# Questions tagged [auto-correlation]

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### Why is SPY daily adjusted close negatively autocorrelated?

I took daily adjusted close prices (all history) from Yahoo Finance and ran the following code: ...
34 views

### Autocorrelation and frequency of occurence

Recently, I started reading Zuckerman's biography of Jim Simons - "The Man Who Solved the Market". There is an interesting para on page 110 - "When you flip a coin, you have a 25% chance of getting ...
34 views

### Serial Correlation in Rolling Change Linear Regression Models

1.) Lets say I have two time series GDP, BUSINV from (1948, 2019); Frequency of Data is Quarterly. 2.) Say I want to predict GDP i.e. GDP ~ BUSINV 3.) Since GDP is not stationary (i.e. level) and ...
48 views

### Is this a good (partial) autocorrelation or bad?

I was playing with some data on deviation of close prices from its smoothed estimated and got these ACF and partial ACFs: I still struggle to get proper intuition to the ACF plots. What do the plots ...
35 views

### Auto-covariance function of station time series

How to show that for any stationary time series its auto-covariance function is symmetric about the origin, that is $\gamma_{k}=\gamma_{-k}$ where, $\gamma_k=cov(z_t,z_{t-k})$
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### Autocovariance of increments of a semimartingale

Say that $X_t$ is an Itō process with \begin{equation} dX_t = \mu_t dt + \sigma_t dW_t \end{equation} where $\mu_t$ and $\sigma_t$ are adapted processes. Is it always true that \begin{equation} E[...
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### Interpreting ACF

I am currently struggling with the interpretation of a price chart and the corresponding ACF graph. The question is, if there is momentum in the price of this asset. This is the corresponding price ...
393 views

### Interpreting ACF/PACF of return series

Researching a return series on some currency pairs I grabbed 2 years worth of daily data and got to work trying to fit an ARIMA/GARCH model to it. Fitting the (log) return series: ...
1k views

### Is an autocorrelation of the abs returns just a consequence of the volatility burst?

In Pfaff's "Financial Risk Modelling and Portfolio Optimization with R" the following stylized facts are stated (among the others, p.26): The volatility of return processes is not constant with ...
123 views

### Detecting stochastic volatility

I have a time series extracted from a financial time series (so my series of prices is described by an arithmetic model $X(t)+Y(t)+Z(t)$, my series is $Z(t)$). I'm trying to model $Z(t)$ by a Levy ...
211 views

### Stationary Process with autocorrelation in Variance; square root rule

i am currently analyzing a time series of portfolio log returns and have conducted a ADF test with the result, that the series is stationary, but also found significant autocorrelation in the squared ...
1k views

### Variance Ratio Test in R

I would like to conduct a variance ratio test for a financial time series in order to examine whether I can apply the square root rule for the variance with the software R. I used the Automatic ...
1k views

### Reasons for negative autocorrelation

I am working with intraday stock prices. I have found that the autocorrelation between the returns is negative (significantly so, but the value is very small). I am aware of how to interpret negative ...
856 views

### How to adjust regression for rolling returns?

I have a predictor variable (x) and dependent variable (y). Both are monthly rolling annualized returns, which naturally induces significant autocorrelation in x and y. They both also fail to be ...
203 views

### VAR models for log-returns?

I am wondering if Vector Autoregression (and other autoregressive models) is a sound modelling for the daily (not high-frequency!) log-returns of time series from liquid financial markets. One can ...
132 views

### residual correlation remains after seasonal lag added

I'm attempting to model operating margins and a time plot indicated that the series may follow an autoregressive process. I initially fitted data to an AR(1) model and it appeared that residual ...
2k views

### Autocorrelation in the GARCH model residuals

I am estimating GARCH model for volatility calculation and as a data input I have used log first difference data (ln(a)-ln(b)). Usually I would check for autocorrelation in residuals(to check the ...
173 views

### volume-returns cross correlation interpretation

I want to find the relationship between volume and price returns in the S&P500. My first thought was to run a cross correlation in order to find who leads and who lags in the relation. It´s my ...
2k views

### When measuring autocorrelation should you use log returns or prices?

Let's say you want to measure intra day autocorrelation from 9:30 am to 1pm using 5-minute prices should you calculate the autocorrelation using raw prices or log returns (i.e. diff(log(prices)))? Can ...
916 views

### Measuring momentum as AR(1) process

I would like to measure the momentum in the price of a stock from the time the market opens until the time I trade each day. I want to use this momentum number in post-trade analysis (regression of ...
974 views

### Cointegration Test: Residual is stationary but not random?

I am testing cointegration relationship on various pairs of stocks by this following these steps. Test for I(1) on a pair of stocks, says X and Y, using Dickey-Fuller test. If both time series are ...
2k views

### How to annualise the volatility of non-iid returns?

I have a series of monthly log-returns; let's assume the log-returns are normally distributed, but exhibit significant serial correlation. In the case of normal, i.i.d. returns, I can annualize the ...
1k 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 AR(1) ...
110 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 ...
137 views

### Infinite autocorrelation - Unit root?

I have a time series of gold prices, on which I want to build an ARIMA model. The series is autocorrelated and if I can difference as often as I want, it always is. First: data: d1gold Dickey-Fuller ...
492 views

### Does GARCH derived variance explain the autocorrelation in a time series?

Given a time series $u_i$ of returns (where $i=1,\dotsc,t$), $\sigma_i$ is calculated from GARCH(1,1) as $$\sigma_i^2=\omega+\alpha u_{i-1}^2 +\beta \sigma_{i-1}^2.$$ What is the mathematical ...
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### How is the MA (moving average model) useful?

How is the MA model useful in modeling financial data, for example the stock indices? For example, from what i understand in the AR (auto-regressive) model portion, we can use the ADF test to check ...
11k views

### What does it mean by autocorrelation coefficient near 1?

It is said that the time series has a stochastic trend if the first autocorrelation coefficient will be near 1. Q1) What does it mean by the above statement? Q2) How do we calculate the first ...
1k views

### Need overlapping sample autocorrelation correction for calculating asset return correlations

I want to measure the covariance structure of various asset returns based on varying investment periods. Campbell and Viceira (2005) do this, using known return predictors (i.e. dividend yield, ...
119 views

### Insignificant or significant explanatory power over risk adjusted returns?

Currently iam working on my master thesis which is about risk adjusted returns in the Asia Pacific REIT market. The goal of the paper is to determine/find variables that conceive explanatory power ...