# Tagged Questions

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### Estimation of regression with autocorrelated errors

In a book it is written that, In regression work we typically assume that the observational errors are pairwise uncorrelated. But in most time series data , the successive residuals have tendency to ...
18 views

### ACF and PACF plot analysis

I am new to ARIMA, and I am trying to understand these lag plots. Are the following ACF and PACF suggesting that the lag of my time series is 4? If I am wrong, please help me understand these plots. ...
8 views

### Methods for measuring snowball effects in a “complete” longitudinal dataset

I'm looking for ways to test for "cumulative advantage" effects in a longitudinal dataset (see image) I guess the data set is principally similar to this: http://www.caldercenter.org/whatis.cfm , ...
94 views

### Can First Differencing Cause Negative Serial Correlation

Ex. series, say stock prices 103 101 102 150 101 102 100 First differenced 2 1 48 -49 1 -2 Notice you could guess a very large negative number following the very large positive in the first ...
27 views

### Testing significance of correlation between two autocorrelated series

Say I collected the shin bones of N different skeletons; they are all around 30cm long, and I measured different properties P1, P2, P3, P4 and P5 along these bones every 3mm (so I have 100 data points ...
56 views

### Whitening Transformation using a Hadamard product Variance Matrix

I want to whiten a vector $X$ by transforming the variance-covariance matrix so the variance-covariance matrix of the transformed series will be the identity matrix $I$. $X$ is a time-series column ...
25 views

### Correlation definition between two set

How can I define correlation between two set x and y: {$(x_1,y_1),(x_2,y_2),(x_3,y_3),...(x_n,y_n)$} Is this definition correct: ...
27 views

### Estimating auto-correlation with unequally spaced data

I'm working on a time series problem where the spacing between observations is usually 12 or 24 hours, but this is not guaranteed. I'd really like to estimate the auto-correlation function, and I've ...
68 views

### How to interpret autocorrelation

I have calculated autocorrelation on time series data on the patterns of movement of a fish based on its positions: X (x.ts) and Y (...
115 views

### Autocorrelation of discrete time series

I am currently planning on calculating the autocorrelation for various lags given a time series. However, my elements of the time series are "discrete" and abstract classes; i.e., no integers. For ...
53 views

### Model estimation using ACF and PACF [on hold]

Can anyone help in model estimation ? The following are the ACF,PACF and the plot of the sample respectively.
51 views

### Interpreting results of an Augmented Dickey-Fuller test

I am running the 3 models of the ADF (Augmented Dickey Fuller) test on a (ln total fertility rate) variable. The results: Intercept only: (lag difference = 0) at level; p-value for Z(t) = 0.9672. ...
35 views

### Understand the PACF Values in R / Correlation over 1

I have a basic problem with the pacf function in R. By applying this function to get the partial auto correlation functions of a time series, the values range in ...
59 views

### Is ARMA(0,0) equivalent to white noise?

If the EACF of my TS suggests ARMA(0,0) and the Box-Ljung test does not suggest my TS has correlation, can I conclude that my TS is white noise or merely that there is no reason to suspect that it is ...
8 views

### Data overlapping

Overlapping data are often present in time-series analysis and the academic studies mention about Heteroskedasticity and Autocovariance Consistent (HAC) estimators to solve this isssue, such as ...
155 views

### Differencing a time series

I am looking to find the ACF of a time series, but after it is differenced. $y_t = a_1y_{t-1} + \epsilon_t , \mid a_1 \mid < 1$ I understand that to find the ACF this process needs to be ...
41 views

### How to interpret the characteristic roots of moment equation of a AR(2) model?

I am learning the financial time series using the book 'Analysis of financial time series' by Ruey Tsay. In chapter 2, they introduced AR(2) models. The moment equation (which is the function between ...
168 views

### What is the autocorrelation function of a time series arising from computing a moving standard deviation?

Say I have a time series of observations and I compute a measure of the variance of that time series as the standard deviation (SD) in a rolling window of width $w$ and that window is moved in single ...
775 views

### How to interpret ACF and PACF and compare with Ljung Box result

I took the residual of a historical stock price $\hat e_t=r_t-\hat \mu_t$, where $r_t$ is the return of a stock and ran ACF and PACF. From the ACF I think that the residual does not follow AR or MA ...
225 views

### Sample ACF and PACF of a random walk

Suppose $X_n$are iid $N(0,1)$ random variables. Define $S_n := \sum_{i=1}^n X_n$. Then $S_n$ is a random walk. Since $Var(S_n) = n$ and $Cov(S_n, S_m) = \min(n,m)$, $S_n$ is not stationary in the ...
30 views

### Covariance between two sample means of correlated data

I have two sets of random data $X=\{x_1,...,x_N\}$ and $Y\{y_1,...,y_N\}$ both of length $N$. The sets are autocorrelated such that the correlation between $x_i$ and $x_j$ depends only on $|i-j|$. ...
147 views

### Can nonstationarity be told from the autocorrelation function?

Here "stationarity" means the first and second moments don't change over time. From a page of Time Series: Theory and Methods, by Peter J. Brockwell, Richard A. Davis In this chapter we shall ...
80 views

### Autocorrelation for regression

I am attempting to use a significant autocorrelation (where it lies outside a 95% interval around 0) indicating periodicity of a signal and use it as predictive variable in a regression. If, for ...
122 views

