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Reasons for negative autocorrelation

Looking at transaction prices, they would occur at the market bid if the active part is a seller, and at the ask if the active part is a buyer. With a random flow of sellers and buyers, the price will ...
Mats Lind's user avatar
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4 votes
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Is an autocorrelation of the abs returns just a consequence of the volatility burst?

I think @zer0hedge has constructed a clever example by which to demonstrate what is implied by the stylized fact by which volatility begets volatility. It is correct to conclude volatility bursts are ...
David Addison's user avatar
4 votes

Interpreting ACF

You need to compute the autocorrelation of the log returns $r_t$, not of the prices, $p_t$. The relationship of the log return series to the price series is $$ r_t = \log \frac{p_t}{p_{t-1}} $$ The ...
Chris Taylor's user avatar
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3 votes

Variance Ratio Test in R

TL;DR: the test statistic's distribution is $N(0,1)$ A bit more information about the Automatic Variance Ratio Test: $H_0$: ${\Delta}r_t$ is serially uncorrelated (where ${\Delta}r_t=r_t-r_{t-1}$) $...
rbm's user avatar
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3 votes
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How does autocorrelation bias annualizing variance?

In Andrew W. Lo's paper, The statistics of Sharpe Ratios (2002) he derives the variance of non-IID returns (returns that can exhibit serial correlation) under the assumption of (covariance) stationary ...
Pleb's user avatar
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3 votes
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Running an autocorrelation with blanks?

One option is just to fill them in - interest rates don't usually jump around, so interpolating from surrounding data would be unsurprising. If you want to know what effect that is having, by all ...
Phil H's user avatar
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3 votes

Do EWMA weights remove autocorrelation in asset returns?

EWMA (and other sort of moving averages) introduces positive autocorrelation into otherwise uncorrelated returns. The fitted values of EWMA are linear combinations of past returns, and the constituent ...
Richard Hardy's user avatar
3 votes

How to use autocorrelation plot to interpret time series data?

Just by looking at the graphs, I'd say: Unit root Constant series Seasonality AR model No AC No AC
confused's user avatar
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3 votes
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Predictive power of lagged features

In its simplest terms, imagine you were just using the yield curve as your single predictor of recessions. Suppose (horribly simplistically) that curve inversions tend to signal downturns in 12-18 ...
demully's user avatar
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3 votes

Auto-covariance function of station time series

Hi: Subtract $k$ from $z_t$ and add $k$ to $z_{t-k}$. Then you have $cov(z_{t-k,} z_{t})$ which by definition is $\gamma_{-k}$. But, by stationarity, this has to be equal to $cov(z_{t}, z_{t-k})= \...
mark leeds's user avatar
  • 1,140
3 votes

Detecting stochastic volatility

I'm not a time series expert but one idea occurs to me: look at the distribution of the increments if Z(t). If the w are stochastic , that distribution should have fat tails relative to the ...
dm63's user avatar
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2 votes

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

Your code basically implements the assumption that you cited: The volatility of return processes is not constant with respect to time. Whether it's a single burst or some kind of a fancy ...
Aksakal almost surely binary's user avatar
2 votes

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

Such volatility pattern is a well-known stylized fact of financial time series (see Cont, Rama. Empirical properties of asset returns: stylized facts and statistical issues. (2001): 223-236 for more ...
JejeBelfort's user avatar
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2 votes

Stationary Process with autocorrelation in Variance; square root rule

You are correct in that the series is not stationary. The ADF test isn't designed to test for stationarity outside the center of location. You are not going to be able to use the square root rule to ...
Dave Harris's user avatar
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2 votes
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Turning a covariance sum into an integral

Note that the function $f$ only depends on $|t-u|$, meaning it is actually symmetric: $f(x)=f(-x)$. Doing the change of variable $\tau:=t-u$: $$\begin{align} \int_0^Tdu\int_0^Tf(t-u)dt &=\int_0^...
Daneel Olivaw's user avatar
2 votes

