0
votes
0answers
21 views

How to improve linear model generalization when autocorrelation is present?

I have features $X_t$ and response $Y_t$ (all continuous variables) and my objective is to find the best estimate of $f(X_t)=Y_t$ where $f$ is linear, and 'best' is defined as lowest generalisation ...
1
vote
1answer
70 views

stationarity in time series

I'm learning a Time series course and I have a few questions. Strictly stationary is a process if the joint distribution of $X_{t1},X_{t2},...,X_{tm}$is the same as the joint distribution of ...
0
votes
0answers
31 views

How to interpret ACF and PACF plots

I just want to check that I am interpreting the ACF and PACF plots correctly: The data corresponds to the errors generated between the actual data points and the estimates generated using an ...
2
votes
1answer
25 views

My transfer function has non-stationary inputs, but a stationary output. Should I difference both the inputs and outputs during structure estimation?

I have a system of two inputs and one output that I'd like to model using the following Box-Jenkins transfer function ("dynamic regression") structure: $$y_t=\frac ...
2
votes
1answer
113 views

Forecasting a seasonal time series in R

Forecasting airline passengers seasonal time series using auto arima Hi, I am trying to model some airline data in an attempt to provide an accurate monthly forecast for June-December this year using ...
1
vote
0answers
32 views

Quantity like correlation

I want to calculate this sort of quantity, $f()$, for my data. $x$ and $y$ are time series. $f$ behaves like a pseudo-correlation, but is different in the sense that even if the values jump up and ...
0
votes
0answers
55 views

Matlab: Unable to plot partial autocorrelation plot

For a time series I wanted to plot separately the partial auto correlation. Below is the graph for a time series which shows PACF plot of the time series $x$ which I wanted to reproduce: This ...
0
votes
0answers
32 views

Rule of Thumb for minimum length of time series for Autocorrection estimation

I had a related question answered here: Rule of Thumb for minimum length of time series for AR(1) estimation However the answer gives rise to a new question. I want to be able to estimate the Auto ...
2
votes
1answer
41 views

Rule of Thumb for minimum length of time series for AR(1) estimation

I have a data set of 350 points, I want to estimate the lag 1 auto correlation for different sub-sets of the data. More precisely I want to take non overlapping windows of length 1,2,3....n and ...
2
votes
0answers
35 views

Interpretation of the partial autocorrelation function for a pure MA process

I have been working with some time-series theory and I noticed something that I can understand "mathematically", but not based on the intuitive explanations of what the partial auto-correlation ...
2
votes
3answers
131 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 ...
1
vote
1answer
43 views

Residual autocorrelation versus lagged dependent variable

When modeling time series one has the possibility to (1) model the correlational structure of the error terms as e.g. an AR(1) process (2) include the lagged dependent variable as an explanatory ...
2
votes
1answer
43 views

Is the Durbin-Watson test appropriate for count data

In determining if there is any serial correlation in a time series of count data, is the Durbin-Watson statistic or similar approaches appropriate? I ask this question because the dwtest implemented ...
1
vote
1answer
99 views

Getting Residuals to be White Noise

I'm on a time series project for an undergraduate course. For the project I'm trying to come up with an ARIMA model for the housing starts data set. ...
1
vote
1answer
76 views

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 ...
3
votes
0answers
76 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. ...
2
votes
0answers
22 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 , ...
2
votes
1answer
137 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 ...
1
vote
0answers
43 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 ...
2
votes
0answers
72 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 ...
1
vote
1answer
27 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: ...
1
vote
1answer
44 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 ...
1
vote
1answer
99 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 (...
2
votes
1answer
203 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 ...
-1
votes
3answers
76 views

Model estimation using ACF and PACF [closed]

Can anyone help in model estimation ? The following are the ACF,PACF and the plot of the sample respectively.
1
vote
0answers
103 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. ...
0
votes
0answers
44 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 ...
1
vote
1answer
80 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 ...
1
vote
0answers
13 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 ...
3
votes
2answers
161 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 ...
2
votes
0answers
61 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 ...
7
votes
1answer
214 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 ...
0
votes
0answers
2k 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 ...
2
votes
1answer
327 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 ...
1
vote
0answers
35 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 $|i-j|$. ...
1
vote
3answers
194 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 ...
1
vote
1answer
87 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 ...
3
votes
3answers
170 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 ...
0
votes
1answer
118 views

Model estimation - 2sls

Firstly, I am applying a 2sls model in my paper: ...
4
votes
2answers
420 views
0
votes
0answers
126 views

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 ...
0
votes
0answers
144 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 ...
3
votes
2answers
256 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 ...
1
vote
1answer
170 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 ...
2
votes
0answers
301 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 ...
0
votes
0answers
133 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 ...
3
votes
2answers
214 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: ...
3
votes
2answers
311 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 ...
0
votes
0answers
21 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 ...
0
votes
0answers
83 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 ...