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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SAS Residual White Noise Test and validity of R^2 value

I have fit an auto-regressive model to a data series. The model seems to explain the given data relatively well given that the total R^2 is 0.95. However, SAS has a diagnostic plot called white noise ...
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14 views

Uncorrelated Real and Imaginary parts of a field in k-space: WHY?

I am in the process of generating a (real) Gaussian random field δ(x⃗ ) from a given power spectrum P(k). The way I define the power spectrum is, in Fourier space, $\left\langle \delta(\vec{k}) ...
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6 views

How to calculate first three orders of PACF function given ARMA model?

Is there a way to calculate the first three orders (i.e. $\phi_{11}$ $\phi_{22}$, and $\phi_{33}$) of PACF given the estimated form of ARMA model, for example: ...
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1answer
65 views

Why do sample ACF/PACF suggest different TS models after box-cox transformation?

I use auto.arima function in R to fit a TS model to a annual data composed of electricity demand. The series is twiced difference to eliminate the trend in the data. After that the data is transformed ...
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1answer
14 views

Variance and autocorrelation with missing and/or unevenly spaced data in time series

This question concerns the general problem of working with data that might have missing and/or unevenly spaced values. Let’s call this real data. Specifically I am calculating rolling variance and ...
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1answer
55 views

How should I test for autocorrelation in this time series context?

I have data sets in which different people estimate a certain quantity. They potentially can see the estimates of anyone who participated before them, but in practice they're only likely to look at ...
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9 views

Autocovariance Estimation and Stationary Processes

I am going to work on a project involving time series and therefore I am trying to understand some basic definitions. I am currently trying to grasp the autocovariance estimation procedure. When we ...
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2answers
135 views

Autocorrelation vs Non-stationary

What is the relationship between autocorrelation and non-stationary? Is it true that non-zero autocorrelation $\implies$ non-stationary, but not vice versa?
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31 views

AR(2) model, convert to smaller step size

Given an AR(2) model with coefficients $\varphi_1$ and $\varphi_2$ and step size of 1.0, is there a possibility to compute new coefficients, but with a different step size (e.g. smaller, 0.5) so that ...
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23 views

Diagnostics and residual analysis for Poisson regression

Recently, I was asked to check for serial correlation after doing a panel Poisson regression. I haven't seen such a test and in general, researchers (at least in the econom(etr)ics literature) don't ...
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1answer
63 views

How do I interpret this ACF and PACF plot?

I am very new to time-series analysis and have got some time-series data regarding product prices. The data set is monthly data collect since 1993 to 2014. I have tried plotting the ACF and PACF but ...
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1answer
29 views

Ljung Box test for residuals of constrained ARIMAX(2,1,0) model

I have this ARIMA(2,1,0) model with one exogenous variable: $$\Delta y_t=c+\phi_2 \Delta y_{t-2}+\beta_x x_t+\varepsilon_t$$ I want to run Ljung Box test of residual autocorrelation with test ...
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Explore the possibility of autocorrelation for discrete factors

I have a dataset looks something like the following: ...
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1answer
51 views

Normal distribution and independence

I was reading about white noise and it stated: Although $\varepsilon_t$ & $y_t$ are serially uncorrelated, they are not necessarily serially independent, because they are not necessarily ...
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0answers
10 views

How to create an autocovariate in ArcGIS for use in autologistic regression model [migrated]

I am trying to create an autocovariate variable for use in an autologistic regression. I have a GIS point Shapefile of the response variable, in binary form for presence/absence of a plant species. ...
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1answer
74 views

Is an auto-correlation plot suitable for determining at what point time series data has become random, and how does one interpret the plot?

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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0answers
17 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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83 views

What is the simplified expression for autocorrelation in 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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56 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
25 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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23 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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23 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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25 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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31 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
50 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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31 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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25 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 ...
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1answer
118 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 ...
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1answer
128 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
42 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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9 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
27 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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51 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
67 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
59 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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16 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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26 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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64 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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40 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
38 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
54 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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0answers
16 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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1answer
188 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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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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102 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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31 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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19 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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0answers
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 ...
2
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1answer
47 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 ...