# Questions tagged [auto-correlation]

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1 vote
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### At which Lag the AutoCorrelation of Rolling 10 Year Returns is not significant?

I believe there are two ways to measure Confidence Intervals of Autocorrelation one assumption is assuming the Autocorrelation is following Gaussian Distribution and assuming Lags other than Lag 0 are ...
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1 vote
406 views

### How does autocorrelation bias annualizing variance?

I read somewhere that autocorrelation prevents someone from annualizing variance. But how does it bias it? Let's say you have daily returns. If autocorrelation is high, should that overstate or ...
• 707
63 views

### Reasons for negative autocorrelation of forward prices

I am working on each trade day's forward prices of gasoline. I noticed that the autocorrelation at lag 6 is significantly negative. I know how to interpret negative autocorrelation in a statistical ...
1 vote
79 views

### Proof that points to an alternative explanation for the absence of autocorrelation in price movement

The absence of linear autocorrelation in asset price movement has been empirically observed countless times. It is usually accompanied by an explanation that goes something like this: If there was ...
• 11
595 views

### How to annualize Sharpe Ratio if monthly returns are serially correlated? Calculation of autocorrelations

I am looking at a data set of 60 monthly returns (last 5 years) and want to calculate an annualized Sharpe Ratio. The usual way of doing this is to calculate the monthly Sharpe Ratio first, and then ...
• 21
1 vote
365 views

### What's the right autocorrelation formula?

I'm trying to see the influence of autocorrelation in my processes and to do so I have to compute it, however it seems to be hard to find a coherent formula over the web. I found pretty much two ...
1 vote
114 views

### Why is the moving average called that way? [closed]

I am a beginner in time-series analysis. The moving average model uses past errors*parameter, so why is it called a moving average model? It seems counter-intuitive to me. The Auto-Regressive model ...
• 123
1 vote
717 views

### Does it make any sense to normalize returns?

I have been going through a course for Time Series Analysis. First we learned to make returns from a time-series of stock index by (Xt - Xt-1)/Xt-1 . This makes the series stationary, which means we ...
• 123
1 vote
136 views

### Persistence and stationarity together in volatility analysis

I am trying to analyse a time series. I want to get only quantitative results (so, I'm excluding things like "looking at this plot we can note..." or "as you can see in the chart ...&...
• 111
171 views

### Calculate and study volatility time series

I am trying to study a time series. I have 10-year daily close prices for some stocks, so my time series is very simple: each day I have a close price for my company. The question is: how can I want ...
• 111
89 views

### Examining the dependence of the fractional difference parameter in ARFIMA(0,d,0) vs bar size for Realized Volatility

Realized volatility is a long-memory process and so I fitted an ARFIMA(0,d,0) to log(RV15) where RV15 is realized volatility calculated from 15-min bars. I proceeded to examine how changing the bar ...
• 452
367 views

### What about autocorrelation and heteroskedasticity in Fama French?

I am analysing ESG and conventional mutual funds. I decided to measure the extra performance of each category using the Fama French 4 factor model, but it seems to me that in previous literature they ...
• 39
70 views

### Show that $\text{Cov}[X_r,X_s]=\text{Cov}[X_{r+h},X_{s+h}]$ for $X_t=a+bZ_t+cZ_{t-2}.$

Problem: Let $\{Zt\}$ be a sequence of independent normal random variables, each with mean $0$ and variance $\sigma^2$, and let $a$, $b$, and $c$ be constants. Is $X_t=a+bZ_t+cZ_{t-2}$ a (weakly) ...
• 221
255 views

### Estimating distribution of rate of return

Let $f[t]$ be the price of a stock at time $t$. We can calculate the rolling rate of return of the stock in a window of length $n$ by computing: $$r[t] = \frac{f[t] - f[t-n]}{f[t-n]}$$ $r[t]$ is ...
1 vote
359 views