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

If you are predicting the return from time "i" to time "i+l" then you cannot use any information beyond time "i" to train your model. As it appears you are getting returns from "i-5" to "i" and ...
wjamdanf1234's user avatar
2 votes
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Monte Carlo simulations of correlated stocks by Geometric Brownian motion

Let $n$ be the number of stocks (here $n=3$) Let $T$ be the number of sequential returns to generate (for example $T=12$ if you want to generate a year's worth of monthly returns) Let $M$ be the ...
nbbo2's user avatar
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2 votes

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

Hmm... some notable implicit assumptions made en passant here ;-) How persistent are these autocorrelations (ACs)? Let's unpick a little. One obvious question is whether your AC process is strong ...
demully's user avatar
  • 5,071
2 votes

What about autocorrelation and heteroskedasticity in Fama French?

If you face heteroskedasticity, you have to check if heteroskedasticity is conditional (e.g., with a Breush-Pagan Chi-square test). If so, you have to use White-corrected standard errors. If you have ...
Felix's user avatar
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2 votes
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Show that $\text{Cov}[X_r,X_s]=\text{Cov}[X_{r+h},X_{s+h}]$ for $X_t=a+bZ_t+cZ_{t-2}.$

in method 1 you did not use the correct definition of the covariance. For two random variables $X$ and $Y$ we have that $$ Cov(X, Y) = E[XY] - E[X]E[Y]. $$ Also, we can use that the covariance is ...
Cettt's user avatar
  • 1,456
1 vote

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

Whilst autocorrelation does not affect the sharpe ratio when using purely returns, positive autocorrelation does reduce the sharpe ratio when considering the price space - all else equal. ...
Newquant's user avatar
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1 vote

What's the right autocorrelation formula?

the autocorrelation is the correlation of a process $X$ and its lagged version, hence you have to consider it from a probabilistic viewpoint. Use the $\sigma_\ell$ notation for the operator that ...
lehalle's user avatar
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1 vote
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Does it make any sense to normalize returns?

As far as I know we use Normalization in reviewing the Financial Statements(PnL,Balance Sheets,Cash Flow) of a Company. Now What is that exactly? If the company is seeking external funding, normalized ...
shantanujoshii's user avatar
1 vote

Persistence and stationarity together in volatility analysis

ADF tests for a unit root. Autocorrelation function of a unit root process does not make sense. For example let $$y_{t+1}=y_t+\epsilon_{t+1}$$ Here $\epsilon_t$ is i.i.d white noise. Then the one ...
fes's user avatar
  • 1,727
1 vote

Running an autocorrelation with blanks?

Are you dealing with overnight rates, such as Fed Funds? In such cases the same rate continues to be paid while the markets are closed. So for example if FF is X on Friday, it means you will earn X ...
nbbo2's user avatar
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1 vote

How to use autocorrelation plot to interpret time series data?

There is a multitude of texts which answer this question the easiest and free source is Rob Hyndmans from Monash Universities online text on forecasting, https://otexts.com/fpp2/, the topic is covered ...
Con Fluentsy's user avatar
1 vote

Autocorrelation and frequency of occurence

I recently had trouble with a similar concept and I managed to develop a proof that related probability of successive occurrence with autocorrelation. Interpreting Autocorrelation as probability. Let ...
vpy's user avatar
  • 187
1 vote

Autocovariance of increments of a semimartingale

**please correct me if the math is wrong!! I think upon breaking down the products $E(dX_tdX_s)$, we have the $dtds$, $dtdW_s$ terms which all turns out to be 0. It leaves $E(dW_tdW_s)$ which comes ...
numerairX's user avatar
  • 609
1 vote

Interpreting ACF

ACF plot suggests there is autocorrelation which lasts for long time. The series is clearly not stationary. You may try differencing once - return time series, then plot boathouse ACF and PACF.
sukusi's user avatar
  • 11
1 vote

How to adjust regression for rolling returns?

It depends how large the overlapping interval is. Conceptually an infinite rolling window is equivalent to the level, and no one would suggest to 'regress on levels and apply Newey West'. I think NW ...
Kiwiakos's user avatar
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