10 votes
Accepted

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 ...
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  • 1,267
8 votes
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How to annualise the volatility of non-iid returns?

The correct answer has some intuition though it doesn't generalize to continuous time very easily: Think about the paper below like this: $Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y)$ The generalization ...
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  • 851
6 votes

How to annualise the volatility of non-iid returns?

The answer is that it depends. In addition to the Lo paper above, there are a number of excellent references that go into depth about annualizing or time scaling non-i.i.d. returns, one of which is ...
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5 votes
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How is the MA (moving average model) useful?

In terms of interpretation, an $MA$ model simply means that the time series is a function of the error from previous periods. You might find it informative to consider plotting simple $AR(1)$ models ...
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  • 5,291
4 votes

What does it mean by autocorrelation coefficient near 1?

Autocorrelation is the correlation of a series with itself. Suppose $X = {X_1, X_2, X_3, ...}$ is your time series. Then the autocorrelation between $X_t$ amd $X_s$ is: $$ \frac{E[(X_t-\mu_t)(X_s-\...
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  • 520
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 ...
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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 ...
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  • 5,603
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})= \...
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  • 1,017
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 ${\Delta}r_t=r_t-r_{t-1}$) $...
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  • 725
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 ...
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3 votes
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Autocorrelation in the GARCH model residuals

You should check for autocorrelation. However, its presence does not necessarily mean your model will produce inaccurate figures. The ARCH family of models were developed to help analyze the ...
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  • 341
3 votes

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

What is the mathematical basis to say that $u^{2}_{t}/\sigma_{t}^{2}$ will exhibit little auto-correlation in the series? Let's $r_{t}$ be a series of returns and let's assume (Assumption I) it ...
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  • 2,504
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
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  • 619
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 ...
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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 ...
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  • 4,886
3 votes
Accepted

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 ...
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  • 3,589
2 votes

What does it mean by autocorrelation coefficient near 1?

1.) Autocorrelation is the correlation of a time series against the lagged version of itself. 2). First autocorrelation is the correlation of the time series against the lag(1) version of itself. ...
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  • 141
2 votes

What is the correct procedure to choose the lag when preforming Johansen cointegration test?

If you are using Spatial Econometrics toolbox in Matlab you could use the lrratio function which implements a sequence of such tests beginning at a maximum lag (specified by the user) down to a ...
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  • 121
2 votes

How to interpret ACF and PACF plots

I can offer my opinion in response to your first two questions: 1.) Unfortunately, this is one of the problems with numbers; the answer is that if the observation is outside of the confidence ...
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  • 21
2 votes

volume-returns cross correlation interpretation

The direction of the relationship cannot be determined from just this information (a set of correlation coefficients). You need to estimate a model of volume based on lagged volume and lagged returns, ...
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  • 9,077
2 votes

When measuring autocorrelation should you use log returns or prices?

The high serial correlation you are getting in the first case is a spurious correlation. The correct way to do it is with returns. The price series has a unit root. You need to take diff(log(prices))) ...
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  • 9,077
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 ...
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  • 4,046
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 ...
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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 ...
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  • 1,209
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 ...
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  • 151
2 votes
Accepted

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^...
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2 votes
Accepted

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 ...
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  • 9,347
2 votes
Accepted

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 ...
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  • 1,386
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 ...
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  • 106
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 ...
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  • 609

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