data. I have a time series representing the number of events happening in a given day. The time series is unequally ...
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1answer
18 views

Are the data stationary or non-stationary and seasonality?

I want to use Arima model for forecasting wind speed.I plot my data. Then i plot ACF and PACF. I used ADF test and KPSS test and they said that data are stationary and doesnt need differencing but ...
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19 views

Model checking for Spatial CAR (Conditional Autoregressive) model

We assume our data follow the model: $$ Y = X\beta +\varepsilon $$ In spatial CAR (SAR) model, we assume that the errors $\varepsilon$ are correlated in a spatial setting. Let's say that we model ...
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5 views

How to measure overall change when data varies with date [closed]

I have data (volume) that looks like this: I want to measure the overall change in volume across each city, so that I can find the cities in which the volume has dropped. How can I determine this?
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20 views

Is it possible to use spatial autocorrelation test to determine the tuning parameter in the thin plate spline smoother?

I am currently working with some insurance data and try to estimate spatial structure of claims frequencies. The common approach is to perform some kind of regression on the non-spatial data then ...
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17 views

DLM, regression and multiple time series

I'm working with incoming traffic data at multiple spots along a long road. Let's denote the traffic at time t at point $j$ by $x_j(t)$. For each spot, a univariate model, such as local level plus ...
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20 views

Difference between Prais-Winsten regression and Random effects cluster robust

after reading a lot about the various types of regressions, I came to the conlusion that I have to either a prais-winsten regression or a random effects regression with the option "cluster robust" in ...
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1answer
41 views

Managing high autocorrelation in MCMC

I'm building a rather complex hierarchical Bayesian model for a meta-analysis using R and JAGS. Simplifying a bit, the two key levels of the model have $$ y_{ij} = \alpha_j + \epsilon_i$$ $$\alpha_j ...
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27 views

Newey-West vs Cochrane-Orcutt

I have time series of 189 observations and I want to regress $y$ on $x$. My modeling procedure is the following: I run an OLS and I get the constant significant and b not significant (but I know ...
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23 views

Comparing / “correlating” time series

Say I have three time series $X_t$, $Y_t$ and $Z_t$ and from the phenomena I'm observing we can be sure that $X_t$ is _caused_$\,$ by at least $Y_t$ and $W_t$ (there might be other processes that ...
3
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1answer
100 views

Multiple ARIMA models fit data well. How to determine order? Correct approach?

I've got two time series (parameters of a model for males and females) and aim to identify an appropriate ARIMA model in order to make forecasts. My time series looks like: The plot and the ACF ...
2
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1answer
123 views

Understand order of time series

I am trying to build a time series model. I looked at the ACF/PACF and adf test of the series and thought that an ARMA(p,q) model will be suitable for the data. However when I run auto.arima(), it's ...
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2answers
30 views

Uncertainty of average due to correlation between auto-correlated time series

I want to calculate the average value of $n_i$ time series each of length $n_t$, i.e. an average of $n_i \times n_t$ values, together with a measure of uncertainty. To be more concrete, I have ...
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7 views

Does it make sense to interpret autocorrelation and box test on 5 data points?

I am trying to see if after I trade a stock the price movements at 2, 5, 7, 10, 30 and 60 seconds after exhibit any autocorrelation. Below I have the returns from my trade price to the trade 2,5,7,10 ...
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1answer
25 views

How to deal with interruption in time series analysis?

I am probing a time series data of transactions. Basically, I want to see the pattern of the number of transactions in each time slice. First of all, I looked at hourly data. However, the opening ...
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36 views

Accounting for overdispersion in binomial glm using proportions, without quasibinomial

I am doing binomial GLM using relative abundance, for example: model<-glm(cbind(number_pres,number_abs)~Var1+Var2+Var3+Var4..., family=binomial, data=Data). My sample size is about 700, and I have ...
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1answer
43 views

Solution for Autocorrelation in Linear Regression Model - Economic Data

I am trying to estimate a multivariate linear regression model in the form of: $Y(t) = c + b_1*X_1(t) + b_2*X_2(t) + b_3*X_3(t) + b_4*X_4(t)$ All my variables (both Xs and Y) are Year on Year ...
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1answer
25 views

Durbin-Watson Critical Values for Large Sample Sizes

My sample includes 3,627 observations but I can only find tables displaying critical values for the Durbin-Watson test for sample sizes 2,000 and below. Where can I find tables for sample sizes ...
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10 views

How to remove autocorrelation in my VECM?

I have a small theoretical question in the process of me validating my VECM. I have executed a VECM, however after testing the model using the lagrange-multiplier test it shows that all my lags (1 to ...
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23 views

Picking block length in a block bootstrap

I am using the Mann-Kendall test to assess trends in a data time-series. I believe there is autocorrelation in my data and therefore need to use a block bootstrap to correct for it. I have plotted ...
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43 views

R : arima : plotting regression line of autocorrelated time-series data when d > 0

I'm interested in determining both the slope regression coefficient and plotting regression lines for autocorrelated time-series datasets of rainfall. Specifically, I'd like to identify the best ...
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34 views

Time series analysis: Periodogram and correlogram

I'm new on time series and I'm trying to analize one of them. The time series is short and it is given by 27 observation with annual frequence: $$ data \leftarrow c(7.92, 13.85, 22.40, 53.89, 35.80, ...
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1answer
35 views

Why do we want low autocorrelation for MCMC convergence?

Usually, autocorrelation is one diagnostical tool for judging the convergence of a MCMC trail. Low autocorrelation is desired as this would mean that the parameter space is well explored. I have a ...
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2answers
51 views

Why is Moran's $I$ coming out greater than $1$?