### Autocorrelation and evidence of iid

Suppose I have the first seven autocorrelations for some variable $x$. And suppose they are -0.2, 0.15, -0.05, -0.10, -0.05, -0.14, 0.04 How can this be used as evidence of my data being or not being ...
110 views

### Model estimation - 2sls

Firstly, I am applying a 2sls model in my paper: ...
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### nonlinear dependence in autocorrelation lagged scatterplot

In lagged scatter Plot we have such a diagramm: if we have an organized curvature in the pattern of dots, that means, nonlinear dependence between time seprated. my question is now: in which time ...
118 views

### why sinusoid pattern in correlogram

Why does the ACF of an AR(1) contains sometimes a sinusoid-like pattern? and what does it mean? EDIT I think the time series is fit to AR(1). As I understand it, in an AR model, the value of x ...
237 views

### Which one of these looks stationary?

Step 1. To answer "Final Question" ( linked: "THE FINAL QUESTION : Order of differencing, to achieve stationary and interpretation of arima() , acf, pacf?") Expecting to find correct order of ...
144 views

### Summing variance of autocorrelated timeseries

Problem: When trying to calculate the variance of timeseries sums I get a negative variance, mostly due to autocovariances at large lag steps. Does not seem realistic. I have a timeseries which is ...
219 views

### Characterizing a time-series using autocorrelation lag values

I am seeking to characterize time-series data (specifically parameters derived from sensor data) for 18 patients collected over 20 days using autocorrelation (see plot below of autocorrelation ...
111 views

### Test for granger causality after fitting a GARCH(1,1)

I have two time series, where i wish to test for Granger causality of lagged values of $x$ on $y$, $y$ is changed to "rate-return" and $x$ is the positive or negative "rate-return", that is everywhere ...
200 views

### Detecting outliers using correlogram

If there is an outlier in a time series, how does its correlogram behave? Is it possible to find outliers using a correlogram? EDIT I have such a Time series: ...
240 views

### Why does differencing time-series introduce negative autocorrelation

For example, this mentioned here: link. I also saw this in my data. I wonder - does anyone know a good reference where this is explained and justified more rigorously with some math and for some ...
20 views

### checking for autocorrelation with many observations and few time periods

How would I go about checking for autocorrelation if I had a few thousand observations for each time period and had about 15 different time periods? The data set I am working with has a lag variable ...
72 views

### Heteroscedasticity in the context of general additive model

For my given data (identity link), my target is to check a political variable, i.e., I intend to check, if a certain impact, given by some treatment at a certain time, affects the intercept and slope ...
172 views

### How to calculated Confidence Interval for autocorrelated and lognormally distributed data?

My data is autocorrelated and is lognormally distributed, how can I calculate Confidence interval of that set of data?
61 views

### Does this autocorrelation plot look correct?

I have time series data that looks like this and I'm getting an autocorrelation plot for this time series as That is zero autocorrelation for every lag. But this would mean that the time-series ...
430 views

### GLM with Temporal Data

This is my first post on here, looking for some help. I am relatively new to analysis of temporal datasets. I have experience with R and developing linear models, so I am trying to figure out if the ...
232 views

### Relation between autocorrelation function and periodogram in time series analysis

I was wondering if anyone could give me some insight on the relation between the ACF and the periodogram of a time series. I have a bunch of timeseries and their ACF's and periodograms are typically ...
131 views

### Forecasting time-series ahead by multiple time horizons

Suppose that I have daily data on the population of a small village, given by $Y(t)$, as well as daily data on various factors that are relevant to the size of the population in the future, given by ...
192 views

### Temporal autocorrelation in perMANOVA?

I have a data set where samples are collected once per year for 15 years at a number of sites. I am worried that these data are temporally autocorrelated and was trying to figure out if I need to ...
314 views

### Autocorrelation and trends

What is the relation between the autocorrelation and the trend? Can a trend exist in a time series of independent variables? And in time series with a non-zero autocorrelation, does a trend always ...
95 views

### Spatial autocorrelation (SAC) while analysing survey data

I am confused about some aspects of spatial autocorrelation usind survey data (survey which is repeated every year). I have data from 1991 to 2012 with sampling region pretty consistent every year. I ...
656 views

### SARIMA estimation

I am trying to manually estimate the non-seasonal components of an SARIMA (p,d,q)x(P,D,Q)[s]. I thought the estimation is going the same way like in ARIMA, but the output says somehow something ...
189 views

### Time series: correcting the standard errors for autocorrelation

I have performed a number of tests to detect any presence of autocorrelation in my monthly return series. The test results confirm that the standard errors are not independent. A Durbin-Watson test ...
1k views

### Autocovariance of an ARMA(2,1) process - derivation of analytical model for $\gamma( k)$

I need to derive analytic expressions for the autocovariance function $\gamma\left(k\right)$ of an ARMA(2,1) process denoted by: $y_t=\phi_1y_{t-1}+\phi_2y_{t-2}+\theta_1\epsilon_{t-1}+\epsilon_t$ ...
430 views

### AR(1) coefficient is correlation?

Is the ar1 coefficient from an AR(1) model the "first order correlation of the noise" of a time series? I'm using R's aws package and one of the arguments of the ...