Questions tagged [auto-correlation]
The auto-correlation tag has no usage guidance.
67
questions
1
vote
1
answer
63
views
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 ...
- 91
1
vote
1
answer
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
0
votes
0
answers
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
1
vote
0
answers
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
2
votes
2
answers
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
1
answer
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
0
answers
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
1
answer
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
1
answer
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
0
votes
0
answers
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
2
votes
0
answers
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
2
votes
1
answer
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
0
votes
1
answer
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
0
votes
2
answers
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
0
answers
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
2
answers
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
2
votes
0
answers
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
0
votes
1
answer
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
0
votes
1
answer
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
5
votes
0
answers
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
1
answer
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 ...
- 25
1
vote
1
answer
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
0
votes
2
answers
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
3
votes
1
answer
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
2
votes
0
answers
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
0
votes
1
answer
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 ...
- 187
3
votes
1
answer
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
4
votes
1
answer
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 ...
- 237
1
vote
0
answers
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 ...
- 11
1
vote
0
answers
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 ...
- 163
1
vote
1
answer
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, $\gamma_k=cov(z_t,z_{t-k})$
- 107
5
votes
1
answer
104
views
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[...
- 1,096
3
votes
3
answers
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 ...
- 31
0
votes
0
answers
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:
...
user20664
8
votes
3
answers
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
2
votes
1
answer
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
2
votes
2
answers
362
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 ...
- 177
2
votes
1
answer
2k
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 ...
- 177
8
votes
4
answers
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 ...
- 183
1
vote
2
answers
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 ...
- 11
2
votes
0
answers
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 ...
- 281
2
votes
3
answers
151
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 ...
- 59
3
votes
3
answers
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 ...
- 107
4
votes
1
answer
218
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 ...
- 121
0
votes
1
answer
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
5
votes
1
answer
2k
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 ...
- 405
1
vote
0
answers
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 ...
- 111
7
votes
2
answers
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 ...
- 73
2
votes
1
answer
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) ...
- 879
1
vote
0
answers
117
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 ...
- 879