### CAPM: Testing for alphas jointly equal to zero

For my project, I need to assess if a certain factor X leads to a CAPM-Anomaly. First, I sorted the monthly stock return (sample size: 500+ observations) according to the X factor in 10 decile ...
• 31
1 vote
61 views

### Running an autocorrelation with blanks?

How does one run an autocorrelation when there are blanks in the dataset? I have a dataset of interest rates and I am plotting day x vs day x-1. I’m unable to run a correlation in Excel if there are ...
• 113
340 views

### Variance of Log Returns

Consider an asset held for $n$ time periods with weakly stationary log-returns $r_t$, $1≤t≤n$. Show that $var(r_1 +r_2 +r_3 +r_4)=var(r_1 +r_2 +r_3)+var(r_1)(1+2ρ_3 +2ρ_2 +2ρ_1)$, where $ρ_k$ is the ...
• 21
159 views

### Should a stock with high return autocorrelation be weighted more heavily in a portfolio?

Some say the presence of autocorrelation (aka serial correlation) in a stock's financial return time series helps with forecasting its next-day movements, unlike a stock that has low serial ...
• 2,980
99 views

### Predictive power of lagged features [closed]

I have to build a classification model to predict recessions. I have selected a set of features (some are economic and some are financial). I have noticed that it is good pratice often to add to the ...
• 326
297 views

### How to model financial HFT time-series data with multi scale autocorrelation

I work with tick level time-series univariate prices data. Tick level means that there are hundreds to thousands observations per second. The observations are timestamped, so one can use both wall ...
• 61
1 vote
436 views

### Monte Carlo simulations of correlated stocks by Geometric Brownian motion

I am trying to simulate using a Geometric Brownian Motion process three autocorrelated stocks. In particular, I need to simulate three different matrices with 1000 scenarios each using a Monte Carlo ...
1 vote
463 views

### Do EWMA weights remove autocorrelation in asset returns?

I know that the exponentially weighted moving average (EWMA) volatility estimator drapes a decaying weight function over historical returns in order to weight the past according to the decay of their ...
• 2,980
321 views

### How to use autocorrelation plot to interpret time series data?

how can we use auto correlation plot or correlogram to interpret time series data? I have 6 different acf plots (a,b,c,d,e,f), from this 6 plots what kind of informations and patterns can I identify? ...
• 647
144 views

### Turning a covariance sum into an integral

I am reading Lorenzo's Bergomi's book Stochastic Volatility Modeling, and I have come to this passage. I just would like to understand the derivation between the first and the second equality. I ...
• 2,570
171 views

### Fama Macbeth and Momentum factor

I am working on a Fama MacBeth regression with excess returns on the LHS and Size, Value an Momentum factors on the RHS. In literature, the Momentum factor is often definded as the cumulative past 6 ...
• 21
120 views

### Interpreting Autocorrelation as probability

I was recently asked: Given a random time series of 1s and -1s. Eg of a sample = [1, 1, 1, -1, -1, 1, -1,..]. The autocorrelation of this series is Z. What can you say about the probability of a 1(or ...
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143 views

### Is there an issue with estimating future returns from autocorrelated returns?

I have a time series $X_t$ generated from a standard GBM $$dS_t = \mu S_t dt + \sigma S_t dW_t$$ If I take the log returns over a rolling window of length $l$ r^{(l)}_i = \log \left( \frac{S_i}{...
• 405
87 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 ...
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1 vote
63 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 ...
1 vote
82 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 ...
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1 vote
64 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 $$dX_t = \mu_t dt + \sigma_t dW_t$$ where $\mu_t$ and $\sigma_t$ are adapted processes. Is it always true that E[...
• 1,096
422 views

### 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 ...
847 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: ...
3k 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 ...
• 1,704
143 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 ...
• 151
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### 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 ...
• 177
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### 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 ...
• 177
2k 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 ...
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1 vote
2k 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 ...
434 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 ...
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### 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 ...
5k 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 ...
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### 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 ...
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3k 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 ...
• 405
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### 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 ...
• 405
1 vote
1k 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 ...
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3k 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) ...
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