Moran's $I$ statistic is defined to be the quantity $$ \frac{N}{\sum_{i,j} w_{ij}}\frac{\sum_{i,j}w_{ij}(X_i-\bar{X})(X_j-\bar{X})}{\sum_i(X_i-\bar{X})^2} $$ where $w_{ij}$ is some matrix of spatial ...
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12 views

How to find cycle from autocorrelation?

I have an ECG data set of length 3380. It provides a cyclic plot diagram like this and autocorrelation diagram like this I am saying that the data set provides cyclic behavior. How can I prove ...
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41 views

Serially Correlated Regressors

I am trying to find information (without success) regarding serially correlated regressors in linear time series regression setting. The topics covered are either correlation between regressors, or ...
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182 views

A closed form formula for the normalizing constant in standard normal auto-regressive series?

Let $Z_t = c_1Z_{t-1} + c_2Z_{t-2} + ... + c_nZ_{t-n} + c\epsilon_t$ where $Z_t, \epsilon_t \sim \mathtt{N}(0,1)$ are iid variables and $Z_s \sim \mathtt{N}(0,1)$ for all $s$. Given the values of ...
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5 views

how to interpret the ACP

How do I interpret this ACP. The data is the daily retail sales in a given territory. I have read a lot of material on ACP and Partial ACP and although they clear the concepts but still to grasp the ...
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98 views

What does the following ACF curve mean ? (Picture attached)

I was checking for seasonality and other dependencies and this is the curve I get . There's no apparent seasonality....but what exctly does the falling slope mean? Any help would be appreciated. ...
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27 views

Vector Autoregressive Model: residual's kurtosis proportional to number of lags?

I have some transformed data set (windspeeds that are nearly-weibull-distributed). I transformed this data which results in near-normal distribution (close to no excess kurtosis and skewness of zero). ...
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15 views

Which time series model to use?

Hi I have a large data set of objects, each containing a list of the same attributes. The data is arranged in a time series so that the value for an attribute for an object is indexed by its time. ...
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16 views

correct for temporal autocorrelation in mantel tests

Hej, I want to compare the community composition of a bacterial assemblage with it's resource use ability. therefore I calculate a distance matrix based on the community composition and a distance ...
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1answer
39 views

Do we need to detrend when do Cross-Correlation between two time series?

I have a group of time series variables and I want to found out the relationship among them. The method I use is to calculate pair-wise correlation between two time series and found out those with ...
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1answer
38 views

Dealing with nonstationarity and autocorrelation

Relationship between interest rates and retail sales. I have a time series sample of quarterly data for 10 years. My dependent variable is retail prices and independent variables are interest rates, ...
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26 views

Sampling Distribution of Sample Correlation Coefficient

For a linear process $X_t=\mu+\sum_j\varphi_jW_{t-j}$ where $W_t$ is white noise and $\mathbb E(W_t^4)<\infty$ , $$ \begin{pmatrix} \hat\rho(1) \\ \hat\rho(2) \\ \vdots \\ ...
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3answers
46 views

Exactly The Same Autocovariance Function of Two Time Series

A MA(2) process : $$X_t=W_t+\frac{5}{2}W_{t-1}-\frac{3}{2}W_{t-2}$$ where $\{W_t\}\sim WN(0,1)$ And another MA(2) process : $$X_t=W_t-\frac{1}{6}W_{t-1}-\frac{1}{6}W_{t-2}$$ where $\{W_t\}\sim ...
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21 views

Mixed effects model with autocorrelation between fixed and random effects

I have never posted here before, so apologies if I do not follow the correct format. My experiment design is I have 12 reps each of 4 different species of plant which I experimented on in 2 blocks, ...
2
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0answers
40 views

Modeling proportions of autocorrelated binary data

I have data on infant crying for three time periods -- 1994-1996, 2000-2002, and 2010-2013 -- with about 15 infants per year. Each infant was observed every minute for 1080 minutes (across 3 days). If ...
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23 views

Autocorrelation in R

I have a data structure as below. There are few experiments where height was measured in different ages (max 5 observation per experiment, min 2). ...
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24 views

Compare distributions in time series

I have a time series (weekly sales data), on which i have made an intervention analysis (to be specific a VARIMAX). The intervention (increased opening hours) ended out being insignificant. But what i ...
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15 views

Autocorrelation for Time-series Crossection data

I am examining whether the market reaction (Y) is influenced by a number of X's variables. My data is gathered per firm at time t. If I understood correctly, this is called Time-series Cross-section ...
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12 views

On the correlation function of a stationary time series (spectral analysis)

I am following a proof of the following fact of which I do not understand only the last step. I will post it entirely for the sake of completeness but do not hesitate to just look at my question at ...
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13 views

GAMM - error when using spline smoother, only allowed to use tensor product

I am familiar with the basics of statistical regression models, including GAMs, but I am stumped on a particular implementation issue. I am constructing a GAMM to fit to data that is autocorrelated. ...
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9 views

How to determine the optimal time averaging window

I have two large time series datasets with some background noises. I would assume the two datasets are either lag correlated or lead correlated. I tried to use time averaging to smooth out the dataset ...
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12 views

How to find covariance matrix from correlation if mean is not given?

I'm given autocorrelation function of gaussian random process: $$ R_x(\tau) = 3e^{|-\tau/3|} $$ Now I should find covariance matrix. I know the formula and solutions, where $$ C_{xx} = R - E[X]^2 $$ ...
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44 views

Autocorrelation in DOLS: will HAC standard errors work?

I am currently estimating a cointegrating regression (DOLS), where my residuals have autocorrelation. Sometimes it is just in one or two lags, but sometimes it is more. My question is: Can I apply HAC ...